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Consider a source moving towards an observer at the speed of vs  = 0.95 v. Deduce the observed frequency if the original is 500 Hz. (Think what would happen if vs >v. Jet planes moving faster than sound are now so common). Here, v is the speed of sound.

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We are given that v = 500 Hz, vs = 0.95 v

Since the observer is at rest and the source is moving towards the observer, the apparent frequency

If vs > v,(v–vs ) is negative and as such v’ is negative which has no meaning. Thus, Doppler formula is applicable so long as the velocity of the source does not exceed the velocity of the wave. In case of jet planes which move with speed greater than the sound, a shock wave is formed whose wavefront is a cone with the plane at its apex. The semivertical angle of the cone is sin–1(v/vs ).

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