## Question

A train has just completed a U-curve in a track which is a semi-circle. The engine is at the forward end of the semicircular part of the track while the last carriage is at the rear end of the semicircular track. The driver blows a whistle of frequency 200 Hz. Velocity of sound is 340 m/s. Then the apparent frequency as observed by a passenger in the middle of the train, when the speed of the train is 30 m/s, is:

### Solution

200 Hz

The Doppler formula holds for non-collinear motion if *v _{s}* and

*v*are taken to be the resolved components along the line of sight. In this case, we have

_{0}

The apparent frequency *n’ *is given by:

#### SIMILAR QUESTIONS

A source of sound *S *is moving with a velocity 50 m/s towards a stationary observer. The observer measured the frequency of the source as 1000 Hz. What will be the apparent frequency of the source when it is moving away from the observer after crossing him? The velocity of the sound in the medium is 350 m/s.

Two factories are sounding their sirens at 800 Hz. A man goes from one factory to the other at a speed of 2 m/s. The velocity of the sound is 320 m/s. The number of beats heard by the person in one second will be:

Two trains, one coming towards and another going away from an observer both at 4 m/s produce a whistle simultaneously of frequency 300 Hz. Find the number of beats produced?

A radio wave of frequency 840 MHz is sent towards an aeroplane. The frequency of the radio echo is 2.8 kHz more than the original frequency. Then the velocity of aeroplane is:

A whistle emitting a sound of frequency 440 Hz is tied to a string of 1.5 m length and rotated with an angular velocity of 20 rad/s in the horizontal plane. Then the range of frequencies heard by an observer stationed at a large distance from the whistle will be:

(*v* = 330 m/s):

Two whistles A and B produce notes of frequencies 660 Hz and 596 Hz respectively. There is a listener at the midpoint of the line joining them. Both the whistle *B* and the listener start moving with speed 30 m/s away from whistle *A*. If speed of sound be 330 m/s, how many beats will be heard by the listener?

Two sources *A* and *B* are sounding notes of frequency 680 Hz. A listener moves from *A* to *B* with a constant velocity *u*. If the speed of sound is 340 m/s, what must be the value of *u* so that he hears 10 beats per sec?

A source of sound of frequency 256 Hz is moving towards a wall with a velocity of 5 m/s. Velocity of sound is 330 m/s. The number of beats per second heard by an observer standing between the source and the wall is nearly:

A source of sound of frequency 256 Hz is moving towards a wall with a velocity of 5 m/s. The velocity of sound is 330 m/s. The number of beats heard by an observer moving along with the sounding object is:

A mass m is suspended separately from two springs of constants *k*_{1} and*k*_{2}. Their time periods are found to be *T*_{1} and *T*_{2} respectively. If the same mass is suspended from the two springs connected in series, then the time period of the combination will be: