Question 1 :
In Young's double slit experiment the two slits act as coherent source of equal amplitude A and <br>wavelength λ. In another experiment with the same set up the two slits are source of equal amplitude A and wave length λ, but are incoherent. The ratio of the intensity of light at the midpoint of the screen -<br>
Question 2 :
If the length of a simple pendulum is equal to the radius <em>R</em> of the earth, its time period will be
Question 4 :
The equation <em>y = a</em> sin{tex}\frac{2\pi}{\lambda}{/tex} (<em>vt – x</em>) is expression for
Question 5 :
A sound is produced by plucking a string in a musical instrument, then <br>
Question 6 :
In an interference experiment third bright is obtained on screen with light of 5000 Å. What should be the wavelength in order to obtain 4<sup>th</sup> bright at same point -<br>
Question 7 : Match the column I with column II.<br><table>
<tr><th>Column I</th> <th>Column II</th> </tr>
<tr><td>(A)Change in apparent frequency due to the relative motion between source and listener is</td> <td>(p)Beats</td> </tr>
<tr><td>(B)Intensity of sound varies with time in</td> <td>(q)Transvers wave</td> </tr>
<tr><td>(C)Sound waves inair are</td> <td>(r)Doppler's effect</td> </tr>
<tr><td>(D)Light waves are</td> <td>(s)Longitudinal wave</td> </tr>
</table>
Question 8 :
If a watch with a wound spring is taken on to the moon, it
Question 9 :
A closed organ pipe of length <em>L</em> is vibrating in its first overtone. There is a point <em>Q</em> inside the pipe at a distance 7<em>L</em>/9 from the open end. The ratio of pressure amplitude at <em>Q</em> to the maximum pressure amplitude in the pipe is
Question 10 :
Two waves traveling in opposite direction produce a standing wave. The individual wave functions are given by {tex}y_{1} = 4 sin(3x - 2t)cm{/tex} and {tex}y_{2} = 4sin(3x + 2t)cm{/tex}, {tex}x {/tex} and {tex}y{/tex} are in {tex}cm{/tex}. Now, select the correct statement:
Question 11 : The frequency and wavelength of the wave shown in figure are (wave speed = 320 m/s) <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c51c1da6d070c2abfaad"/>
Question 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
Question 13 :
The amplitude of a wave disturbance propagating in the positive x-direction is given by y =1/ (1 + x<sup>2</sup>) at time t = 0 and by y = 1/[1 + (x - 1)<sup>2</sup> at t = 2 seconds, where x and y are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of the wave is<br>
Question 14 :
A beam of light of wavelength 600 nm from a distant source falls on a single slit 1mm wide and the resulting diffraction pattern is observed on a screen 2m away. The distance between the first dark fringes on either side of central bright fringe is-<br>
Question 15 :
Two strings of copper are stretched to the same tension. If their cross-section area are in the ratio 1 : 4, then the respective wave velocities will be -<br>
Question 16 : Three masses 700 gm, 500 gm and 400 gm are suspended at the end of a spring as shown and are in equilibrium. When the 700 gm mass is removed, the system oscillates with a period of 3 seconds; when the 500 gm mass is also removed, it will oscillate with a period of <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c4591da6d070c2abfa60"/>
Question 17 :
A whistle giving out 450 Hz, approaches a stationary observer at a speed of 33 m/s. The frequency heard by the observer in Hz is (speed of sound = 330 m/s)
Question 18 :
Two masses {tex} m _ { 1 } {/tex} and {tex} m _ { 2 } {/tex} are suspended together by a massless spring of constant {tex} k {/tex}. When the masses are in equilibrium, {tex} m _ { 1 } {/tex} is removed without disturbing the system. Then the angular frequency of oscillation of {tex} m _ { 2 } {/tex} is
Question 19 :
Two identical wires are stretched by the same tension of 100{tex} \mathrm { N } {/tex} and each emits a note of frequency 200{tex} \mathrm { Hz } {/tex} . If tension in one wire is increased by 1{tex} \mathrm { N } {/tex} , the number of beats heard per second when the wires are plucked is
Question 20 :
The displacement of a particle from its mean position (in metre) is given by {tex} y = 0.2 \sin ( 10 \pi t + 1.5 \pi ) \cos ( 10 \pi + 1.5 \pi ) . {/tex} The motion of particle is
Question 21 :
The frequency of sound wave is n and its velocity is v if the frequency is increased to 4n the velocity of the wave will be<br>
