Listener and Source Moving

Q. Source of sound of frequency 256 Hz is moving rapidly towards a wall with a velocity of 5m/s. The speed of sound is 330 m/s. If the observer is between the wall and the source, then beats per second heard will be

1. 7.7 Hz
2. 3.9 Hz
3. Zero
4. 7.8 Hz

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

1. 
2. 
3. 
4. 

Q.

Two coherent source of light can be obtained by

1. Two different lamps

2. Two different lamps of different power

3. Two different lamps of same power

4. By dividing a wavefront

Q.

Coherent sources can be created by the division of

Q.

A source of sound emitting a note of frequency 200 Hz moves towards an observer with a velocity $v$ equal to the velocity of sound. If the observer also moves away from the source with the same velocity $v$, the apparent frequency heard by the observer is

1. 150 Hz

2. 200 Hz

3. 100 Hz

4. 50 Hz

Q. Figure shows the graph of acceleration of particle as a function of time. The maximum speed of the particle is (particle starts from rest)

1. $8m/s$
2. $16m/s$
3. $7m/s$
4. $4m/s$

Q.

A particle moves rectilinearly with a constant acceleration $1m/s^2$. Its speed after $10$ second is $5m/s$. The distance covered by the particle in this duration is

1. $25m$

2. $50m$

3. $30m$

4. $20m$

Q. A band playing music at frequency f is moving towards a wall at a speed $v_b$. A motorist is following the band with a speed $v_m$. If v is the speed of sound, the expression for the beat frequency heard by the motorist is

1. 
2. 
3. 
4. 

Q. An engine running at speed v/10 sounds a whistle of frequency 600 Hz. A passenger in a train coming from the opposite side at speed v/15 experiences this whistle to be of frequency f. If v is speed of sound in air and there is no wind, f is nearest to

1. 711 Hz
2. 510 Hz
   
3. 630 Hz
4. 580 Hz

Q. A particle is given velocity
$4m/s$ along the $y$-axis subjected to constant acceleration $10m/s^2$ at ${53}^{\circ }$ with the $x$-axis. The displacement of the particle along the coordinate axes after $3s$ is $(x,y)m$. Find $(y-x)$.

Q. A sound wave of frequency n travels horizontally to the right with speed c. It is reflected from a broad wall moving to the left with speed v. The number of beats heard by a stationary observer to the left of the wall is

1. 
2. 
3. 
4. zero

Q.

How do you obtain coherent sources?

Q.

The frequency of a whistle of an engine is 600 cycles/sec is moving with the speed of 30 m/sec towards an observer. The apparent frequency will be (velocity of sound = 330 m/s)

1. 600 cps

2. 660 cps

3. 990 cps

4. 330 cps

Q. A stationary sound source $‘S^{\prime }$ of frequency $334\text{Hz}$ and a stationary observer $‘O^{\prime }$ are placed near a reflecting surface moving away from the source with velocity $2\text{m/s}$ as shown in the figure. If the velocity of the sound waves in air is $V=330\text{m/s}$, the apparent frequency (in $\text{Hz}$) of the echo is

Q. A particle executes the motion described by

\(x(t)=x_0(1-e^{\gamma t})\); \(t\geq0, x_0>0\).

Where does the particle start and with what velocity?

Q. A particle is moving along the $x-$ axis with its coordinate with the time ${}^{\prime }{t}^{\prime }$ given be $x\left(t\right)=10+8t-3t^2$. Another particle is moving the $y-$ axis with its coordinate as a function of time given by $y\left(t\right)=5-8t^3$. At $t=1s$, the speed of the second particle as measured in the frame of the first particle is given as $\sqrt{v}$. Then $v$ (in $m/s)$ is

Q. A boy is walking away from a wall at a speed of 1.0 m/s in a direction at right angles to the wall. The boy blows a whistle steadily. An observer towards whom the boy is moving hears 4 beats/s. If the speed of sound is 340 m/s, the frequency of whistle is

1. 680 Hz
2. 840 Hz
3. 1000 Hz
4. 480 Hz

Q.

