How speed of train, which is moving higher than speed of sound(1000 m/s), can be calculated using doppler effect ? Take observer is producing sound (source) towards train & train is reflecting the sound back.

Asked by DEEPAK KOTHARI | 30th May, 2011, 11:48: PM

Expert Answer:

A change in the observed frequency of a wave, as of sound or light, occurring when the source and observer are in motion relative to each other, with the frequency increasing when the source and observer approach each other and decreasing when they move apart. The motion of the source causes a real shift in frequency of the wave, while the motion of the observer produces only an apparent shift in frequency. Also called Doppler shift.

If the source moving away from the observer is emitting waves through a medium with an actual frequency f0, then an observer stationary relative to the medium detects waves with a frequency f given by

where vs is positive if the source is moving away from the observer, and negative if the source is moving towards the observer.

A similar analysis for a moving observer and a stationary source yields the observed frequency (the receiver's velocity being represented as vr):

where the similar convention applies: vr is positive if the observer is moving towards the source, and negative if the observer is moving away from the source.

These can be generalized into a single equation with both the source and receiver moving.

With a relatively slow moving source, vs,r is small in comparison to v and the equation approximates to

where .

In other words, if the siren approached the observer directly, the pitch would remain constant (as vs, r is only the radial component) until the vehicle hit him, and then immediately jump to a new lower pitch. Because the vehicle passes by the observer, the radial velocity does not remain constant, but instead varies as a function of the angle between his line of sight and the siren's velocity:

where vs is the velocity of the object (source of waves) with respect to the medium, and ? is the angle between the object's forward velocity and the line of sight from the object to the observer.

Answered by  | 31st May, 2011, 02:12: AM

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