Question 22 :
The displacement y of a particle in a medium can be expressed as,<br>{tex} y = 10 ^ { - 6 } \sin \left( 100 t + 20 x + \frac { \pi } { 4 } \right) m {/tex} where {tex} t {/tex} is in second and {tex} x {/tex} in meter. The speed of the wave is<br>
Question 24 :
Beats are produced with the help of two sound waves on amplitude 3 and 5 units. The ratio of maximum to minimum intensity in the beats is<br>
Question 25 :
A clock which keeps correct time at {tex} 20 ^ { \circ } \mathrm { C } , {/tex} is subjected to {tex} 40 ^ { \circ } \mathrm { C } . {/tex} If coefficient of linear expansion of the pendulum is {tex} 12 \times 10 ^ { - 6 } / ^ { \circ } \mathrm { C } {/tex}. How much will it gain or loose in time
Question 26 : A wave is represented by the equation <br>y = 7 sin <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e7847c6a6b42b703af26b5b' height='41' width='109' >x is in metres and t is in seconds. The speed of the wave is -<br>
Question 28 :
P and Q are two wires whose fundamental frequencies are 256 Hz and 382 Hz respectively. How many beats in two seconds will be heard by the third harmonic of A and second harmonic of B?<br>
Question 29 :
In Young's double slit experiment, λ is the wavelength of light used, d is the separation between the two slits and D is the distance of the screen from the slits. The fringe width would remain unchanged if _<br>
Question 30 :
Any periodic function can be expressed as a superposition of sine and cosine functions of different time periods with suitable coefficients. Which of the following mathematicians proved this result?
Question 31 : If x = a sin <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e7847c7135d6370e9dbfa3e' height='41' width='53' > and x′ = a cosωt, then what is the phase difference between the two waves ?<br>
Question 32 :
The scale of a spring balance reading from {tex}0{/tex} to {tex}10 k g {/tex} is {tex} 0.25\ { m } {/tex} long. A body suspended from the balance oscillates vertically with a period of {tex} \pi / 10 {/tex} second. The mass suspended is (neglect the mass of the spring)
Question 33 :
The equation of SHM of a particle is a + 4π<sup>2</sup>x = 0 where a is instantaneous linear acceleration at displacement x, the frequency of motion is -
Question 34 :
A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the 4<sup>th</sup> bright fringe of the unknown light. From this data, the wavelength of the unknown light is -<br>
Question 35 :
In young's experiment total number of maxima that can be obtained over screen with light of wavelength 5000Å and d = 15000Å<br>
Question 36 :
The displacement {tex} y {/tex} of a particle in a medium can be expressed as:<br>{tex} y = 10 ^ { - 6 } \sin ( 100 t + 20 x + \pi / 4 ) \mathrm { m } , {/tex} where {tex} t {/tex} is in second and {tex} x {/tex} in meter. The speed of the wave is
Question 37 : {tex}\mathrm {Assertion}\quad{/tex} : Consider motion for a mass spring system under gravity, motion of {tex} M {/tex} is not a simple harmonic motion unless Mg is negligibly small.<br>{tex}\mathrm {Reason}\quad{/tex} : For simple harmonic motion acceleration must be proportional to displacement and is directed towards the mean position<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5dc29b06ec8cf4127b936b4f">
Question 38 :
An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is {tex} 15\ { cm } / { sec } {/tex} and the period is {tex}628{/tex} milli-seconds. The amplitude of the motion in<br>centimeters is<br>
Question 39 :
A boat at anchor is rocked by waves whose crests are 100 m apart and velocity is 25 m/s. The boat bounces up once in every -<br>
Question 40 :
A simple pendulum consisting of a ball of mass {tex} m {/tex} tied to a thread of length {tex} l {/tex} is made to swing on a circular are of angle {tex} \theta {/tex} in a vertical plane. At the end of this are, another ball of mass {tex} m {/tex} is placed at rest. The momentum transferred to this ball at rest by the swinging<br>ball is<br>
Question 41 :
The Doppler effect can be observed for the following case (s)
Question 42 :
A particle is executing SHM with an amplitude of {tex} 4 \mathrm { cm } . {/tex} At the mean position, velocity of the particle is {tex}10 \mathrm { cm } / \mathrm { s } {/tex} . The distance of the particle from the mean position when its speed becomes {tex}5 \mathrm { cm } / \mathrm { s } {/tex} is
