How many questions from Waves appear in JEE?

Waves has appeared in 109 of the last 186 JEE Main and JEE Advanced papers — about 59% of them — contributing 135 questions in total across those papers.

Is Waves an important chapter for JEE?

Judged by how often it is actually tested, it appears in roughly 59% of papers. Chapters above about 50% are effectively guaranteed to show up every session, so they repay thorough preparation; lower-frequency chapters are better treated as targeted revision.

Where do these Waves questions come from?

Every question is from an official JEE Main or JEE Advanced paper, transcribed from the original paper and tagged to this chapter. Answers follow the official answer key.

Waves JEE Previous Year Questions with Answers

Q1·PhysicsSingle correctJEE Advanced 2026

List-I shows four configurations made of straight and semi-circular narrow tubes containing air. A sound wave of wavelength

\lambda = 0.29

m enters these structures at the point

S

and a sound detector is placed at

D

. Between the points

S

and

D

, the sound travels only through the tubes. List-II contains the possible smallest values of

l

(refer to the figures) for which the detector

D

records maximum amplitude. Ignore effects of sharp corners. [Given:

\cos(15^\circ) = 0.97

] Choose the option that best describes the match between the entries in List-I to those in List-II.

List-I	List-II
P.see figure	1.1.32 m
Q.see figure	2.1.19 m
R.see figure	3.0.51 m
S.see figure	4.0.29 m
	5.0.13 m

(A)P→4, Q→3, R→5, S→1
(B)P→4, Q→3, R→1, S→5
(C)P→3, Q→4, R→1, S→2
(D)P→3, Q→4, R→5, S→2

Q2·PhysicsNumericalJEE Main 2026

A transverse wave on a string is described by

y = 3\sin(36t + 0.018x + \pi/4)

, where

x, y

are in cm and

t

in seconds. The least distance between the two successive crests in the wave is _____ cm. (Nearest integer) (

\pi = 3.14

)

Q3·PhysicsSingle correctJEE Main 2026

The equation of a plane progressive wave is given by

y = 5\cos\pi\left(200t - \frac{x}{150}\right)

where

x

and

y

are in cm and

t

is in second. The velocity of the wave is ______ m/s.

(A)120
(B)150
(C)200
(D)300

Q4·PhysicsNumericalJEE Main 2026

Two tuning forks A and B are sounded together giving rise to 8 beats in 2 s. When fork A is loaded with wax, the beat frequency is reduced to 4 beats in 2 s. If the original frequency of tuning fork B is 380 Hz, then the original frequency of tuning fork A is _______ Hz.

Q5·PhysicsSingle correctJEE Main 2026

The speed of a longitudinal wave in a metallic bar is 400 m/s. If the density and Young's modulus of the bar material are increased by 0.5% and 1% respectively then the speed of the wave is changed approximately to _____ m/s.

(A)399
(B)398
(C)402
(D)401

Q6·PhysicsSingle correctJEE Main 2026

A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by 8 times, the intensity will

(A)increase by 8 times
(B)increase by 64 times
(C)decrease by 8 times
(D)decrease by 4 times

Q7·PhysicsSingle correctJEE Main 2026

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is

5/x

. The value of x is_______.

(A)4
(B)2
(C)1
(D)3

Q8·PhysicsNumericalJEE Main 2026

The velocity of sound in air is doubled when the temperature is raised from 0°C to α°C. The value of α is _______.

Q9·PhysicsSingle correctJEE Main 2026

In an open organ pipe

\nu_{3}

and

\nu_{6}

are

3^{\text{rd}}

and

6^{\text{th}}

harmonic frequencies, respectively. If

\nu_{6} - \nu_{3}

= 2200 Hz then length of the pipe is ______ mm. (Take velocity of sound in air is 330 m/s.)

(A)275
(B)225
(C)200
(D)250

Q10·PhysicsNumericalJEE Main 2026

Two loudspeakers (

L_1

and

L_2

) are placed with a separation of 10 m, as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point

A

, at equidistance to both loud speakers, is moved by 25 m along the line

AB

while monitoring the audio signal. The measured signal was found to undergo 10 cycles of minima and maxima during the movement. The frequency of the input signal is ______ Hz (Speed of sound in air is 324 m/s and

\sqrt{5}

= 2.23)

Q11·PhysicsSingle correctJEE Main 2026

Two strings (A, B) having linear densities

\mu_A = 2 \times 10^{-4}

kg/m and

\mu_B = 4 \times 10^{-4}

kg/m and lengths

L_A = 2.5

m and

L_B = 1.5

m respectively are joined. Free ends of A and B are tied to two rigid supports C and D, respectively creating a tension of 500 N in the wire. Two identical pulses, sent from C and D ends, take time

t_1

and

t_2

, respectively, to reach the joint. The ratio

t_1/t_2

is :

(A)1.08
(B)1.90
(C)1.67
(D)1.18

Q12·PhysicsNumericalJEE Advanced 2025

An audio transmitter (T) and a receiver (R) are hung vertically from two identical massless strings of length 8 m with their pivots well separated along the X axis. They are pulled from the equilibrium position in opposite directions along the X axis by a small angular amplitude

\theta_0 = \cos^{-1}(0.9)

and released simultaneously. If the natural frequency of the transmitter is 660 Hz and the speed of sound in air is 330 m/s, the maximum variation in the frequency (in Hz ) as measured by the receiver (Take the acceleration due to gravity g = 10 m/s

^2

) is ______

Q13·PhysicsMultiple correctJEE Advanced 2025

Consider a system of three connected strings,

S_{1}

,

S_{2}

and

S_{3}

with uniform linear mass densities μ kg/m, 4μ kg/m and 16μ kg/m, respectively, as shown in the figure.

S_{1}

and

S_{2}

are connected at the point P, whereas

S_{2}

and

S_{3}

are connected at the point Q, and the other end of

S_{3}

is connected to a wall. A wave generator O is connected to the free end of

S_{1}

. The wave from the generator is represented by

y = y_{0}\cos(\omega t - kx)

cm, where

y_{0}

,

\omega

and k are constants of appropriate dimensions. Which of the following statements is/are correct:

(A)When the wave reflects from P for the first time, the reflected wave is represented by $y = \alpha_{1}y_{0}\cos(\omega t + kx + \pi)$ cm, where $\alpha_{1}$ is a positive constant.
(B)When the wave transmits through P for the first time, the transmitted wave is represented by $y = \alpha_{2}y_{0}\cos(\omega t - kx)$ cm, where $\alpha_{2}$ is a positive constant.
(C)When the wave reflects from Q for the first time, the reflected wave is represented by $y = \alpha_{3}y_{0}\cos(\omega t - kx + \pi)$ cm, where $\alpha_{3}$ is a positive constant.
(D)When the wave transmits through Q for the first time, the transmitted wave is represented by $y = \alpha_{4}y_{0}\cos(\omega t - 4kx)$ cm, where $\alpha_{4}$ is a positive constant.

