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

## Chemistry

Oscillations and Waves

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Q 1. The period of oscillation of a simple pendulum of length {tex} L {/tex} suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination {tex} \alpha , {/tex} is given by

{tex} 2 \pi \sqrt { \frac { L } { g \cos \alpha } } {/tex}

B

{tex} 2 \pi \sqrt { \frac { L } { g \sin \alpha } } {/tex}

C

{tex} 2 \pi \sqrt { \frac { L } { g } } {/tex}

D

{tex} 2 \pi \sqrt { \frac { L } { g \tan \alpha } } {/tex}

##### Explanation

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Q 2. A particle executes simple harmonic motion between {tex} x = - A {/tex} and {tex} x = + A . {/tex} The time taken for it to go from 0 to {tex} A / 2 {/tex} is {tex} T _ { 1 } {/tex} and to go from {tex} A / 2 {/tex} to {tex} A {/tex} is {tex} T _ { 2 } {/tex}. Then

{tex} T _ { 1 } < T _ { 2 } {/tex}

B

{tex} T _ { 1 } > T _ { 2 } {/tex}

C

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

D

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

##### Explanation

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Q 3. For a particle executing {tex}SHM{/tex} the displacement {tex} x {/tex} is given by {tex} x = A {/tex} coswt. Identify the graph which represents the variation of potential energy {tex} ( P E ) {/tex} as a function of time {tex} t {/tex} and displacement {tex} x {/tex}

{tex} \mathrm I , \mathrm { III } {/tex}

B

{tex} \mathrm { I I } , \mathrm { I V } {/tex}

C

{tex} \mathrm { I I } , \mathrm { III } {/tex}

D

{tex} \mathrm { I } , \mathrm { IV } {/tex}

##### Explanation

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Q 4. A simple pendulum has time period {tex} T _ { 1 } {/tex}. The point of suspension is now moved upward according to the relation {tex} y = K t ^ { 2 } , \left( K = 1 \mathrm { m } / \mathrm { s } ^ { 2 } \right) {/tex} where {tex} y {/tex} is the vertical displacement. The time period now becomes {tex} T _ { 2 } . {/tex} The ratio of {tex} \frac { T _ { 1 } ^ { 2 } } { T _ { 2 } ^ { 2 } } {/tex} is {tex} \left( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right) {/tex}

A

{tex} 5 / 6 {/tex}

{tex} 6 / 5 {/tex}

C

{tex}1{/tex}

D

{tex} 4 / 5 {/tex}

##### Explanation

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Q 5. A uniform rod of length {tex} L {/tex} and mass {tex} M {/tex} is pivoted at the centre. Its two ends are attached to two springs of equal spring constants {tex} k . {/tex} The springs are fixed to rigid supports as shown in the
figure, and the rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle {tex} \theta {/tex} in one direction and released. The frequency of oscillation is

A

{tex} \frac { 1 } { 2 \pi } \sqrt { \frac { 2 k } { M } } {/tex}

B

{tex} \frac { 1 } { 2 \pi } \sqrt { \frac { k } { M } } {/tex}

{tex} \frac { 1 } { 2 \pi } \sqrt { \frac { 6 k } { M } } {/tex}

D

{tex} \frac { 1 } { 2 \pi } \sqrt { \frac { 24 k } { M } } {/tex}

##### Explanation

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Q 6. The mass {tex} M {/tex} shown in the figure oscillates in simple harmonic motion with amplitude {tex} A . {/tex} The amplitude of the point {tex} P {/tex} is

A

{tex}\frac{k_1 A}{k_2}{/tex}

B

{tex}\frac{k_2 A}{k_1}{/tex}

C

{tex}\frac{k_1 A}{k_1+k_2}{/tex}

{tex}\frac{k_2 A}{k_1+k_2}{/tex}

##### Explanation

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Q 7. A cylindrical tube open at both ends has a fundamental frequency {tex}f{/tex} in air. The tube is dipped vertically in the air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column in now

