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JEE Main

Explore popular questions from Oscillations and Waves for JEE Main. This collection covers Oscillations and Waves previous year JEE Main questions hand picked by experienced teachers.

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Oscillations and Waves

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Q 1. A simple harmonic motion (SHM) has an amplitude {tex} A {/tex} and time period {tex} T {/tex} . The time required by it to travel from {tex} x = A {/tex} to {tex} x = A / 2 {/tex} is

{tex} T / 6 {/tex}

B

{tex} T / 4 {/tex}

C

{tex} T / 3 {/tex}

D

{tex} T / 2 {/tex}

Explanation

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Q 2. Two SHMs are represented by the equations {tex} Y _ { 1 } = 10 {/tex} {tex} \sin \left( 3 \pi t + \frac { \pi } { 4 } \right) {/tex} and {tex} Y _ { 2 } = 5 ( \sin 3 \pi t + \sqrt { 3 } \cos 3 \pi t ) {/tex} Their amplitudes are in the ratio of

A

{tex} 2 : 1 {/tex}

B

{tex} 3 : 1 {/tex}

C

{tex} 1 : 3 {/tex}

{tex} 1 : 4 {/tex}

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Q 3. The periodic time of a mass suspended by a spring (force constant {tex} k ) {/tex} is {tex} T {/tex} . If the spring is cut in three equal pieces, the force constant of each part and the periodic time if the same mass is suspended from one piece are

A

{tex} k , T / \sqrt { 3 } {/tex}

B

{tex} 3 k , T {/tex}

C

{tex} 3 k , \sqrt { 3 } T {/tex}

{tex} 3 k , T / \sqrt { 3 } {/tex}

Explanation

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Q 4. A person measures the time period of a simple pendulum inside a stationary lift and finds it to be {tex} T . {/tex} If the lift starts accelerating upwards with an acceleration of {tex} \mathrm { g } / 3 , {/tex} the time period of the pendulum will be

A

{tex} \sqrt { 3 } T {/tex}

{tex} \frac { \sqrt { 3 } } { 2 } T {/tex}

C

{tex} T / \sqrt { 3 } {/tex}

D

{tex} T / 3 {/tex}

Explanation


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Q 5. The displacement {tex} x {/tex} (in centimeters) of an oscillating particle varies with time (in seconds as) {tex} x = 2 \cos \left( 0.5 \pi t + \frac { \pi } { 3 } \right) . {/tex} The magnitude of the maximum acceleration of the particle in {tex} \mathrm { cms } ^ { - 2 } {/tex} is

A

{tex} \frac { \pi } { 2 } {/tex}

B

{tex} \frac { \pi } { 4 } {/tex}

{tex} \frac { \pi ^ { 2 } } { 2 } {/tex}

D

{tex} \frac { \pi ^ { 2 } } { 4 } {/tex}

Explanation

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Q 6. The amplitude of a wave disturbance propagating in the positive {tex} y {/tex} -direction is given by {tex} y = \frac { 1 } { 1 + x ^ { 2 } } {/tex} at {tex} t = {/tex} 0 and {tex} y = \frac { 1 } { \left[ 1 + ( x - 1 ) ^ { 2 } \right] } {/tex} at {tex} t = 2 {/tex} second, where {tex} x {/tex} and {tex} y {/tex} are in {tex} m {/tex} . If the shape of the wave disturbance does not {tex} y {/tex} change during the propagation, what is the velocity of the wave?

A

1{tex} \mathrm { m } / \mathrm { s } {/tex}

B

1.5{tex} \mathrm { m } / \mathrm { s } {/tex}

0.5{tex} \mathrm { m } / \mathrm { s } {/tex}

D

2{tex} \mathrm { m } / \mathrm { s } {/tex}

Explanation

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Q 7. The two waves having intensities in the ratio {tex} 1 : 9 {/tex} produce interference. The ratio of the maximum to the minimum intensities is equal to

A

{tex} 10 : 8 {/tex}

B

{tex} 9 : 1 {/tex}

{tex} 4 : 1 {/tex}

D

{tex} 2 : 1 {/tex}

Explanation

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Q 8. A uniform cord has a mass of {tex} 0.3 \mathrm { kg } {/tex} and length of {tex} 6 \mathrm { m } . {/tex} (see Fig. {tex} 9.25 ) . {/tex} The speed of a pulse on this cord is {tex} \left( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right) {/tex}

