Question 1: Palette 1/107

JEE Mains 2026 MCQ

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

3

B

2

C

4

D

1

Question 2: Palette 2/107

JEE Mains 2026 MCQ

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 64 times

B

decrease by 4 times

C

decrease by 8 times

D

increase by 8 times

Question 3: Palette 3/107

JEE Mains 2026 MCQ

In an open organ pipe $\nu_3$ and $\nu_6$ are $3^{\text {rd }}$ and $6^{\text {th }}$ harmonic frequencies, respectively. If $\nu_6-\nu_3=2200 \mathrm{~Hz}$ then length of the pipe is $\_\_\_\_$ mm .

(Take velocity of sound in air is $330 \mathrm{~m} / \mathrm{s}$.)

A

200

B

225

C

275

D

250

Question 4: Palette 4/107

JEE Mains 2026 MCQ

Two strings $(A, B)$ having linear densities $\mu_A=2 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$ and, $\mu_B=4 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$ and lengths $L_A=2.5 \mathrm{~m}$ and $L_B=1.5 \mathrm{~m}$ 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

1.90

B

1.18

C

1.08

D

1.67

Question 5: Palette 5/107

JEE Mains 2026 MCQ

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

Question 6: Palette 6/107

JEE Mains 2025 MCQ

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 $y_2(x, t) = 2 \sin (kx - \omega t + \frac{2\pi}{3})$, are:

(Take the angular frequency of initial waves same as $\omega$)

A

$\left[\sqrt{3}, \frac{\pi}{6}\right]$

B

$\left[2\sqrt{3}, \frac{\pi}{6}\right]$

C

$\left[6, \frac{2\pi}{3}\right]$

D

$\left[6, \frac{\pi}{3}\right]$

Question 7: Palette 7/107

JEE Mains 2025 MCQ

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 $\frac{v_2}{v_1}$ =

A

8

B

4

C

2

D

$\sqrt{2}$

Question 8: Palette 8/107

JEE Mains 2025 MCQ

The equation of a wave travelling on a string is y = sin[20πx + 10πt], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

A

10 cm

B

2.5 cm

C

20 cm

D

5.0 cm

Question 9: Palette 9/107

JEE Mains 2025 MCQ

Two harmonic waves moving in the same direction superimpose to form a wave $x=\mathrm{a} \cos (1.5 \mathrm{t}) \cos (50.5 \mathrm{t})$ where t is in seconds. Find the period with which they beat. (close to nearest integer)

A

1 s

B

4 s

C

2 s

D

6 s

Question 10: Palette 10/107

JEE Mains 2025 MCQ

Displacement of a wave is expressed as $x(t)=5 \cos \left(628 t+\frac{\pi}{2}\right) \mathrm{m}$. The wavelength of the wave when its velocity is $300 \mathrm{~m} / \mathrm{s}$ is :

$(\pi=3.14)$

A

0.33 m

B

0.5 m

C

3 m

D

5 m

Question 11: Palette 11/107

JEE Mains 2025 MCQ

In an experiment with a closed organ pipe, it is filled with water by $\left(\frac{1}{5}\right)$ th of its volume. The frequency of the fundamental note will change by

A

$20 \%$

B

$25 \%$

C

$-20 \%$

D

$-25 \%$

Question 12: Palette 12/107

JEE Mains 2025 MCQ

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

$370 \mathrm{~m} / \mathrm{s}$

B

$340 \mathrm{~m} / \mathrm{s}$

C

$335 \mathrm{~m} / \mathrm{s}$

D

$360 \mathrm{~m} / \mathrm{s}$

Question 13: Palette 13/107

JEE Mains 2025 MCQ

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 $\mathrm{t}=0 \mathrm{sec}$ and maximum displacement of the wave is 2 cm . Which equation correctly represents this wave?

A

$y=2 \cos (0.83 x-3.35 t) \mathrm{cm}$

B

$y=2 \sin (0.83 x-3.5 \mathrm{t}) \mathrm{cm}$

C

$y=2 \cos (0.13 x-0.5 t) \mathrm{cm}$

D

$y=2 \cos (3.35 x-0.83 \mathrm{t}) \mathrm{cm}$

Question 14: Palette 14/107

JEE Mains 2025 MCQ

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$

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 $\mathbf{A}$ and $\mathbf{R}$ are true and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$

B

$\mathbf{A}$ is false but $\mathbf{R}$ is true

C

$\mathbf{A}$ is true but $\mathbf{R}$ is false

D

Both $\mathbf{A}$ and $\mathbf{R}$ are true but $\mathbf{R}$ is NOT the correct explanation of $\mathbf{A}$