Q14·PhysicsSingle correctJEE Main 2025

The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves,

y_1(x,t)=4\sin(kx-\omega t)

and

y_2(x,t)=2\sin\left(kx-\omega t+\dfrac{2\pi}{3}\right)

, are: (Take the angular frequency of initial waves same as

\omega

)

(A) $\left[6,\dfrac{2\pi}{3}\right]$
(B) $\left[6,\dfrac{\pi}{3}\right]$
(C) $\left[\sqrt3,\dfrac{\pi}{6}\right]$
(D) $\left[2\sqrt3,\dfrac{\pi}{6}\right]$

Q15·PhysicsSingle correctJEE Main 2025

Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section

R

is

v_1

and that in the other string having radius of cross section

R/2

is

v_2

. Then

\dfrac{v_2}{v_1}=

(A) $\sqrt2$
(B) $2$
(C) $8$
(D) $4$

Q16·PhysicsSingle correctJEE Main 2025

Two harmonic waves moving in the same direction superimpose to form a wave

x=a\cos(1.5t)\cos(50.5t)

where

t

is in seconds. Find the period with which they beat (close to nearest integer)

(A)6 s
(B)4 s
(C)1 s
(D)2 s

Q17·PhysicsSingle correctJEE Main 2025

Two plane polarized light waves combine at a certain point whose electric field components are

E_1=E_0\sin\omega t

,

E_2=E_0\sin\left(\omega t+\dfrac{\pi}{3}\right)

. Find the amplitude of the resultant wave.

(A) $0.9\,E_0$
(B) $E_0$
(C) $1.7\,E_0$
(D) $3.4\,E_0$

Q18·PhysicsSingle correctJEE Main 2025

In an experiment with a closed organ pipe, it is filled with water by

\dfrac{1}{5}

th of its volume. The frequency of the fundamental note will change by

(A)25%
(B)20%
(C) $-20$ %
(D) $-25$ %

Q19·PhysicsSingle correctJEE Main 2025

Displacement of a wave is expressed as

x(t)=5\cos\left(628t+\dfrac{\pi}{2}\right)

m. The wavelength of the wave when its velocity is 300 m/s is:

(A)1.5 m
(B)3 m
(C)0.5 m
(D)0.33 m

Q20·PhysicsSingle correctJEE Main 2025

In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is:

(A)335 m/s
(B)370 m/s
(C)340 m/s
(D)360 m/s

Q21·PhysicsSingle correctJEE Main 2025

A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x-direction in 0.3 sec. The crest P is at

x=0

at

t=0

sec and maximum displacement of the wave is 2 cm. Which equation correctly represents this wave?

(A) $y=2\cos(0.83x-3.35t)$ cm
(B) $y=2\sin(0.83x-3.5t)$ cm
(C) $y=2\cos(3.35x-0.83t)$ cm
(D) $y=2\cos(0.13x-0.5t)$ cm

Q22·PhysicsSingle correctJEE Main 2025

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: A sound wave has higher speed in solids than gases. Reason R: Gases have higher value of Bulk modulus than solids. In the light of the above statements, choose the correct answer from the options given below

(A)Both A and R are true and R is the correct explanation of A
(B)A is false but R is true
(C)Both A and R are true but R is NOT the correct explanation of A
(D)A is true but R is false

Q23·PhysicsSingle correctJEE Main 2025

The equation of a transverse wave travelling along a string is

y(x,t)=4.0\sin[20\times10^{-3}x+600t]

mm, where

x

is in the mm and

t

is in second. The velocity of the wave is :

(A) $+30$ m/s
(B) $-60$ m/s
(C) $-30$ m/s
(D) $+60$ m/s

Q24·PhysicsSingle correctJEE Main 2025

A closed organ pipe and an open organ pipe are filled with two different gases having the same bulk modulus but different densities ρ₁ and ρ₂ respectively. The frequency of the 9th harmonic of the closed pipe is identical with the 4th harmonic of the open pipe. If the length of the closed pipe is 10 cm and the density ratio of the gases is ρ₁ : ρ₂ = 1 : 16, the length of the open pipe is:

(A)20/7 cm
(B)15/7 cm
(C)20/9 cm
(D)15/9 cm

Q25·PhysicsIntegerJEE Advanced 2024

A source (S) of sound has frequency 240 Hz. When the observer (O) and the source move towards each other at a speed

v

with respect to the ground (as shown in Case 1 in the figure), the observer measures the frequency of the sound to be 288 Hz. However, when the observer and the source move away from each other at the same speed

v

with respect to the ground (as shown in Case 2 in the figure), the observer measures the frequency of sound to be

n

Hz. The value of

n

is ______.

Q26·PhysicsMultiple correctJEE Advanced 2024

Two uniform strings of mass per unit length

\mu

and

4\mu

, and length

L

and

2L

, respectively, are joined at point

O

, and tied at two fixed ends

P

and

Q

, as shown in the figure. The strings are under a uniform tension

T

. If we define the frequency

v_{0} = \frac{1}{2L}\sqrt{\frac{T}{\mu}}

, which of the following statement(s) is(are) correct?

(A)With a node at $O$ , the minimum frequency of vibration of the composite string is $v_{0}$ .
(B)With an antinode at $O$ , the minimum frequency of vibration of the composite string is $2v_{0}$ .
(C)When the composite string vibrates at the minimum frequency with a node at $O$ , it has 6 nodes, including the end nodes.
(D)No vibrational mode with an antinode at $O$ is possible for the composite string.

Q27·PhysicsSingle correctJEE Main 2024

A plane progressive wave is given by

y=2\cos 2\pi(330\,t-x)

m. The frequency of the wave is:

(A)165 Hz
(B)330 Hz
(C)660 Hz
(D)340 Hz

Q28·PhysicsNumericalJEE Main 2024

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is

\left(\dfrac{a-1}{a}\right)

then the value of

a

is ___

Q29·PhysicsNumericalJEE Main 2024

Two open organ pipes of length 60 cm and 90 cm resonate at

6^{th}

and

5^{th}

harmonics respectively. The difference of frequencies for the given modes is ______ Hz. (Velocity of sound in air = 333 m/s)

Q30·PhysicsNumericalJEE Main 2024

A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with a fundamental frequency of 600 Hz under the same tension is __________ cm.

