# 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.

## Mathematics

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}

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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}

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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}

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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}

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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}

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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}

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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}

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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}

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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}

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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

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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}

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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.

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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}

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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}

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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

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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}

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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}

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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}

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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}

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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}

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Q 22. The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

A

First decrease and then increase to the original value

First increase and then decrease to the original value

C

Increase towards a saturation value

D

Remain unchanged

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Q 23. Tube {tex} A {/tex} has both ends open while tube {tex} B {/tex} has one end closed, otherwise they are identical. The ratio of fundamental, frequency of tube {tex} A {/tex} and {tex} B {/tex} is

A

{tex} 1 : 2 {/tex}

B

{tex} 1 : 4 {/tex}

{tex} 2 : 1 {/tex}

D

{tex} 4 : 1 {/tex}

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Q 24. A point mass oscillates along the {tex} x {/tex} -axis according to the {tex} \operatorname { law } x = x _ { 0 } \cos ( \omega t - \pi / 4 ) \cdot {/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}

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Q 25. 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

{tex}286 \mathrm { cps } {/tex}

{tex} 292\mathrm { cps } {/tex}

C

{tex}294 \mathrm { cps } {/tex}

D

{tex}288 \mathrm { cps } {/tex}

##### Explanation

Beat Frequency - wherein Where v1 and v2 are frequency of two wave differ slightly in value of frequency. The wax decreases the frequency of the unknown fork. The possible unknown frequencies are (288+4) cps and (288-4) cps Wax reduces 284 cps and so beats should increases. It is not given in the question. This frequency is ruled out. Wax reduced 292 cps and so beats should decrease. It is given that the beats decrease to 2 from 4.