Question 15: Palette 15/107

JEE Mains 2025 MCQ

The equation of a transverse wave travelling along a string is $y(x, t)=4.0 \sin \left[20 \times 10^{-3} x+600 t\right] \mathrm{mm}$, where $x$ is in mm and $t$ is in second. The velocity of the wave is :

A

$-60 \mathrm{~m} / \mathrm{s}$

B

$+60 \mathrm{~m} / \mathrm{s}$

C

$+30 \mathrm{~m} / \mathrm{s}$

D

$-30 \mathrm{~m} / \mathrm{s}$

Question 16: Palette 16/107

JEE Mains 2025 MCQ

A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities $\rho_1$ and $\rho_2$, respectively. The frequency of $9^{\text {th }}$ harmonic of closed tube is identical with $4^{\text {th }}$ harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is $\rho_1: \rho_2=1: 16$, then the length of the open tube is :

A

$\frac{15}{7} \mathrm{~cm}$

B

$\frac{20}{9} \mathrm{~cm}$

C

$\frac{20}{7} \mathrm{~cm}$

D

$\frac{15}{9} \mathrm{~cm}$

Question 17: Palette 17/107

JEE Mains 2024 MCQ

A plane progressive wave is given by $y=2 \cos 2 \pi(330 \mathrm{t}-x) \mathrm{m}$. The frequency of the wave is :

A

660 Hz

B

340 Hz

C

330 Hz

D

165 Hz

Question 18: Palette 18/107

JEE Mains 2024 MCQ

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 $60 \mathrm{~cm}$, the length of the closed pipe will be:

A

15 cm

B

60 cm

C

45 cm

D

30 cm

Question 19: Palette 19/107

JEE Mains 2023 MCQ

A car P travelling at $20 \mathrm{~ms}^{-1}$ sounds its horn at a frequency of $400 \mathrm{~Hz}$. Another car $\mathrm{Q}$ is travelling behind the first car in the same direction with a velocity $40 \mathrm{~ms}^{-1}$. The frequency heard by the passenger of the car $\mathrm{Q}$ is approximately [Take, velocity of sound $=360 \mathrm{~ms}^{-1}$ ]

A

485 Hz

B

514 Hz

C

421 Hz

D

471 Hz

Question 20: Palette 20/107

JEE Mains 2023 MCQ

For a periodic motion represented by the equation

$y=\sin \omega \mathrm{t}+\cos \omega \mathrm{t}$

the amplitude of the motion is

A

1

B

$\sqrt2$

C

0.5

D

2

Question 21: Palette 21/107

JEE Mains 2023 MCQ

The engine of a train moving with speed $10 \mathrm{~ms}^{-1}$ towards a platform sounds a whistle at frequency $400 \mathrm{~Hz}$. The frequency heard by a passenger inside the train is: (neglect air speed. Speed of sound in air $=330 \mathrm{~ms}^{-1}$ )

A

200 Hz

B

412 Hz

C

400 Hz

D

388 Hz

Question 22: Palette 22/107

JEE Mains 2023 MCQ

A steel wire with mass per unit length $7.0 \times 10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$ is under tension of $70 \mathrm{~N}$. The speed of transverse waves in the wire will be:

A

$10 \mathrm{~m} / \mathrm{s}$

B

$50 \mathrm{~m} / \mathrm{s}$

C

$100 \mathrm{~m} / \mathrm{s}$

D

$200 \pi\mathrm{~m} / \mathrm{s}$

Question 23: Palette 23/107

JEE Mains 2023 MCQ

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

A

10 Hz

B

55 Hz

C

80 Hz

D

33 Hz

Question 24: Palette 24/107

JEE Mains 2023 MCQ

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

$\mathrm{4~ms^{-1}}$

B

$\mathrm{2~ms^{-1}}$

C

$\mathrm{8~ms^{-1}}$

D

$\mathrm{0.5~ms^{-1}}$

Question 25: Palette 25/107

JEE Mains 2022 MCQ

In the wave equation

$ y=0.5 \sin \frac{2 \pi}{\lambda}(400 \mathrm{t}-x) \,\mathrm{m} $

the velocity of the wave will be:

A

200 m/s

B

200$\sqrt2$ m/s

C

400 m/s

D

400$\sqrt2$ m/s

Question 26: Palette 26/107

JEE Mains 2022 MCQ

A transverse wave is represented by $y=2 \sin (\omega t-k x)\, \mathrm{cm}$. The value of wavelength (in $\mathrm{cm}$) for which the wave velocity becomes equal to the maximum particle velocity, will be :

A

4$\pi$

B

2$\pi$

C

$\pi$

D

2

Question 27: Palette 27/107

JEE Mains 2022 MCQ

Which of the following equations correctly represents a travelling wave having wavelength $\lambda$ = 4.0 cm, frequency v = 100 Hz and travelling in positive x-axis direction?