Q31·PhysicsSingle correctJEE Main 2024

The equation of stationary wave is

y=2a\sin\left(\dfrac{2\pi nt}{\lambda}\right)\cos\left(\dfrac{2\pi x}{\lambda}\right)

. Which of the following is NOT correct:

(A)The dimensions of $nt$ is $[L]$ .
(B)The dimensions of $n$ is $[LT^{-1}]$ .
(C)The dimensions of $n/\lambda$ is $[T]$ .
(D)The dimensions of $x$ is $[L]$ .

Q32·PhysicsNumericalJEE Main 2024

A tuning fork resonates with a sonometer wire of length

1\,m

stretched with a tension of

6\,N

. When the tension in the wire is changed to

54\,N

, the same tuning fork produces

12

beats per second with it. The frequency of the tuning fork is ___ Hz.

Q33·PhysicsSingle correctJEE Main 2024

The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is 60 cm, the length of the closed pipe will be :

(A)60 cm
(B)45 cm
(C)30 cm
(D)15 cm

Q34·PhysicsSingle correctJEE Main 2024

The speed of sound in oxygen at S.T.P. will be approximately: (Given,

R=8.3\ \text{JK}^{-1}

,

\gamma=1.4

)

(A)310 m/s
(B)333 m/s
(C)341 m/s
(D)325 m/s

Q35·PhysicsNumericalJEE Main 2024

In a closed organ pipe, the frequency of fundamental note is

30\,Hz

. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to

110\,Hz

. If the organ pipe has a cross-sectional area

2\,cm^2

, the amount of water poured in the organ pipe is ___

g

. (Take speed of sound in air is

330\,m/s

)

Q36·PhysicsNumericalJEE Main 2024

A closed organ pipe 150 cm long gives 7 beats per second with an open organ pipe of length 350 cm, both vibrating in fundamental mode. The velocity of sound is ________ m/s.

Q37·PhysicsNumericalJEE Advanced 2023

S_1

and

S_2

are two identical sound sources of frequency 656 Hz. The source

S_1

is located at O and

S_2

moves anti-clockwise with a uniform speed

4\sqrt{2}

m s

^{-1}

on a circular path around O, as shown in the figure. There are three points P, Q and R on this path such that P and R are diametrically opposite while Q is equidistant from them. A sound detector is placed at point

P

. The source

S_1

can move along direction OP. [Given: The speed of sound in air is 324 m s

^{-1}

] When only

S_2

is emitting sound and it is at Q, the frequency of sound measured by the detector in Hz is _________.

Q38·PhysicsNumericalJEE Advanced 2023

S_1

and

S_2

are two identical sound sources of frequency 656 Hz. The source

S_1

is located at O and

S_2

moves anti-clockwise with a uniform speed

4\sqrt{2}

m s

^{-1}

on a circular path around O, as shown in the figure. There are three points P, Q and R on this path such that P and R are diametrically opposite while Q is equidistant from them. A sound detector is placed at point

P

. The source

S_1

can move along direction OP. [Given: The speed of sound in air is 324 m s

^{-1}

] Consider both sources emitting sound. When

S_2

is at R and

S_1

approaches the detector with a speed 4 m s

^{-1}

, the beat frequency measured by the detector is ________Hz.

Q39·PhysicsIntegerJEE Advanced 2023

A string of length 1 m and mass

2 \times 10^{-5}

kg is under tension

T

. When the string vibrates, two successive harmonics are found to occur at frequencies 750 Hz and 1000 Hz. The value of tension

T

is _____ Newton.

Q40·PhysicsNumericalJEE Main 2023

The fundamental frequency of vibration of a string stretched between two rigid support is

50

Hz. The mass of the string is

18

g and its linear mass density is

20

g/m. The speed of the transverse waves so produced in the string is __________ ms

^{-1}

.

Q41·PhysicsNumericalJEE Main 2023

In an experiment with sonometer when a mass of 180 g is attached to the string, it vibrates with fundamental frequency of 30 Hz. When a mass m is attached, the string vibrates with fundamental frequency of 50 Hz. The value of m is ____ g.

Q42·PhysicsNumericalJEE Main 2023

For a certain organ pipe, the first three resonance frequencies are in the ratio of 1:3:5 respectively. If the frequency of fifth harmonic is 405 Hz and the speed of sound in air is 324 m s

^{-1}

, the length of the organ pipe is _________ m.

Q43·PhysicsNumericalJEE Main 2023

The equation of wave is given by

Y = 10^{-2} \sin 2\pi \left( 160t - 0.5x + \frac{\pi}{4} \right)

Where x and Y are in m and t in s. The speed of the wave is ____

\text{km h}^{-1}

Q44·PhysicsNumericalJEE Main 2023

A wire of density

8\times10^{3}

kg/m

^3

is stretched between two clamps

0.5

m apart. The extension developed in the wire is

3.2\times10^{-4}

m. If

Y=8\times10^{10}

N/m

^2

, the fundamental frequency of vibration in the wire will be ____ Hz.

Q45·PhysicsSingle correctJEE Main 2023

A car P travelling at

20

ms

^{-1}

sounds its horn at a frequency of

400

Hz. Another car Q is travelling behind the first car in the same direction with a velocity

40

ms

^{-1}

. The frequency heard by the passenger of car Q is approximately [Take velocity of sound

=360

ms

^{-1}

]

(A) $514$ Hz
(B) $421$ Hz
(C) $485$ Hz
(D) $471$ Hz

Q46·PhysicsNumericalJEE Main 2023

A transverse harmonic wave on a string is given by

y(x,t)=5\sin(6t+0.003x)

where x and y are in cm and t in sec. The wave velocity is _________ ms

^{-1}

.

Q47·PhysicsSingle correctJEE Main 2023

The engine of a train moving with speed

10\,\text{ms}^{-1}

towards a platform sounds a whistle at frequency

400\,\text{Hz}

. The frequency heard by a passenger inside the train is (neglect air speed. Speed of sound in air

330\,\text{ms}^{-1}

)

(A) $200\,\text{Hz}$
(B) $400\,\text{Hz}$
(C) $412\,\text{Hz}$
(D) $388\,\text{Hz}$

Q48·PhysicsNumericalJEE Main 2023

A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be ____ cm.