20{tex} \mathrm { m } / \mathrm { s } {/tex}

B

10{tex} \mathrm { m } / \mathrm { s } {/tex}

C

40{tex} \mathrm { m } / \mathrm { s } {/tex}

D

5{tex} \mathrm { m } / \mathrm { s } {/tex}

Explanation

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Q 9. Figure 9.27 shows the circular motion of a particle. The radius of the circle, the period, sense of revolution, and the initial position are indicated in the Fig. 9.27. The SHM of the x-projection of the radius vector of the rotating particle P is

{tex} x ( t ) = B \sin \left( \frac { 2 \pi t } { 30 } \right) {/tex}

B

{tex} x ( t ) = B \cos \left( \frac { \pi t } { 15 } \right) {/tex}

C

{tex} x ( t ) = B \sin \left( \frac { \pi t } { 15 } + \frac { \pi } { 2 } \right) {/tex}

D

{tex} x ( t ) = B \cos \left( \frac { \pi t } { 15 } + \frac { \pi } { 2 } \right) {/tex}

Explanation



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Q 10. Two waves having the intensities in the ratio of {tex} 9 : 1 {/tex} produce interference. The ratio of maximum to minimum intensity is equal to

A

{tex} 10 : 8 {/tex}

B

{tex} 9 : 1 {/tex}

{tex} 4 : 1 {/tex}

D

{tex} 2 : 1 {/tex}

Explanation

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Q 11. A tuning fork of frequency 256 Hz is excited and held at the mouth of resonance column of frequency 254 Hz. Choose the correct statement;

A

2 beats per second will be heard

B

4 beats per second will be heard

C

1 beat per second will be heard

No beat will be heard

Explanation

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Q 12. The frequency of sound emitted from a source in water is 600{tex} \mathrm { Hz } {/tex} . If speed of sound in water is 1500{tex} \mathrm { m } / \mathrm { s } {/tex} and in air is 300{tex} \mathrm { m } / \mathrm { s } {/tex} , then the frequency of sound heard above the surface of water is

A

300{tex} \mathrm { Hz } {/tex}

B

750{tex} \mathrm { Hz } {/tex}

600{tex} \mathrm { Hz } {/tex}

D

1200{tex} \mathrm { Hz } {/tex}

Explanation

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Q 13. A string of mass {tex} m {/tex} and length {tex} L {/tex} is hung vertically from a ceiling, and a mass {tex} M {/tex} is attached at its lower end. A wave pulse is generated at the lower end. The velocity of the generated pulse as it moves up towards the ceiling will

A

remain constant.

increase.

C

decrease linearly.

D

decrease non-linearly.

Explanation

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Q 14. Two waves represented by {tex} y _ { 1 } = 10 \sin 2000 \pi t {/tex} {tex} y _ { 2 } = 20 \sin \left( 2000 \pi t + \frac { \pi } { 2 } \right) {/tex} are superimposed at any point at a particular instant. The amplitude of the resultant wave is

A

200

B

30

10{tex} \sqrt { 5 } {/tex}

D

10{tex} \sqrt { 3 } {/tex}

Explanation

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Q 15. The ratio of maximum to minimum intensity at a place due to superposition of two waves represented by {tex} y _ { 1 } = 3 \sin ( 200 t ) \mathrm { cm } {/tex} and {tex} y _ { 2 } = 4 \cos ( 208 t ) \mathrm { cm } {/tex} will be

A

{tex} 7 : 1 {/tex}

{tex} 49 : 1 {/tex}

C

{tex} 4 : 3 {/tex}

D

{tex} 16 : 9 {/tex}

Explanation

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Q 16. Two waves are represented by the following equations {tex} y _ { 1 } = 5 \sin 2 \pi ( 10 t - 0.1 x ) ; y _ { 2 } = 10 \sin 2 \pi ( 20 t - 0.2 x ) {/tex} Ratio of intensities {tex} I _ { 2 } / I _ { 1 } {/tex} will be

A

1

B

2

C

4

16

Explanation

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Q 17. The equation of a plane progressive wave is {tex} y = 0.09 \sin 8 \pi \left( t - \frac { x } { 20 } \right) {/tex} . When it is reflected at rigid support, its amplitude becomes two-third of its previous value. The equation of the reflected wave is