A

$y = A\sin [(0.50\,\pi \,c{m^{ - 1}})x - (100\,\pi \,{s^{ - 1}})t]$

B

$y = A\sin \,\,2\pi [(0.25\,\,c{m^{ - 1}})x - (50\,{s^{ - 1}})t]$

C

$y = A\sin \left[ {\left( {{{2\pi } \over 4}\,c{m^{ - 1}}} \right)x - \left( {{{2\pi } \over {100}}\,{s^{ - 1}}} \right)t} \right]$

D

$y = A\sin \,\pi [(0.5\,\,c{m^{ - 1}})x - (200\,\,{s^{ - 1}})t]$

Question 28: Palette 28/107

JEE Mains 2022 MCQ

A longitudinal wave is represented by $x = 10\sin 2\pi \left( {nt - {x \over \lambda }} \right)$ 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

${{5\pi } \over 2}$

Question 29: Palette 29/107

JEE Mains 2022 MCQ

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

282.8 ms^$-$1

B

175.5 ms^$-$1

C

353.6 ms^$-$1

D

707.2 ms^$-$1

Question 30: Palette 30/107

JEE Mains 2022 MCQ

If a wave gets refracted into a denser medium, then which of the following is true?

A

wavelength, speed and frequency decreases.

B

wavelength increases, sped decreases and frequency remains constant.

C

wavelength and speed decreases but frequency remains constant.

D

wavelength, speed and frequency increases.

Question 31: Palette 31/107

JEE Mains 2022 MCQ

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%

Question 32: Palette 32/107

JEE Mains 2022 MCQ

The equations of two waves are given by :

y₁ = 5 sin 2$\pi$(x - vt) cm

y₂ = 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

Question 33: Palette 33/107

JEE Mains 2021 MCQ

The motion of a mass on a spring, with spring constant K is as shown in figure.


The equation of motion is given by
x(t) = A sin$\omega$t + B cos$\omega$t with $\omega$ = $\sqrt {{K \over m}} $

Suppose that at time t = 0, the position of mass is x(0) and velocity v(0), then its displacement can also be represented as x(t) = C cos($\omega$t $-$ $\phi$), where C and $\phi$ are :

A

$C = \sqrt {{{2v{{(0)}^2}} \over {{\omega ^2}}} + x{{(0)}^2}} ,\phi = {\tan ^{ - 1}}\left( {{{x(0)\omega } \over {2v(0)}}} \right)$

B

$C = \sqrt {{{v{{(0)}^2}} \over {{\omega ^2}}} + x{{(0)}^2}} ,\phi = {\tan ^{ - 1}}\left( {{{x(0)\omega } \over {v(0)}}} \right)$

C

$C = \sqrt {{{v{{(0)}^2}} \over {{\omega ^2}}} + x{{(0)}^2}} ,\phi = {\tan ^{ - 1}}\left( {{{v(0)} \over {x(0)\omega }}} \right)$

D

$C = \sqrt {{{2v{{(0)}^2}} \over {{\omega ^2}}} + x{{(0)}^2}} ,\phi = {\tan ^{ - 1}}\left( {{{v(0)} \over {x(0)\omega }}} \right)$

Question 34: Palette 34/107

JEE Mains 2021 MCQ

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 from through a total distance of 6 cm. What will be the mathematical expression of this travelling wave?

A

Y(x, t) = 0.03 [ sin 5.1x $-$ (0.2 $\times$ 10³)t ]

B

Y(x, t) = 0.03 [ sin 5.1x $-$ (1.5 $\times$ 10³)t ]

C

Y(x, t) = 0.06 [ sin 5.1x $-$ (1.5 $\times$ 10³)t ]

D

Y(x, t) = 0.06 [ sin 0.8x $-$ (0.5 $\times$ 10³)t ]

Question 35: Palette 35/107

JEE Mains 2021 MCQ

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

A

335 Hz

B

345 Hz

C

338 Hz

D

342 Hz

Question 36: Palette 36/107

JEE Mains 2021 MCQ

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

18.4 cm

C

16.6 cm

D

14.8 cm

Question 37: Palette 37/107

JEE Mains 2021 MCQ

Which of the following equations represents a travelling wave?