Q49·PhysicsNumericalJEE Main 2023

An organ pipe

40\,\text{cm}

long is open at both ends. The speed of sound in air is

360\,\text{ms}^{-1}

. The frequency of the second harmonic is ______

\text{Hz}

Q50·PhysicsNumericalJEE Main 2023

A person driving car at a constant speed of

15\,m/s

is approaching a vertical wall. The person notices a change of

40\,Hz

in the frequency of his car's horn upon reflection from the wall. The frequency of horn is _____ Hz. (Given: Speed of sound:

330\,m/s

)

Q51·PhysicsSingle correctJEE Main 2023

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

(A) $4 : 1$
(B) $1 : 2$
(C) $1 : 4$
(D) $1 : 1$

Q52·PhysicsSingle correctJEE Main 2023

A steel wire with mass per unit length

7.0\times10^{-3}

kg m

^{-1}

is under tension of

70

N. The speed of transverse waves in the wire will be:

(A) $100$ m/s
(B) $10$ m/s
(C) $50$ m/s
(D) $200\pi$ m/s

Q53·PhysicsNumericalJEE Main 2023

The displacement equations of two interfering waves are given by

y_1=10\sin\left(\omega t+\dfrac{\pi}{3}\right)

cm,

y_2=5[\sin\omega t+\sqrt3\cos\omega t]

cm respectively. The amplitude of the resultant wave is _________ cm.

Q54·PhysicsNumericalJEE Main 2023

Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is ________ degree.

Q55·PhysicsSingle correctJEE Main 2023

A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of 30 m/s. If both trains emit sounds with frequency 300 Hz (speed of sound = 330 m/s), the approximate difference of frequencies heard by the person will be:

(A)55 Hz
(B)80 Hz
(C)33 Hz
(D)10 Hz

Q56·PhysicsNumericalJEE Main 2023

A train blowing a whistle of frequency 320 Hz approaches an observer standing on the platform at a speed of 66 m/s. The frequency observed by the observer will be (given speed of sound

= 330\,\text{ms}^{-1}

) ______ Hz.

Q57·PhysicsNumericalJEE Main 2023

The distance between two consecutive points with phase difference of

60^{\circ}

in a wave of frequency 500 Hz is 6.0 m. The velocity with which the wave is travelling is _______ km/s.

Q58·PhysicsSingle correctJEE Main 2023

A travelling wave is described by the equation

y(x,t)=[0.05\sin(8x-4t)]

m. The velocity of the wave is: [all the quantities are in SI unit]

(A) $8$ ms $^{-1}$
(B) $4$ ms $^{-1}$
(C) $0.5$ ms $^{-1}$
(D) $2$ ms $^{-1}$

Q59·PhysicsSingle correctJEE Main 2022

In the wave equation

y = 0.5\sin\frac{2\pi}{\lambda}\left(400t - x\right)m

the velocity of the wave will be :

(A)200 m/s
(B)200 $\sqrt{2}$ m / s
(C)400 m/s
(D)400 $\sqrt{2}$ m / s

Q60·PhysicsNumericalJEE Main 2022

The frequency of echo will be ________ Hz if the train blowing a whistle of frequency 320 Hz is moving with a velocity of 36 km/h towards a hill from which an echo is heard by the train driver. Velocity of sound in air is 330 m/s.

Q61·PhysicsNumericalJEE Main 2022

A wire of length 30 cm, stretched between rigid supports, has it's n

^{th}

and (n + 1)

^{th}

harmonics at 400 Hz and 450 Hz, respectively. If tension in the string is 2700 N, it's linear mass density is……..kg/m.

Q62·PhysicsNumericalJEE Main 2022

When a car is approaching the observer, the frequency of horn is 100Hz. After passing the observer, it is 50Hz. If the observer moves with the car, the frequency will be

\frac{x}{3}

Hz where x = ____

Q63·PhysicsSingle correctJEE Main 2022

A transverse wave is represented by y = 2sin

\left(\omega t - kx\right)

cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be ;

(A) $4\pi$
(B) $2\pi$
(C) $\pi$
(D)2

Q64·PhysicsNumericalJEE Main 2022

An observer is riding on a bicycle and moving towards a hill at 18

kmh^{-1}

. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is 640 Hz and velocity of the sound in air is 320 m/s, the beat frequency between the two sounds heard by observer will be _______ Hz.

Q65·PhysicsSingle correctJEE Main 2022

A longitudinal wave is represented by

x = 10 \sin 2\pi\left(nt - \frac{x}{\lambda}\right)

cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to :

(A) $2\pi$
(B) $5\pi$
(C) $\pi$
(D) $\frac{5\pi}{2}$

Q66·PhysicsNumericalJEE Main 2022

In an experiment to determine the velocity of sound in air at room temperature using a resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms

^{-1}

. The third resonance is observed when the air column has a length of _____cm.

Q67·PhysicsSingle correctJEE Main 2022

The velocity of sound in a gas. in which two wavelengths

4.08

m and

4.16

m produce 40 beats in 12s, will be :

(A)2.82.8 ms $^{-1}$
(B) $175.5$ ms $^{-1}$
(C) $353.6$ ms $^{-1}$
(D) $707.2$ ms $^{-1}$

Q68·PhysicsSingle correctJEE Main 2022

An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be :

(A)20%
(B)10%
(C)5%
(D)0%

Q69·PhysicsNumericalJEE Main 2022

A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is______Hz.

Q70·PhysicsNumericalJEE Main 2022

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm. The length of the open organ pipe is ______ cm.

Q71·PhysicsNumericalJEE Main 2022

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by

y = (10 \cos \pi x \sin \dfrac{2\pi t}{T})

cm The amplitude of the particle at

x = \dfrac{4}{3}

cm will be ________ cm.

Q72·PhysicsSingle correctJEE Main 2022

The equations of two waves are given by :

y_{1}=5\sin 2\pi(x-vt)

cm

y_{2}=3\sin 2\pi(x-vt+1.5)

cm These waves are simultaneously passing through a string. The amplitude of the resulting wave is

(A)2 cm
(B)4 cm
(C)5.8 cm
(D)8 cm

Q73·PhysicsMultiple correctJEE Advanced 2021

A source, approaching with speed

u

towards the open end of a stationary pipe of length

L

, is emitting a sound of frequency

f_s

. The farther end of the pipe is closed. The speed of sound in air is

v

and

f_0

is the fundamental frequency of the pipe. For which of the following combination(s) of

u

and

f_s

, will the sound reaching the pipe lead to a resonance ?

(A) $u = 0.8 v$ and $f_s = f_0$
(B) $u = 0.8 v$ and $f_s = 2f_0$
(C) $u = 0.8 v$ and $f_s = 0.5 f_0$
(D) $u = 0.5 v$ and $f_s = 1.5 f_0$

Q74·PhysicsNumericalJEE Main 2021

A wire having a linear mass density 9.0

\times

10

^{-4}

kg/m is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500 Hz. The next higher frequency at which the same wire resonates is 550 Hz. The length of the wire is ___ m.