Statement I Average speed of a continuously moving particle can never decrease with time.

Statement II Distance travelled by a continuously moving particle is always increasing.

1. Statement I is True, Statement II is True; Statement II is a correct explanation for Statement I

2. Statement I is True, Statement II is True; Statement II is not a correct explanation for Statement I

3. Statement I is True, Statement II is False

4. Statement I is False, Statement II is True

Q. Position of a particle moving along $x-$ axis is given by $x=t-4$, where $x$ is in meter and $t$ in second. Time (in $s$) at which it crosses the origin is

Q. An open organ pipe has a fundamental frequency of $300Hz$. The first overtone of a closed organ pipe has the same frequency as the first overtone of open organ pipe. How long is each pipe?

1. $41.25cm$
2. $42.3cm$
3. $40.5cm$
4. $49.5cm$

Q. An isotropic stationary source is emitting waves of frequency n and wind is blowing due north. An observer A is on north of the source while observer B is on south the source. If both the observers are stationary, then

1. frequencies received by A and B cannot be calculated unless velocity of waves in still air and velocity of wind are known
2. frequency received by A equals to that received by B
3. frequency received by A is greater than n
4. frequency received by B is less than n

Q.

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

1. 242/252

2. 2

3. 11/6

4. 5/6

Q. A police car moving at 22 m/s chases a motorcyclist. The police man sounds his horn of frequency 176 Hz, while both of them move towards a stationary siren of frequency 165 Hz. Calculate the speed of motorcyclist if it is given that he does not hear any beat (speed of sound in air is 330 m/s)

1. 33 m/s
2. 22 m/s
3. 11 m/s
4. zero

Q.

A particle starts from rest and undergoes an acceleration as shown in figure. The velocity-time graph from figure will have a shape

1. diagram
2. diagram
3. diagram
4. diagram

Q.

A police car moving at 22 m/s, chases a motorcyclist. The police man sounds his horn at 176 Hz, while both of them move towards a stationary siren of frequency 165 Hz. Calculate the speed of the motorcycle, if it is given that he does not observe any beats.

1. 11 m/s

2. 33 m/s

3. Zero

4. 22 m/s

Q. A particle is moving in $x-y$ plane. The positive vector of the particle at time $t$ is $r=b(1-\cos \omega t)\hat{i}+b\sin \omega t\hat{j}$, where $b$ and $\omega$ are positive constants. The speed of the particle at instant $t=\frac{\pi }{3}$ is

1. $v=b\omega$
2. $v=b^2\omega$
3. $v=\sqrt{b\omega }$
4. None of these

Q. A particle is moving in $x-y$ plane. The positive vector of the particle at time $t$ is $r=b(1-\cos \omega t)\hat{i}+b\sin \omega t\hat{j}$, where $b$ and $\omega$ are positive constants. The distance of the particle at instant $t=\frac{\pi }{3}$ is

1. $2\pi b$
2. $3\pi b$
3. None of these
4. $\pi b$

Q. A particle moves along the positive branch of the curve $y=2x$ where $x=t^2,x$ and $y$ are measured in metre and $t$ in second. At $t=2s$, the velocity (in $m/s$) of the particle is:

1. $\hat{i}+2\hat{j}$

2. $2\hat{i}+4\hat{j}$
3. $4\hat{i}+2\hat{j}$
4. $4\hat{i}+8\hat{j}$

Q.

A particle moves along x-axis as $x=4(t-2)+a(t-2{)}^2$

Which of the following is true?

1. The acceleration of particle is $2a$

2. None of these

3. The initial velocity of particle is 4

4. The particle is at origin at $t=0$

Q.

Starting from rest, a particle is imparted a constant acceleration of 5 units. For this situation, mark out the correct statement(s).

1. Velocity-time graph is a straight line passing through origin and having slope of 5 units.

2. Position-time graph is not a straight line.

3. Position-time graph is a straight line.

4. Slope of position-time graph increases as the time increases.