A

y = Ae^xcos($\omega$t $-$ $\theta$)

B

y = Ae^$-$x2(vt + $\theta$)

C

y = A sin (15x $-$ 2t)

D

y = A sinx cos$\omega$t

Question 38: Palette 38/107

JEE Mains 2020 MCQ

A sound source S is moving along a straight track with speed v, and is emitting, sound of frequency v₀ (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:
(t₀ represents the instant when the distance between the source and observer is minimum)

A

B

C

D

Question 39: Palette 39/107

JEE Mains 2020 MCQ

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

36 km/hr

B

54 km/hr

C

24 km/hr

D

18 km/hr

Question 40: Palette 40/107

JEE Mains 2020 MCQ

Assume that the displacement(s) of air is proportional to the pressure difference ($\Delta $p) created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air ($\rho $) and the frequency (f). If $\Delta $p ~ 10 Pa, v ~ 300 m/s, $\rho $ ~ 1 kg/m³ and f ~ 1000 Hz, then s will be of the order of (take the multiplicative constant to be 1) :

A

1 mm

B

${3 \over {100}}$ mm

C

10 mm

D

${1 \over {10}}$ mm

Question 41: Palette 41/107

JEE Mains 2020 MCQ

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

2200 Hz

B

3300 Hz

C

1100 Hz

D

550 Hz

Question 42: Palette 42/107

JEE Mains 2020 MCQ

The driver of a 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

91 kmh^–1

B

81 kmh^–1

C

61 kmh^–1

D

71 kmh^–1

Question 43: Palette 43/107

JEE Mains 2020 MCQ

For a transverse wave travelling 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 are :

A

1, 3, 5, .....

B

${1 \over 1},{1 \over 3},{1 \over 5},$ .....

C

1, 2, 3, .....

D

${1 \over 2},{1 \over 4},{1 \over 6},$

Question 44: Palette 44/107

JEE Mains 2020 MCQ

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 wavetrain of wavelength 6 cm is produced at the lower end of the rope. What is the wavelength of the wavetrain (in cm) when it reaches the top of the rope ?

A

12

B

3

C

9

D

6

Question 45: Palette 45/107

JEE Mains 2020 MCQ

Two identical strings X and Z made of same material have tension T_X and T_Z in them. If their fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio T_X/T_Z is

A

2.25

B

0.44

C

1.25

D

1.5

Question 46: Palette 46/107

JEE Mains 2020 MCQ

A wire of length L and mass per unit length 6.0 × 10^–3 kgm^–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

5.1 m

B

2.1 m

C

1.1 m

D

8.1 m

Question 47: Palette 47/107

JEE Mains 2020 MCQ

Three harmonic waves having equal frequency $\nu $ and same intensity ${I_0}$, have phase angles 0, ${\pi \over 4}$ and $ - {\pi \over 4}$ respectively. When they are superimposed the intensity of the resultant wave is close to :

A

5.8 I₀

B

3 I₀

C

0.2 I₀

D

I₀

Question 48: Palette 48/107

JEE Mains 2020 MCQ

A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × 10⁴ N. When the tension is changed to T, the velocity changed to v/2. The value of T is close to :

A

30.5 × 10⁴ N

B

2.50 × 10⁴ N

C

10.2 × 10² N

D

5.15 × 10³ N

Question 49: Palette 49/107

JEE Mains 2020 MCQ

A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears 2 beats/sec. The oscillation frequency of each tuning fork is v₀ = 1400 Hz and the velocity of sound in air is 350 m/s. The speed of each tuning fork is close to :

A

1 m/s

B

${1 \over 8}$ m/s

C

${1 \over 4}$ m/s

D

${1 \over 2}$ m/s

Question 50: Palette 50/107

JEE Mains 2020 MCQ

Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm²) is 90 ms^-1. If the Young's modulus of wire is 16 $ \times $ 10¹¹ Nm^-2, the extension of wire over its natural length is :

A

0.03 mm

B

0.04 mm

C

0.02 mm

D

0.01 mm

Question 51: Palette 51/107

JEE Mains 2019 MCQ

Two sources of sound S₁ and S₂ produce sound waves of same frequency 660 Hz. A listener is moving from source S₁ towards S₂ 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

10.0 m/s

B

5.5 m/s

C

15.0 m/s

D

2.5 m/s

Question 52: Palette 52/107

JEE Mains 2019 MCQ

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, l₁ = 30 cm and l₂ = 70 cm. Then, v is equal to -

