Source and Listener Moving in Different Lines

Q. The transverse displacement of a string fixed at both ends is given by
$y=0.06sin\left(\frac{2\pi x}{3}\right)cos\left(120\pi t\right)$
where x and y are in metres and t is in seconds. The length of the string is 1.5 m and its mass is $3.0\times {10}^{-2}kg$. What is the tension in the string?

1. 648 N
2. 724 N
3. 832 N
4. 980 N

Q. A stationary observer receives a sound from a sound of frequency $v_0$ moving with a constant velocity $v_s=30m/s.$ The apparent frequency varies with time as shown in figure. Velocity of sound v = 300 m/s. Then which of the following is incorrect?

1. The minimum value of apparent frequency is 889 Hz.
2. The natural frequency of source is 1000 Hz.
3. The frequency-time curve corresponds to a source moving at an angle to the stationary observer.
4. The maximum value of apparent frequency is 1111 Hz.

Q. Source and observer start moving simultaneously along x and y-axis, respectively. The speed of source is twice the speed of observer, V₀. If the ratio of observed frequency to the frequency of the source is 0.75, find the velocity of sound.

1. $\frac{11}{\sqrt{5}}{V}_0$
2. $\frac{17}{\sqrt{5}}{V}_0$
3. $\frac{16}{\sqrt{5}}{V}_0$
4. $\frac{19}{\sqrt{5}}{V}_0$

Q.

A boy riding on his bike is going towards east at a speed of $4\sqrt{2}m{s}^{-1}$. At a certain point he produces a sound pulse of frequency 1650 Hz that travels in air at a speed of 334$m{s}^{-1}$. A second boy stands on the ground 45${}^{\circ }C$ south of east from him. Find the frequency of the pulse as received by the second boy.

1. 1670
2. 1640
3. 1650
4. None of these

Q. Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of 72 km/h and 36 km/h. If second car blows horn of frequency 280 Hz, then the frequency of horn heard by the driver of first car when the line joining the cars makes angle of ${45}^{\circ }$ with the roads, will be (velocity of sound is 330 m/s)

1. 321 Hz
2. 298 Hz
3. 289 Hz
4. 280 Hz

Q. A stationary observer receives a sound from a sound of frequency $v_0$ moving with a constant velocity $v_s=30m/s.$ The apparent frequency varies with time as shown in figure. Velocity of sound v = 300 m/s. Then which of the following is incorrect?

1. The minimum value of apparent frequency is 889 Hz.
2. The natural frequency of source is 1000 Hz.
3. The frequency-time curve corresponds to a source moving at an angle to the stationary observer.
4. The maximum value of apparent frequency is 1111 Hz.

Q. Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of 72 km/h and 36 km/h. If second car blows horn of frequency 280 Hz, then the frequency of horn heard by the driver of first car when the line joining the cars makes angle of ${45}^{\circ }$ with the roads, will be (velocity of sound is 330 m/s)

1. 321 Hz
2. 298 Hz
3. 289 Hz
4. 280 Hz

Q. A train is moving in an elliptical orbit in anticlockwise sense with a speed of 110 m/s. Guard is also moving in the given direction with same speed as that of train. The ratio of the length of major and minor axes is $\frac{4}{3}.$ Driver blows a whistle of 1900 Hz at P, which is received by guard at S. The frequency received by guard is (velocity of sound v = 330 m/s)

1. 1900 Hz
2. 1800 Hz
3. 2000 Hz
4. 1500 Hz