Question 43 :
The velocities of sound at the same temperature in two monoatomic gases of densities ρ<sub>1</sub> and ρ<sub>2</sub> and v<sub>1</sub> and v<sub>2</sub> respectively. If ρ<sub>1</sub>/ρ<sub>2</sub> = 4, then the value of v<sub>1</sub>/ v<sub> 2</sub> is -<br>
Question 44 :
A vibrating tuning fork generates a wave given by y = 0.1 sin π(0.1x - 2t), where x and y are in metre and t in second. The distance travelled by the wave while the fork completes 30 vibrations is -<br>
Question 45 : A string is tied at two rigid support. A pulse is generated on the string as shown in figure. Minimum time after which string will regain its shape : (Neglect the time during reflection) <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e7847a68ad4296d0cdf68b9' height='86' width='200' ><br>
Question 47 :
The time period of simple pendulum measured inside a stationary lift is found to be <em>T</em>. If the lift start accelerating upwards with an acceleration <em>g</em>/3, the time period of pendulum will be
Question 48 :
The intensity of sound after passing through a slab decreases by 20%. On passing through two such slabs, the intensity will decrease by
Question 49 :
In YDSE, we get 60 fringes in field of view for light of wavelength 4000 Å. If we use light of wavelength 6000 Å, the number of fringes obtained in the same field of view are<br>
Question 50 :
A beam of light of wavelength 600 nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2m away. The distance between the first dark fringes on either side of the central bright fringe is -<br>
Question 51 :
Speed of sound wave is <em>v</em>. If a reflector moves towards a stationary source emitting waves of frequency <em>f</em> with speed <em>u</em>, the frequency of reflected wave will be
Question 52 :
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
Question 53 :
A sound wave is passing through air column in the form of compression and rarefaction. In consecutive compressions and rarefactions,
Question 54 :
Radiation of wavelength 2 × 10<sup>-3</sup> m falls on a slit of width 4 × 10<sup>-3</sup> m. The angular spread of the central maximum will be -<br>
Question 55 :
There is a set of four tuning forks, one with the lowest frequency vibrating at 550 Hz. By using any two tuning forks at a time, the following beat frequencies are heard: 1,2,3, 5, 7, 8. The possible frequencies of the other three forks are:<br>
Question 56 :
A string is stretched along x-axis. Shape of string transferring wave at t = t<sub>1</sub> sec is given by y = e<sup>-2x</sup>. If wave velocity is 'v<sub>0</sub>' in negative x-direction, then equation of waves is -<br>
Question 57 :
A tuning fork of frequency {tex}340 \mathrm { Hz } {/tex} is vibrated just above a cylindrical tube of length {tex} 120 \mathrm { cm } . {/tex} Water is slowly poured in the tube. If the speed of sound is {tex}340 \mathrm { m } / \mathrm { s } , {/tex} then the minimum height of water required for resonance is
Question 58 : A source that is continuously emitting sound at constant frequency, starts moving away from the detector with initial speed 4 m/s, along the line joining them. The acceleration a of the source is opposite to velocity having value 1 m/ s<sup>2</sup>. If the motion starts at t = 0 s then frequency as recorded by the detector from t = 0 to t = 8s<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e78471aa6b42b703af26a3f' height='72' width='275' ><br>
Question 59 :
Two trains, one coming towards and another going away from an observer both at 4{tex} \mathrm { m } / \mathrm { s } {/tex} produce a whistle of simultaneously of frequency 300{tex} \mathrm { Hz } {/tex} . The number of of beats heard by observer will be (velocity of sound = 340{tex} \mathrm { m } / \mathrm { s } ) {/tex}
Question 60 :
Two longitudinal waves propagating in the <em>X</em> and <em>Y</em> directions superimpose. The wave equations are as below <em>ψ</em><sub>1</sub> = <em>A</em>cos(ωt − kx) and <em>ψ</em><sub>2</sub> = <em>A</em>cos(ωt − ky). Trajectory of the motion of a particle lying on the line {tex}y = x + \frac{(2n + 1)\lambda}{2}{/tex} will be
Question 62 :
The relation between acceleration and displacement of four particles are given below.