A

338 ms^–1

B

384 ms^–1

C

379 ms^–1

D

332 ms^–1

Question 53: Palette 53/107

JEE Mains 2019 MCQ

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/m² ]

A

20 cm

B

10 cm

C

40 cm

D

30 cm

Question 54: Palette 54/107

JEE Mains 2019 MCQ

A progressive wave travelling along the positive x-direction is represented by y(x,t) = Asin(kx – $\omega $t + $\phi $). Its snapshot at t = 0 is given in the figure.
For this wave, the phase $\phi $ is :

A

${\pi \over 2}$

B

$\pi $

C

0

D

$ - {\pi \over 2}$

Question 55: Palette 55/107

JEE Mains 2019 MCQ

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 $\upsilon $. The value of $\upsilon $ is close to: (Speed of sound in water =1500 ms^–1)

A

507 Hz

B

502 Hz

C

499 Hz

D

504 Hz

Question 56: Palette 56/107

JEE Mains 2019 MCQ

A source of sound S is moving with a velocity of 50 m/s towards a stationary observer. The observer measures the frequency of the source 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

750 Hz

B

857 Hz

C

807 Hz

D

1143 Hz

Question 57: Palette 57/107

JEE Mains 2019 MCQ

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

A

B

C

D

Question 58: Palette 58/107

JEE Mains 2019 MCQ

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

12, 18

B

16, 14

C

12, 16

D

8, 18

Question 59: Palette 59/107

JEE Mains 2019 MCQ

A string 2.0 m long and fixed at its ends 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

180m/s, 80 Hz

B

180m/s, 120 Hz

C

320m/s, 120 Hz

D

320m/s, 80 Hz

Question 60: Palette 60/107

JEE Mains 2019 MCQ

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 in car B ?
(speed of sound in air = 340 ms^–1) :-

A

2300 Hz

B

2060 Hz

C

2250 Hz

D

2150 Hz

Question 61: Palette 61/107

JEE Mains 2019 MCQ

The pressure wave, P = 0.01 sin [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

15°C

C

4°C

D

11°C

Question 62: Palette 62/107

JEE Mains 2019 MCQ

A string is clamped 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(200pt). The length of the string is : (All quantities are in SI units.)

A

60 m

B

20 m

C

80 m

D

40 m

Question 63: Palette 63/107

JEE Mains 2019 MCQ

A wire of length 2L, is made by joining two wires A and B of same length 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

3 : 5

B

4 : 9

C

1 : 2

D

1 : 4

Question 64: Palette 64/107

JEE Mains 2019 MCQ

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

335 ms^–1

B

328 ms^–1

C

341 ms^–1

D

322 ms^–1

Question 65: Palette 65/107

JEE Mains 2019 MCQ

A travelling harmonic wave is represented by the equation y(x,t) = 10^–3sin (50t + 2x), where, x and y are in mater and t is in seconds. Which of the following is a correct statement about the wave ?

A

The wave is propagating along the positive x-axis with speed 100 ms^–1

B

The wave is propagating along the positive x-axis with speed 25 ms^–1

C

The wave is propagating along the negative x-axis with speed 25 ms^–1

D

The wave is propagating along the negative x-axis with speed 100 ms^–1

Question 66: Palette 66/107

JEE Mains 2019 MCQ

Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin(450 t – 9x) where distance and time are measured in SI units. The tension in the string is :

A

10 N

B

7.5 N

C

5 N

D

12.5 N

Question 67: Palette 67/107

JEE Mains 2019 MCQ

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

16.6 cm

B

10.0 cm

C

20.0 cm

D

33.3 cm

Question 68: Palette 68/107

JEE Mains 2019 MCQ

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 ƒ₁. If the speed of the train is reduced to 17 m/s, the frequency registered is ƒ₂. If speed of sound is 340 m/s, then the ratio ƒ₁/ƒ₂ is -

A

19/18

B

20/19

C

21/20

D

18/17

Question 69: Palette 69/107

JEE Mains 2019 MCQ

A musician using an open flute of length 50 cm producess second harmonic sound waves. A person runs towards the musician from another end of 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

Question 70: Palette 70/107

JEE Mains 2019 MCQ

A heavy ball of mass M is suspendeed from the ceiling of a 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

${g \over {30}}$

B

${g \over 5}$

C

${g \over 10}$

D

${g \over 20}$

Question 71: Palette 71/107

JEE Mains 2018 MCQ

The end correction of a resonance column is 1 cm. If the shortest length resonating with the tunning fork is 10 cm, the next resonating length should be :