Q75·PhysicsNumericalJEE Main 2021

Two cars X and Y are approaching each other with velocities 36 km/h and 72 km/h respectively. The frequency of a whistle sound as emitted by a passenger in car X, heard by the passenger in car Y is 1320 Hz. If the velocity of sound in air is 340 m/s, the actual frequency of the whistle sound produced is ........ Hz.

Q76·PhysicsNumericalJEE Main 2021

A tuning fork is vibrating at 250 Hz. The length of the shortest closed organ pipe that will resonate with the tuning fork will be _____ cm. (Take speed of sound in air as 340 ms

^{-1}

)

Q77·PhysicsNumericalJEE Main 2021

Two waves are simultaneously passing through a string and their equations are :

y_1 = A_1 \sin k(x-vt)

,

y_2 = A_2 \sin k(x-vt + x_0)

. Given amplitudes

A_1 = 12

mm and

A_2 = 5

mm,

x_0 = 3.5

cm and wave number

k = 6.28

cm

^{-1}

. The amplitude of resulting wave will be .......... mm.

Q78·PhysicsNumericalJEE Main 2021

A source and a detector move away from each other in absence of wind with a speed of 20 m/s with respect to the ground. If the detector detects a frequency of 1800 Hz of the sound coming from the source, then the original frequency of source considering speed of sound in air 340 m/s will be ........ Hz.

Q79·PhysicsNumericalJEE Main 2021

Two travelling waves produces a standing wave represented by equation,

y = 1.0\ \mathrm{mm}\ \cos(1.57\ \mathrm{cm^{-1}})\ x\ \sin(78.5\ \mathrm{s^{-1}})t.

The node closest to the origin in the region

x > 0

will be at

x =

......... cm.

Q80·PhysicsNumericalJEE Main 2021

The frequency of a car horn encountered a change from 400 Hz to 500 Hz, when the car approaches a vertical wall. If the speed of sound is 330 m /s. Then the speed of car is __________ km /h.

Q81·PhysicsNumericalJEE Main 2021

The amplitude of wave disturbance propagating in the positive x-direction is given by

y = \frac{1}{1+(x)^2}

at time

t = 0

and

y = \frac{1}{1+(x-2)^2}

at

t = 1

s , where x and y are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be ________ m /s.

Q82·PhysicsSingle correctJEE Main 2021

A sound wave of frequency 245 Hz travels with the speed of 300 ms

^{-1}

along the positive x-axis. Each point of the wave moves to and fro through a total distance of 6 cm. What will be the mathematical expression of this travelling wave ?

(A)Y(x,t) = 0.03 [sin 5.1 x − (0.2 × 10 $^{3}$ )t]
(B)Y(x,t) = 0.06 [sin 5.1 x − (1.5 × 10 $^{3}$ )t]
(C)Y(x,t) = 0.06 [sin 0.8 x − (0.5 × 10 $^{3}$ )t]
(D)Y(x,t) = 0.03 [sin 5.1 x − (1.5 × 10 $^{3}$ )t]

Q83·PhysicsNumericalJEE Main 2021

A closed organ pipe of length L and an open organ pipe contain gases of densities ρ

_{1}

and ρ

_{2}

respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is

\frac{x}{3}L\sqrt{\frac{\rho_{1}}{\rho_{2}}}

where x is ________. (Round off to the Nearest Integer)

Q84·PhysicsNumericalJEE Main 2021

The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form y=−0.21sin(x+30t) is produced in it, where x is in meter and t is in second. Then, the expected value of tension in the wire is x × 10

^{-2}

N. Value of x is ____________. (Round-off to the nearest integer)

Q85·PhysicsSingle correctJEE Main 2021

A tuning fork A of unknown frequency produces 5beats/s with a fork of known frequency 340 HZ. When fork A filed, the beat frequency decreases to 2beats/s. What is the frequency of fork A?

(A)342 Hz
(B)335 Hz
(C)338 Hz
(D)345 Hz

Q86·PhysicsSingle correctJEE Main 2021

A student is performing the experiment of resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is 336 m/s. The zero of the metre scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is :

(A)13 cm
(B)14.8 cm
(C)16.6 cm
(D)18.4 cm

Q87·PhysicsNumericalJEE Main 2021

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4% will be___________%.

Q88·PhysicsNumericalJEE Main 2021

Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having frequency of 676 Hz. The beat frequency heard by each driver will be _________ Hz. [Velocity of sound in air is 340 m/s.]

Q89·PhysicsSingle correctJEE Main 2021

Which of the following equations represents a travelling wave?

(A) $y = Ae^{-x^{2}}(vt + \theta)$
(B) $y = A\sin(15x - 2t)$
(C) $y = Ae^{x}\cos(\omega t - \theta)$
(D) $y = A\sin x\cos\omega t$

Q90·PhysicsNumericalJEE Advanced 2020

A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2

ms^{-1}

in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320

ms^{-1}

, the smallest value of the percentage change required in the length of the pipe is ____________.

Q91·PhysicsSingle correctJEE Main 2020

A sound source S is moving along a straight track with speed v, and is emitting sound of frequency

\nu_0

(see figure). An observer is standing at a finite distance, at the point O, from the track. The time variation of frequency heard by the observer is best represented by: (

t_0

represents the instant when the distance between the source and observer is minimum)

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q92·PhysicsSingle correctJEE Main 2020

Two coherent sources of sound,

S_1

and

S_2

produce source waves of the same wavelength,

\lambda = 1

m, in phase.

S_1

and

S_2

are placed 1.5 m apart (see fig). A listener located at L, directly in front of

S_2

finds that the intensity is at a minimum when he is 2 m away from

S_2

. The listener moves away from

S_1

, keeping his distance from

S_2

fixed. The adjacent maximum of intensity is observed when the listener is at a distance d from

S_1

. Then, d is:

(A)12 m
(B)3 m
(C)5 m
(D)2 m

Q93·PhysicsSingle correctJEE Main 2020

In a resonance tube experiment when the tube is filled with water up to a height of 17.0 cm from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of 24.5 cm. If the velocity of sound in air is 330 m/s, the tuning fork frequency is:

(A)1100 Hz
(B)2200 Hz
(C)3300 Hz
(D)550 Hz

Q94·PhysicsSingle correctJEE Main 2020

A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from 440 Hz to 480 Hz, when it gets reflected from the wall. If the speed of sound in air is 345 m/s, then the speed of the car is:

(A)24 km/hr
(B)36 km/hr
(C)18 km/hr
(D)54 km/hr

Q95·PhysicsSingle correctJEE Main 2020

The driver of bus approaching a big wall notices that the frequency of his bus's horn changes from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of the sound is 330 ms

^{-1}

:

(A)90 kmh $^{-1}$
(B)80 kmh $^{-1}$
(C)61 kmh $^{-1}$
(D)71 kmh $^{-1}$

Q96·PhysicsSingle correctJEE Main 2020

For a transverse wave traveling along a straight line, the distance between two peaks (crests) is 5 m, while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in m) of the waves are:

(A)1, 3, 5, …..
(B) $\frac{1}{1}, \frac{1}{3}, \frac{1}{5}, ....$
(C) $\frac{1}{2}, \frac{1}{4}, \frac{1}{6}, ....$
(D)1, 2, 3, ……

Q97·PhysicsSingle correctJEE Main 2020

A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wave-train of wavelength 6 cm is produced at the lower and the rope. What is the wavelength of the wave train (in cm) when it reaches the top of the tope?