Question 63 : An open pipe of sufficient length is dipping in water with a speed v vertically. If at any instant l is the length of the tube above water then the rate at which fundamental frequency of pipe changes, is: <br>(speed of sound = c)<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e784892a6b42b703af26cbc' height='107' width='127' ><br>
Question 64 :
A stationary wave is set up on a string fixed at both ends. The distance between two consecutive nodes is 18{tex} \mathrm { cm } {/tex} at a particular mode of vibration and for the next higher mode of vibration in the same string the distance between two consecutive nodes is {tex} 16 \mathrm { cm } . {/tex} The length of string is
Question 65 :
A string of length {tex}l{/tex} is fixed at both ends. It is vibrating in its third overtone. Maximum amplitude of the particles on the string is {tex}A{/tex}. The amplitude of the particle at a distance {tex}l/3{/tex} from one end is
Question 66 :
For the stationary wave {tex} y = 4 \sin \left( \frac { \pi x } { 15 } \right) \cos ( 96 \pi t ) {/tex} {tex} ( x \text { and } y \text { are in } \mathrm { cm } \text { and } t \text { in second)}{/tex} the distance between a node and the next antinodes is
Question 67 :
Following are equations of four waves: <br> (i) {tex} y _ { 1 } = a \sin \omega \left( t - \frac { x } { v } \right) {/tex} <br> (ii) {tex} y _ { 2 } = a \sin \omega \left( t + \frac { x } { v } \right) {/tex} <br> (iii) {tex} z _ { 1 } = a \sin \omega \left( t - \frac { x } { v } \right) {/tex} <br> (iv) {tex} z _ { 2 } = a \cos \omega \left( t + \frac { x } { v } \right) {/tex} <br> Which of the following statement is correct?
Question 68 :
Four sources of sound each of sound level {tex}10 \mathrm { dB } {/tex} are sounded together; the resultant intensity level will be {tex} ( \log 2 = 0.3 ) {/tex}
Question 69 :
A mass {tex} M {/tex} attached to a spring oscillates with a period of {tex}2{/tex} seconds. If the mass is increased by {tex}2 \mathrm { kg } {/tex} the period increases by {tex}1{/tex} second. The initial mass {tex} M {/tex} will be
Question 70 :
Find the de Broglie wavelength of Earth. Mass of Earth is 6 × 10<sup>24</sup> kg. Mean orbital radius of Earth around Sun is 150 × 10<sup>6</sup> km<br>
Question 71 : <font>A string is tied at two rigid support. A pulse is generated on the string as shown in figure. Minimum time after which string will regain its shape : (Neglect the time during reflection) </font> </p> <p> <img style='object-fit:contain' align="bottom" height="86" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5fc0ef9475b85f121f5424e5" width="200"/> </p>
Question 72 :
<font>A sound wave of wavelength </font><font face="Symbol, serif"><font></font></font><font> travels towards the right horizontally with a velocity V. It strikes and reflects from a vertical plane surface, travelling at a speed v towards the left. The number of positive crests striking in a time interval of three seconds on the wall is</font></p>
Question 73 : <font>Two coherent light sources P and Q each of wavelength </font><font face="Symbol, serif"><font></font></font><font> are separated by a distance 3</font><font face="Symbol, serif"><font></font></font><font> as shown. The maximum number of minima formed on line AB which runs from _ </font><font face="Symbol, serif"><font></font></font><font> to + </font><font face="Symbol, serif"><font></font></font><font>is -</font></p> <p> <img style='object-fit:contain' align="bottom" height="131" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5fc0f04ce6377b2e815f5024" width="94"/> </p>
Question 74 :