A

28 cm

B

32 cm

C

36 cm

D

40 c

Question 72: Palette 72/107

JEE Mains 2018 MCQ

Two sitar strings, A and B, playing the note 'Dha' are slightly out of tune and produce beats of frequency 5 Hz. The tension of the string B s slightly increased and the beat frequency is found to decrease by 3Hz. If the frequency of A is 425 Hz, the original frequency of B is :

A

430 Hz

B

420 Hz

C

428 Hz

D

422 Hz

Question 73: Palette 73/107

JEE Mains 2018 MCQ

A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 $\times$ 10³ kg/m³ and its Young’s modulus is 9.27 $\times$ 10¹⁰ Pa. What will be the fundamental frequency of the longitudinal vibrations ?

A

7.5 kHz

B

5 kHz

C

2.5 kHz

D

10 kHz

Question 74: Palette 74/107

JEE Mains 2018 MCQ

5 beats / econd are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or 1 m. The frequency of the fork will be :

A

195 Hz

B

150 Hz

C

300 Hz

D

251 Hz

Question 75: Palette 75/107

JEE Mains 2018 MCQ

A tuning fork vibrates with frequency $256$ $Hz$ and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe ? (Speed of sound in air is $340\,m{s^{ - 1}}$)

A

$220$ $cm$

B

$190$ $cm$

C

$180$ $cm$

D

$200$ $cm$

Question 76: Palette 76/107

JEE Mains 2017 MCQ

A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by

y(x, t) = 0.5 sin $\left( {{{5\pi } \over 4}x} \right)\,$ cos(200 $\pi $t).

What is the speed of the travelling wave moving in the positive x direction ?

(x and t are in meter and second, respectively.)

A

160 m/s

B

90 m/s

C

180 m/s

D

120 m/s

Question 77: Palette 77/107

JEE Mains 2017 MCQ

In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r₁ and r₂ . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5×10⁻⁴ s, the difference in radii, $\left| {} \right.$r₁ $-$ r₂ $\left| {} \right.$ is best given by :

A

1 cm

B

0.05 cm

C

0.5 cm

D

0.01 cm

Question 78: Palette 78/107

JEE Mains 2017 MCQ

Two wires W₁ and W₂ have the same radius r and respective densities $\rho $₁ and $\rho $₂ such that ρ₂ = 4$\rho $₁ . They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept under tension T. The point O is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in W₁ to W₂ is :

A

1 : 1

B

1 : 2

C

1 : 3

D

4 : 1

Question 79: Palette 79/107

JEE Mains 2017 MCQ

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer? (speed of light = 3 ×10⁸ ms^–1)

A

15.3 GHz

B

10.1 GHz

C

12.1 GHz

D

17.3 GHz

Question 80: Palette 80/107

JEE Mains 2016 MCQ

A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall. An observer, towards whom the toy car is moving, is able to hear 5 beats per second. If the velocity of sound in air is 340 m/s, the frequency of the horn of the toy car is close to :

A

680 Hz

B

510 Hz

C

340 Hz

D

170 Hz

Question 81: Palette 81/107

JEE Mains 2016 MCQ

Two engines pass each other moving in opposite directions with uniform speed of 30 m/s. One of them is blowing a whistle of frequency 540 Hz. Calculate the frequency heard by driver of second engine before they pass each other. Speed of sound is 330 m/sec :

A

450 Hz

B

540 Hz

C

648 Hz

D

270 Hz

Question 82: Palette 82/107

JEE Mains 2016 MCQ

A uniform string of length $20$ $m$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the supports is :
(take ${\,\,g = 10m{s^{ - 2}}}$ )

A

$2\sqrt 2 s$

B

$2\pi \sqrt 2 s$

C

$2\pi \sqrt 2 s$

D

$2$ $s$

Question 83: Palette 83/107

JEE Mains 2016 MCQ

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now :

A

$2f$

B

$f$

C

${f \over 2}$

D

${3f \over 4}$

Question 84: Palette 84/107

JEE Mains 2015 MCQ

A train is moving on a straight track with speed $20\,m{s^{ - 1}}.$ It is blowing its whistle at the frequency of $1000$ $Hz$. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound $ = 320\,m{s^{ - 1}}$) close to :

A

$18\% $

B

$24\% $

C

$6\% $

D

$12\% $

Question 85: Palette 85/107

JEE Mains 2014 MCQ

A pipe of length $85$ $cm$ is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below $1250$ $Hz$. The velocity of sound in air is $340$ $m/s$.