(A)6
(B)12
(C)3
(D)9

Q98·PhysicsSingle correctJEE Main 2020

Three harmonic waves having equal frequency

\nu

and same intensity

I_{0}

, have phase angles

0, \dfrac{\pi}{4}

and

-\dfrac{\pi}{4}

respectively. When they are superimposed the intensity of the resultant wave is close to:

(A)3 $I_{0}$
(B) $I_{0}$
(C)0.2 $I_{0}$
(D)5.8 $I_{0}$

Q99·PhysicsSingle correctJEE Main 2020

A wire of length L and mass per unit length

6.0 \times 10^{-3}

kg

\mathrm{m}^{-1}

is put under tension of 540 N. Two consecutive frequencies that it resonates at are: 420 Hz and 490 Hz. Then L in meters is

(A)1.1 m
(B)5.1 m
(C)2.1 m
(D)8.1 m

Q100·PhysicsSingle correctJEE Main 2020

A transverse wave travels on a taut steel wire wit a velocity of v when tension in it is 2.06

\times

10

^{4}

N. When the tension is changed to T, the velocity changed to v/2. The value of T is close to:

(A)10.2 $\times$ 10 $^{2}$ N
(B)30.5 $\times$ 10 $^{4}$ N
(C)5.15 $\times$ 10 $^{3}$ N
(D)2.50 $\times$ 10 $^{4}$ N

Q101·PhysicsSingle correctJEE Main 2020

A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much les than the speed of sound). The observers hears 2 beats/sec. The oscillation frequency of each tuning fork is

\nu_0

= 1400 Hz and the velocity of sound in air is 350 m/s. The speed of each tuning fork is close to:

(A) $\dfrac{1}{4}$ m/s
(B)1 m/s
(C) $\dfrac{1}{2}$ m/s
(D) $\dfrac{1}{8}$ m/s

Q102·PhysicsNumericalJEE Advanced 2019

A train S1, moving with a uniform velocity of 108 km/h, approaches another train S2 standing on a platform. An observer O moves with a uniform velocity of 36 km/h towards S2, as shown in figure. Both the trains are blowing whistles of same frequency 120 Hz. When O is 600 m away from S2 and distance between S1 and S2 is 800 m, the number of beats heard by O is ______. [Speed of the sound = 330 m/s]

Q103·PhysicsSingle correctJEE Advanced 2019

Answer the following by appropriately matching the list based on the information given in the paragraph. A musical instrument is made using four different metal strings, 1, 2, 3 and 4 with mass per unit length

\mu

,

2\mu

,

3\mu

and

4\mu

respectively. The instrument is played by vibrating the strings by varying the free length in between the range

L_0

and

2L_0

. It is found that in string-1 (

\mu

) at free length

L_0

and tension

T_0

the fundamental mode frequency is

f_0

. List-I gives the above four strings while list-II lists the magnitude of some quantity. The length of the string 1, 2, 3 and 4 are kept fixed at

L_0

,

\frac{3L_0}{2}

,

\frac{5L_0}{4}

and

\frac{7L_0}{4}

, respectively. Strings 1, 2, 3 and 4 are vibrated at their

1^{st}

,

3^{rd}

,

5^{th}

and

14^{th}

harmonics, respectively such that all the strings have same frequency. The correct match for the tension in the four strings in the units of

T_0

will be,

List-I	List-II
I.String-1 ( $\mu$ )	P. $1$
II.String-2 ( $2\mu$ )	Q. $\frac{1}{2}$
III.String-3 ( $3\mu$ )	R. $\frac{1}{\sqrt{2}}$
IV.String-4 ( $4\mu$ )	S. $\frac{1}{\sqrt{3}}$
	T. $\frac{3}{16}$
	U. $\frac{1}{16}$

(A)I $\to$ P, II $\to$ Q, III $\to$ T, IV $\to$ U
(B)I $\to$ P, II $\to$ Q, III $\to$ R, IV $\to$ T
(C)I $\to$ P, II $\to$ R, III $\to$ T, IV $\to$ U
(D)I $\to$ T, II $\to$ Q, III $\to$ R, IV $\to$ U

Q104·PhysicsSingle correctJEE Advanced 2019

Answer the following by appropriately matching the list based on the information given in the paragraph. A musical instrument is made using four different metal strings, 1, 2, 3 and 4 with mass per unit length

\mu

,

2\mu

,

3\mu

and

4\mu

respectively. The instrument is played by vibrating the strings by varying the free length in between the range

L_0

and

2L_0

. It is found that in string-1 (

\mu

) at free length

L_0

and tension

T_0

the fundamental mode frequency is

f_0

. List-I gives the above four strings while list-II lists the magnitude of some quantity. If the tension in each string is

T_0

, the correct match for the highest fundamental frequency in

f_0

units will be,

List-I	List-II
I.String-1 ( $\mu$ )	P. $1$
II.String-2 ( $2\mu$ )	Q. $\frac{1}{2}$
III.String-3 ( $3\mu$ )	R. $\frac{1}{\sqrt{2}}$
IV.String-4 ( $4\mu$ )	S. $\frac{1}{\sqrt{3}}$
	T. $\frac{3}{16}$
	U. $\frac{1}{16}$

(A)I $\to$ P, II $\to$ R, III $\to$ S, IV $\to$ Q
(B)I $\to$ Q, II $\to$ S, III $\to$ R, IV $\to$ P
(C)I $\to$ P, II $\to$ Q, III $\to$ T, IV $\to$ S
(D)I $\to$ Q, II $\to$ P, III $\to$ R, IV $\to$ T

Q105·PhysicsSingle correctJEE Main 2019

A submarine (A) travelling at 18 km/hr is being chased along the line of its velocity by another submarine (B) travelling at 27 km/hr. B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of frequency