A

{tex} \frac { f } { 2 } {/tex}

B

{tex} \frac { 3 f } { 4 } {/tex}

{tex} f {/tex}

D

{tex}2f{/tex}

##### Explanation

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Q 8. Two monatomic ideal gases 1 and 2 of molecular masses {tex} m _ { 1 } {/tex} and {tex} m _ { 2 } {/tex} respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to that in gas 2 is given by

A

{tex} \sqrt { \frac { m _ { 1 } } { m _ { 2 } } } {/tex}

{tex} \sqrt { \frac { m _ { 2 } } { m _ { 1 } } } {/tex}

C

{tex} \frac { m _ { 1 } } { m _ { 2 } } {/tex}

D

{tex} \frac { m _ { 2 } } { m _ { 1 } } {/tex}

##### Explanation

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Q 9. A siren placed at a railway platform is emitting sound of frequency {tex} 5 \mathrm { kHz } {/tex}. A passenger sitting in a moving train {tex} A {/tex} records a frequency of {tex} 5.5 \mathrm { kHz } {/tex} while the train approaches the siren. During his return journey in a different train {tex} B {/tex} he records a frequency of {tex} 6.0 \mathrm { kHz } {/tex} while approaching the same siren. The ratio of the velocity of train {tex} B {/tex} to that train {tex} A {/tex} is

A

{tex} 242 / 252 {/tex}

{tex}2{/tex}

C

{tex} 5 / 6 {/tex}

D

{tex} 11 / 6 {/tex}

##### Explanation

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Q 10. A massless rod of length {tex} L {/tex} is suspended by two identical strings {tex} A B {/tex} and {tex} C D {/tex} of equal length. A block of mass {tex}{ m } {/tex} is suspended from point {tex} O {/tex} such that {tex} B O {/tex} is equal to {tex} x {/tex}. Further it is observed that the frequency of 1st harmonic in {tex} A B {/tex} is equal to 2nd harmonic frequency in {tex} C D . x {/tex} is

{tex} \frac { L } { 5 } {/tex}

B

{tex} \frac { 4 L } { 5 } {/tex}

C

{tex} \frac { 3 L } { 4 } {/tex}

D

{tex} \frac { L } { 4 } {/tex}

##### Explanation

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Q 11. A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of {tex} 10 \mathrm { cm } / \mathrm { s } {/tex}. The wavelength of the wave is {tex} 0.5 \mathrm { m } {/tex} and its amplitude is {tex} 10 \mathrm { cm } {/tex}. At a particular time {tex} \mathrm { t } {/tex}, the snap-shot of the wave is shown in figure. The velocity of point {tex} \mathrm { P } {/tex} when its displacement is {tex} 5 \mathrm { cm } {/tex} is -

{tex} \frac { \sqrt { 3 } \pi } { 50 } \hat { j } \mathrm { m } / \mathrm { s } {/tex}

B

{tex} - \frac { \sqrt { 3 } \pi } { 50 } \hat { j } \mathrm { m } / \mathrm { s } {/tex}

C

{tex} \frac { \sqrt { 3 } \pi } { 50 } \hat { \mathrm { i } } \mathrm { m } / \mathrm { s } {/tex}

D

{tex} - \frac { \sqrt { 3 } \pi } { 50 } \hat { i } m / s {/tex}

##### Explanation

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Q 12. A vibrating string of certain length {tex} \ell {/tex} under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length {tex} 75 \mathrm { cm } {/tex} inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency {tex}n{/tex}. Now when the tension of the string is slightly increased the number of beats reduces {tex}2{/tex} per second. Assuming the velocity of sound in air to be {tex} 340 \mathrm { m } / \mathrm { s } {/tex}, the frequency n of the tuning fork in {tex} \mathrm { Hz } {/tex} is

344

B

336

C

1173

D

109.3