A

$12$

B

$8$

C

$6$

D

$4$

Question 86: Palette 86/107

JEE Mains 2013 MCQ

A sonometer wire of length $1.5$ $m$ is made of steel. The tension in it produces an elastic strain of $1\% $. What is the fundamental frequency of steel if density and elasticity of steel are $7.7 \times {10^3}\,kg/{m^3}$ and $2.2 \times {10^{11}}\,N/{m^2}$ respectively ?

A

$188.5$ $Hz$

B

$178.2$ $Hz$

C

$200.5$ $Hz$

D

$770$ $Hz$

Question 87: Palette 87/107

JEE Mains 2012 MCQ

A cylindrical tube, open at both ends, has a fundamental frequency, $f,$ in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now :

A

$f$

B

$f/2$

C

$3/4$

D

$2f$

Question 88: Palette 88/107

JEE Mains 2011 MCQ

The transverse displacement $y(x, t)$ of a wave on a string is given by $y\left( {x,t} \right) = {e^{ - \left( {a{x^2} + b{t^2} + 2\sqrt {ab} \,xt} \right)}}.$ This represents $a:$

A

wave moving in $-x$ direction with speed $\sqrt {{b \over a}} $

B

standing wave of frequency $\sqrt b $

C

standing wave of frequency ${1 \over {\sqrt b }}$

D

wave moving in $+x$ direction speed $\sqrt {{a \over b}} $

Question 89: Palette 89/107

JEE Mains 2010 MCQ

The equation of a wave on a string of linear mass density $0.04\,\,kg\,{m^{ - 1}}$ is given by $$y = 0.02\left( m \right)\,\sin \left[ {2\pi \left( {{t \over {0.04\left( s \right)}} - {x \over {0.50\left( m \right)}}} \right)} \right].$$

The tension in the string is

A

$4.0N$

B

$12.5$ $N$

C

$0.5$ $N$

D

$6.25$ $N$

Question 90: Palette 90/107

JEE Mains 2009 MCQ

Three sound waves of equal amplitudes have frequencies $\left( {v - 1} \right),\,v,\,\left( {v + 1} \right).$ They superpose to give beats. The number of beats produced per second will be :

A

$3$

B

$2$

C

$1$

D

$4$

Question 91: Palette 91/107

JEE Mains 2009 MCQ

A motor cycle starts from rest and accelerates along a straight path at $2m/{s^2}.$ At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at $94\% $ of its value when the motor cycle was at rest? (Speed of sound $ = 330\,m{s^{ - 1}}$)

A

$98$ $m$

B

$147$ $m$

C

$196\,m$

D

$49$ $m$

Question 92: Palette 92/107

JEE Mains 2008 MCQ

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of $18$ $cm$ during winter. Repeating the same experiment during summer, she measures the column length to be $x$ $cm$ for the second resonance. Then

A

$18 > x$

B

$x > 54$

C

$54 > x > 36$

D

$36 > x > 18$

Question 93: Palette 93/107

JEE Mains 2008 MCQ

A wave travelling along the $x$-axis is described by the equation $y(x, t)=0.005$ $\cos \,\left( {\alpha \,x - \beta t} \right).$ If the wavelength and the time period of the wave are $0.08$ $m$ and $2.0s$, respectively, then $\alpha $ and $\beta $ in appropriate units are

A

$\alpha = 25.00\pi ,\,\beta = \pi $

B

$\alpha = {{0.08} \over \pi },\,\beta = {{2.0} \over \pi }$

C

$\alpha = {{0.04} \over \pi },\,\beta = {{1.0} \over \pi }$

D

$\alpha = 12.50\pi ,\,\beta = {\pi \over {2.0}}$

Question 94: Palette 94/107

JEE Mains 2007 MCQ

A sound absorber attenuates the sound level by $20$ $dB$. The intensity decreases by a factor of

A

$100$

B

$1000$

C

$10000$

D

$10$

Question 95: Palette 95/107

JEE Mains 2006 MCQ

A string is stretched between fixed points separated by $75.0$ $cm.$ It is observed to have resonant frequencies of $420$ $Hz$ and $315$ $Hz$. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is

A

$105$ $Hz$

B

$1.05$ $Hz$

C

$1050$ $Hz$

D

$10.5$ $Hz$

Question 96: Palette 96/107

JEE Mains 2006 MCQ

A whistle producing sound waves of frequencies $9500$ $Hz$ and above is approaching a stationary person with speed $v$ $m{s^{ - 1}}.$ The velocity of sound in air is $300\,m{s^{ - 1}}.$ If the person can hear frequencies upto a maximum of $10,000$ $HZ,$ the maximum value of $v$ upto which he can hear whistle is

A

$15\sqrt 2 \,\,m{s^{ - 1}}$

B

${{15} \over {\sqrt 2 }}\,m{s^{ - 1}}$

C

$15\,\,m{s^{ - 1}}$

D

$30\,\,m{s^{ - 1}}$

Question 97: Palette 97/107

JEE Mains 2005 MCQ

An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency ?

A

$0.5\% $

B

zero

C

$20\% $

D

$5\% $

Question 98: Palette 98/107

JEE Mains 2005 MCQ

When two tuning forks (fork $1$ and fork $2$) are sounded simultaneously, $4$ beats per second are heated. Now, some tape is attached on the prong of the fork $2.$ When the tuning forks are sounded again, $6$ beats per second are heard. If the frequency of fork $1$ is $200$ $Hz$, then what was the original frequency of fork $2$ ?

A

$202$ $Hz$

B

$200$ $Hz$

C

$204$ $Hz$

D

$196$ $Hz$

Question 99: Palette 99/107

JEE Mains 2004 MCQ

The displacement $y$ of a particle in a medium can be expressed as, $y = {10^{ - 6}}\,\sin $ $\left( {100t + 20x + {\pi \over 4}} \right)$ $m$ where $t$ is in second and $x$ in meter. The speed of the wave is

A

$20\,\,m/s$

B

$5\,m/s$

C

$2000\,m/s$

D

$5\,\pi \,m/s$

Question 100: Palette 100/107

JEE Mains 2003 MCQ

A tuning fork of known frequency $256$ $Hz$ makes $5$ beats per second with the vibrating string of a piano. The beat frequency decreases to $2$ beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

A

$256 + 2Hz$

B

$256 - 2Hz$

C

$256 - 5Hz$

D

$256 + 5Hz$

Question 101: Palette 101/107

JEE Mains 2003 MCQ

A metal wire of linear mass density of $9.8$ $g/m$ is stretched with a tension of $10$ $kg$-$wt$ between two rigid supports $1$ metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency $n.$ The frequency $n$ of the alternating source is

A

$50$ $Hz$

B

$100$ $Hz$

C

$200$ $Hz$

D

$25$ $Hz$

Question 102: Palette 102/107

JEE Mains 2003 MCQ

The displacement $y$ of a wave travelling in the $x$-direction is given by $$y = {10^{ - 4}}\,\sin \left( {600t - 2x + {\pi \over 3}} \right)\,\,metres$$
where $x$ is expressed in metres and $t$ in seconds. The speed of the wave - motion, in $m{s^{ - 1}}$, is

A

$300$

B

$600$

C

$1200$

D

$200$

Question 103: Palette 103/107

JEE Mains 2002 MCQ

length of a string tied to two rigid supports is $40$ $cm$. Maximum length (wavelength in $cm$) of a stationary wave produced on it is

A

$20$

B

$80$

C

$40$

D

$120$

Question 104: Palette 104/107

JEE Mains 2002 MCQ

A wave $y=a$ $\sin \left( {\omega t - kx} \right)$ on a string meets with another wave producing a node at $x=0.$ Then the equation of the unknown wave is

A

$y = a\,\sin \,\left( {\omega t + kx} \right)$

B

$y = - a\,\sin \,\left( {\omega t + kx} \right)$

C

$y = a\,\sin \,\left( {\omega t - kx} \right)$

D

$y = - a\,\sin \,\left( {\omega t - kx} \right)$

Question 105: Palette 105/107

JEE Mains 2002 MCQ

When temperature increases, the frequency of a tuning fork

A

increases

B

decreases

C

remains same

D

increases or decreases depending on the material

Question 106: Palette 106/107

JEE Mains 2002 MCQ

Tube $A$ has bolt ends open while tube $B$ has one end closed, otherwise they are identical. The ratio of fundamental frequency of tube $A$ and $B$ is

A

$1:2$

B

$1:4$

C

$2:1$

D

$4:1$

Question 107: Palette 107/107

JEE Mains 2002 MCQ

A tuning fork arrangement (pair) produces $4$ beats/sec with one fork of frequency $288$ $cps.$ A little wax is placed on the unknown fork and it then produces $2$ beats/sec. The frequency of the unknown fork is

A

$286$ $cps$

B

$292$ $cps$

C

$294$ $cps$

D

$288$ $cps$