\nu

. The value of

\nu

is close to : (Speed of sound in water = 1500 ms

^{-1}

)

(A)499 Hz
(B)502 Hz
(C)504 Hz
(D)507 Hz

Q106·PhysicsSingle correctJEE Main 2019

Two sources of sound S

_{1}

and S

_{2}

produce sound waves of same frequency 660 Hz. A listener is moving from source S

_{1}

towards S

_{2}

with a constant speed u m/s and he hears 10 beats/s. The velocity of sound is 330 m/s. Then, u equals:

(A)15.0 m/s
(B)10.0 m/s
(C)5.5 m/s
(D)2.5 m/s

Q107·PhysicsSingle correctJEE Main 2019

A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column,

\ell_{1} = 30

cm and

\ell_{2} = 70

cm. Then n is equal to :

(A)332 ms $^{-1}$
(B)338 ms $^{-1}$
(C)384 ms $^{-1}$
(D)379 ms $^{-1}$

Q108·PhysicsSingle correctJEE Main 2019

A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB intensity sound? [Given reference intensity of sound as

10^{-12}

W/m

^{2}

]

(A)30 cm
(B)10 cm
(C)40 cm
(D)20 cm

Q109·PhysicsSingle correctJEE Main 2019

A progressive wave travelling along the positive x-direction is represented by y(x, t) = A sin(kx

-

\omega

t +

\phi

). Its snapshot at t = 0 is given in the figure: For this wave, the phase

\phi

is :

(A) $\pi$
(B) $\dfrac{\pi}{2}$
(C) $-\dfrac{\pi}{2}$
(D)0

Q110·PhysicsSingle correctJEE Main 2019

A stationary source emits sound waves of frequency 500 Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480 Hz and 530 Hz. Their respective speeds are, in ms

^{-1}

(Given speed of sound = 300 m/s)

(A)16, 14
(B)12, 16
(C)8, 18
(D)12, 18

Q111·PhysicsSingle correctJEE Main 2019

The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of frequencies 9 Hz and 11 Hz,

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q112·PhysicsSingle correctJEE Main 2019

A source of sound S is moving with the velocity of 50 m/s towards a stationary observer. The observer measures the frequency of the sound as 1000 Hz. What will be the apparent frequency of the source when it is moving away from the observer after crossing him? (Take velocity of sound in air is 350 m/s)

(A)1143 Hz
(B)857 Hz
(C)750 Hz
(D)807 Hz

Q113·PhysicsSingle correctJEE Main 2019

A string 2.0 m long and fixed at its end is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is:

(A)320 m/s, 120 Hz
(B)180 m/s, 80 Hz
(C)180m/s, 120 Hz
(D)320 m/s, 80 Hz

Q114·PhysicsSingle correctJEE Main 2019

The pressure wave, P =

0.01sin[1000t-3x]

NM

^{-2}

, corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is 0°C. On some other day when temperature is T, the speed of sound produced by the same blade and at the same frequency is found to be 336 ms

^{-1}

. Approximate value of T is:

(A)12°C
(B)11°C
(C)15°C
(D)4°C

Q115·PhysicsSingle correctJEE Main 2019

Two cars A and B are moving away from each other in opposite directions. Both the cars are moving with a speed of 20 ms

^{-1}

with respect to the ground. If an observer in car A detects a frequency 2000 Hz of the sound coming from car B, what is the natural frequency of the sound source of car B? (speed of sound in air = 340 ms

^{-1}

)

(A)2250 Hz
(B)2060 Hz
(C)2150 Hz
(D)2300 Hz

Q116·PhysicsSingle correctJEE Main 2019

A string is clamed at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is

Y = 0.3\sin(0.157x)\cos(200\pi t)

. The length of the string is: (all quantities are in SI units)

(A)80 m
(B)60 m
(C)40 m
(D)20 m

Q117·PhysicsSingle correctJEE Main 2019

A wire of length 2L is made by joining two wires A and b of same lengths but different radii r and 2r and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire A is p and that in B is q then the ratio p : q is:

(A)1 : 4
(B)1 : 2
(C)3 : 5
(D)4 : 9

Q118·PhysicsSingle correctJEE Main 2019

A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60° with ground level. But he finds the aeroplane right vertically above his position. If

\upsilon

is the speed of sound, speed of the plane is:

(A) $\frac{\sqrt{3}}{2}\upsilon$
(B) $\frac{2\upsilon}{\sqrt{3}}$
(C) $\upsilon$
(D) $\frac{\upsilon}{2}$

Q119·PhysicsSingle correctJEE Main 2019

A travelling harmonic wave is represented by the equation

y(x, t) = 10^{-3}\sin(50t + 2x)

, where x and y are in meter and t is in seconds. Which of the following is a correct statement about the wave?

(A)The wave is propagating along the negative x-axis with speed 25 ms $^{-1}$ .
(B)The wave is propagating along the positive x-axis with speed 100 ms $^{-1}$ .
(C)The wave is propagating along the positive x-axis with speed 25 ms $^{-1}$ .
(D)The wave is propagating along the negative x-axis with speed 100 ms $^{-1}$ .

Q120·PhysicsSingle correctJEE Main 2019

A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark. The velocity of sound in air, obtained in the experiment, is close to :

(A)322 ms $^{-1}$
(B)341 ms $^{-1}$
(C)335 ms $^{-1}$
(D)328 ms $^{-1}$

Q121·PhysicsSingle correctJEE Main 2019

Equation of travelling wave on a stretched string of linear density 5 g/m is

y = 0.03\sin(450t - 9x)

where distance and time are measured in SI united. The tension in the string is:

(A)10 N
(B)7.5 N
(C)12.5 N
(D)5 N

Q122·PhysicsSingle correctJEE Main 2019

A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close to:

(A)10.0 cm
(B)33.3 cm
(C)16.6 cm
(D)20.0 cm

Q123·PhysicsSingle correctJEE Main 2019

A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is

f_{1}

. If the speed of the train is reduced to 17 m/s, the frequency registered is

f_{2}

. If speed of sound is 340 m/s, then the ratio

f_{1}/f_{2}

is:

(A)18/17
(B)19/18
(C)20/19
(D)21/20

Q124·PhysicsSingle correctJEE Main 2019

A heavy ball of mass M is suspended from the ceiling of car by a light string of mass m (m << M). When the car is at rest, the speed of transverse waves in the string is 60 ms

^{-1}

. When the car has acceleration a, the wave-speed increases to 60.5 ms

^{-1}

. The value of a, in terms of gravitational acceleration g is closest to:

(A) $\frac{g}{30}$
(B) $\frac{g}{5}$
(C) $\frac{g}{10}$
(D) $\frac{g}{20}$

Q125·PhysicsSingle correctJEE Main 2019

A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to:

(A)666 Hz
(B)753 Hz
(C)500 Hz
(D)333 Hz

Q126·PhysicsNumericalJEE Advanced 2018

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed

1.0\ ms^{-1}

and the man behind walks at a speed

2.0\ ms^{-1}

. A third man is standing at a height

12\ m

above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency

1430\ Hz

. The speed of sound in air is

330\ ms^{-1}

. At the instant, when the moving men are

10\ m

apart, the stationary man is equidistant from them. The frequency of beats in

Hz

, heard by the stationary man at this instant, is __________.