A

{tex} y = - 0.09 \sin 8 \pi \left( t - \frac { x } { 20 } \right) {/tex}

B

{tex} y = - 0.06 \sin 8 \pi \left( t - \frac { x } { 20 } \right) {/tex}

C

{tex} y = 0.06 \sin 8 \pi \left( t + \frac { x } { 20 } \right) {/tex}

{tex} y = - 0.06 \sin 8 \pi \left( t + \frac { x } { 20 } \right) {/tex}

Explanation

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Q 18. If the temperature is raised by 1{tex} \mathrm { K } {/tex} from 300{tex} \mathrm { K } {/tex} the percentage change in the speed of sound in a gaseous mixture is {tex} ( R = 8.31 \mathrm { J } / \mathrm { mole } - \mathrm { K } ) {/tex}

0.167{tex} \% {/tex}

B

2{tex} \% {/tex}

C

1{tex} \% {/tex}

D

0.334{tex} \% {/tex}

Explanation

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Q 19. A wave is represented by the equation: {tex} y = 0.1 \sin ( 100 \pi t - k x ) . {/tex} If wave velocity is {tex} 100 \mathrm { m } / \mathrm { s } , {/tex} its wave number is equal to

A

1{tex} \mathrm { m } ^ { - 1 } {/tex}

B

2{tex} m ^ { - 1 } {/tex}

{tex} \pi m ^ { - 1 } {/tex}

D

2{tex} \pi \mathrm { m } ^ { - 1 } {/tex}

Explanation

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Q 20. A wave {tex} y = a \sin ( \omega t - k x ) {/tex} on a string meets with another wave producing a node at {tex} x = 0 . {/tex} Then the equation of the unknown wave is

A

{tex} y = a \sin ( \omega t + k x ) {/tex}

{tex} y = - a \sin ( \omega t + k x ) {/tex}

C

{tex} y = a \sin ( \omega t - k x ) {/tex}

D

{tex} y = - a \sin ( \omega t - k x ) {/tex}

Explanation

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Q 21. Two particles {tex} A {/tex} and {tex} B {/tex} of equal masses are suspended from two massless springs of spring constants {tex} k _ { 1 } {/tex} and {tex} k _ { 2 } {/tex}, respectively. If the maximum velocities, during oscillations, are equal, the ratio of amplitudes of {tex} A {/tex} and {tex} B {/tex} is

A

{tex} \sqrt { k _ { 1 } / k _ { 2 } } {/tex}

B

{tex} k _ { 2 } / k _ { 1 } {/tex}

{tex} \sqrt { k _ { 2 } / k _ { 1 } } {/tex}

D

{tex} k _ { 1 } / k _ { 2 } {/tex}

Explanation





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Q 22. A cylindrical tube, open at both ends, has a fundamental frequency, {tex} f , {/tex} 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:

{tex} f {/tex}

B

{tex} f / 2 {/tex}

C

{tex} 3f / 4 {/tex}

D

{tex}2 f {/tex}

Explanation



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Q 23. A particle at the end of a spring executes simple harmonic motion with a period {tex} t _ { 1 } , {/tex} while the corresponding period for another spring is {tex} t _ { 2 } {/tex}. If the period of oscillation with the two springs in series is {tex} T , {/tex} then

A

{tex} T = t _ { 1 } + t _ { 2 } {/tex}

{tex} T ^ { 2 } = t _ { 1 } ^ { 2 } + t _ { 2 } ^ { 2 } {/tex}

C

{tex} T ^ { - 1 } = t _ { 1 } ^ { - 1 } + t _ { 2 } ^ { - 1 } {/tex}

D

{tex} T ^ { - 2 } = t _ { 1 } ^ { - 2 } + t _ { 2 } ^ { - 2 } {/tex}

Explanation





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Q 24. The total energy of a particle, executing simple harmonic motion is
{tex} x {/tex} is the displacement from the mean position.

A

{tex} \propto x {/tex}

B

{tex} \propto x ^ { 2 } {/tex}

independent of {tex} x {/tex}

D

{tex} \propto x ^ { 1 / 2 } {/tex}

Explanation



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Q 25. A point mass oscillates along the {tex} x {/tex} -axis according to the law
{tex} x = x _ { 0 } \cos ( \omega t - \pi / 4 ) {/tex}.
If the acceleration of the particle is written as {tex} a = A \cos ( \omega t + \delta ) , {/tex} then

{tex} A = x _ { 0 } \omega ^ { 2 } , \delta = 3 \pi / 4 {/tex}

B

{tex} A = x _ { 0 , } \delta = - \pi / 4 {/tex}

C

{tex} A = x _ { 0 } \omega ^ { 2 } , \delta = \pi / 4 {/tex}

D

{tex} A = x _ { 0 } \omega ^ { 2 } , \delta = - \pi / 4 {/tex}

Explanation