<font>A closed organ pipe and an open organ pipe of same length produce four beats in their fundamental mode when sounded together. If length of the open organ pipe is increased, then the number of beats will -</font></p>
Question 75 : </font><font color="#000000"><font>Figure shows a sinusoidal wave at a given instant. </font></font><font>Which points are in phase?</font></p> <p align="center"> <img style='object-fit:contain' align="bottom" height="96" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5fc100053e65343a882864eb" width="195"/> </p>
Question 76 :
<font>If intensity of both slits is equal, then ratio of intensity at the centre of a bright fringe to intensity at a point on quarter of the distance between two fringes from the centre is -</font></p>
Question 77 :
</font><font color="#000000"><font>A sound wave is a passing through air column in the form of compressions and rarefactions. In consecutive compressions and rarefactions,</font></font></p>
Question 78 :
<font>Two strings of copper are stretched to the same tension. If their cross-section area are in the ratio 1 : 4, then the respective wave velocities will be -</font></p>
Question 79 : <font>What is the difference between PA and PB ?</font></p> <p> <img style='object-fit:contain' align="bottom" height="119" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5fc0f07ba00b633c04f3a1d4" width="153"/> </p>
Question 81 : <font color="#000000"><font>The speed of an electron having a wavelength of 10</font></font><font color="#000000"><sup><font>-10</font></sup></font><font color="#000000"><font> m is -</font></font></p> <p align="justify"> <font color="#000000">
Question 83 : <font>Which relation is giving the correct information for the shown tuning forks -</font></p> <p> <img style='object-fit:contain' align="bottom" height="168" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5fc0f0b2a89a512aab212729" width="75"/> <img style='object-fit:contain' align="bottom" height="178" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5fc0f0b3a89a512aab21272a" width="66"/> </p>
Question 84 :
<font>A progressive wave of frequency 500 Hz is travelling with a velocity of 360 m/s. How far apart are two points 60</font><sup><font>0</font></sup><font> out of phase ?</font></p>
Question 85 : <font color="#000000"><font>The wavelength of de Broglie waves associated with a particle at rest is -</font></font></p> <p align="justify"> <font color="#000000">
Question 86 :
<font>In YDSE, we get 60 fringes in field of view for light of wavelength 4000 Å. If we use light of wavelength 6000 Å, the number of fringes obtained in the same field of view are</font></p>
Question 87 :
Two trains {tex} ( A \text { and } B ) {/tex} are moving towards each other on two parallel tracks at the same speed with respect to the ground. The whistle of train {tex} A {/tex} blows. In which of the following cases, the frequency of the sound heard by a passenger on the other train {tex} B {/tex} will be greatest?
Question 88 : <font>Speed of sound wave in a gas is v</font><sub><font>1</font></sub><font> and rms speed of molecules of the gas at the same temperature is v</font><sub><font>2</font></sub><font>. Then -</font></p> <p align="justify"> <font color="#000000">
Question 89 :
<font>The amplitude of a wave disturbance propagating in the positive x-direction is given by y =1/ (1 + x</font><sup><font>2</font></sup><font>) at time t = 0 and by y = 1/[1 + (x - 1)</font><sup><font>2</font></sup><font> at t = 2 seconds, where x and y are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of the wave is</font></p>
Question 90 :
<font>Which of the following travelling wave will produce standing wave, with node at x = 0, when superimposed in y = Asin (</font><font face="Symbol, serif"><font></font></font><font>t - kx) -</font></p>