Q127·PhysicsMultiple correctJEE Advanced 2018

In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true?

(A)The speed of sound determined from this experiment is 332 ms $^{-1}$
(B)The end correction in this experiment is 0.9 cm
(C)The wavelength of the sound wave is 66.4 cm
(D)The resonance at 50.7 cm corresponds to the fundamental harmonic

Q128·PhysicsIntegerJEE Advanced 2017

A stationary source emits sound of frequency

f_{0}

= 492 Hz. The sound is reflected by a large car approaching the source with a speed of 2

ms^{-1}

. The reflected signal is received by the soruce and superposed with the original. What will be the beat frequency of the resulting signal in Hz? (Given that the speed of sound in air is 330

ms^{-1}

and the car reflects the sound at the frequency it has received).

Q129·PhysicsMultiple correctJEE Advanced 2017

A block M hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at O. A transverse wave pulse (Pulse 1) of wavelength

\lambda_{0}

is produced at point O on the rope. The pulse takes time

T_{OA}

to reach point A. If the wave pulse of wavelength

\lambda_{0}

is produced at point A (Pulse 2) without disturbing the position of M it takes time

T_{AO}

to reach point O. Which of the following options is/are correct?

(A)The time $T_{AO} = T_{OA}$
(B)The velocities of the two pulses (Pulse 1 and Pulse 2) are the same at the midpoint of rope.
(C)The wavelength of Pulse 1 becomes longer when it reaches point A.
(D)The velocity of any pulse along the rope is independent of its frequency and wavelength.

Q130·PhysicsMultiple correctJEE Advanced 2016

Two loudspeakers M and N are located 20 m apart and emit sound at frequencies 118 Hz and 121 Hz, respectively. A car is initially at a point P, 1800 m away from the midpoint Q of the line MN and moves towards Q constantly at 60 km/hr along the perpendicular bisector of MN. It crosses Q and eventually reaches a point R, 1800 m away from Q. Let

\nu(t)

represent the beat frequency measured by a person sitting in the car at time t. Let

\nu_P

,

\nu_Q

and

\nu_R

be the beat frequencies measured at locations P, Q and R, respectively. The speed of sound in air is

330\ \text{m s}^{-1}

. Which of the following statement(s) is(are) true regarding the sound heard by the person?

(A) $\nu_P + \nu_R = 2\nu_Q$
(B)The rate of change in beat frequency is maximum when the car passes through Q
(C)The plot below represents schematically the variation of beat frequency with time [first plot]
(D)The plot below represents schematically the variation of beat frequency with time [second plot]

Q131·PhysicsIntegerJEE Advanced 2015

Four harmonic waves of equal frequencies and equal intensities

I_{0}

have phase angles 0,

\pi/3

,

2\pi/3

and

\pi

. When they are superposed, the intensity of the resulting wave is

nI_{0}

. The value of n is

Q132·PhysicsMultiple correctJEE Advanced 2014

One end of a taut string of length

3 \text{ m}

along the

x

axis is fixed at

x = 0

. The speed of the waves in the string is

100 \text{ ms}^{-1}

. The other end of the string is vibrating in the

y

direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is (are)

(A) $y(t) = A \sin \frac{\pi x}{6} \cos \frac{50\pi t}{3}$
(B) $y(t) = A \sin \frac{\pi x}{3} \cos \frac{100\pi t}{3}$
(C) $y(t) = A \sin \frac{5\pi x}{6} \cos \frac{250\pi t}{3}$
(D) $y(t) = A \sin \frac{5\pi x}{2} \cos 250\pi t$

Q133·PhysicsMultiple correctJEE Advanced 2014

A student is performing an experiment using a resonance column and a tuning fork of frequency

244 \text{ s}^{-1}

. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is

(0.350 \pm 0.005) \text{ m}

, the gas in the tube is (Useful information:

\sqrt{167RT} = 640 \text{ J}^{1/2} \text{mole}^{-1/2}

;

\sqrt{140RT} = 590 \text{ J}^{1/2} \text{mole}^{-1/2}

. The molar masses

M

in grams are given in the options. Take the values of

\sqrt{\frac{10}{M}}

for each gas as given there.)

(A)Neon $\left(M = 20, \sqrt{\frac{10}{20}} = \frac{7}{10}\right)$
(B)Nitrogen $\left(M = 28, \sqrt{\frac{10}{28}} = \frac{3}{5}\right)$
(C)Oxygen $\left(M = 32, \sqrt{\frac{10}{32}} = \frac{9}{16}\right)$
(D)Argon $\left(M = 36, \sqrt{\frac{10}{36}} = \frac{17}{32}\right)$

Q134·PhysicsMultiple correctJEE Advanced 2013

Two vehicles, each moving with speed

u

on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity

w

. One of these vehicles blows a whistle of frequency

f_{1}

. An observer in the other vehicle hears the frequency of the whistle to be

f_{2}

. The speed of sound in still air is

V

. The correct statement(s) is (are)

(A)If the wind blows from the observer to the source, $f_{2} > f_{1}$ .
(B)If the wind blows from the source to the observer, $f_{2} > f_{1}$ .
(C)If the wind blows from observer to the source, $f_{2} < f_{1}$ .
(D)If the wind blows from the source to the observer $f_{2} < f_{1}$ .

Q135·PhysicsMultiple correctJEE Advanced 2013

A horizontal stretched string fixed at two ends, is vibrating in its fifth harmonic according to the equation

y(x, t) = 0.01 \sin[(62.8 \text{ m}^{-1})x]\cos[(628 \text{ s}^{-1})t]

m. Assuming

\pi = 3.14

, the correct statement(s) is (are)

(A)The number of nodes is 5.
(B)the length of the string is 0.25 m.
(C)The maximum displacement of the midpoint of the string, from its equilibrium position is 0.01 m.
(D)The fundamental frequency is 100 Hz.

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