9702/Oct Nov/13/2017/Q25

A source of sound of frequency F at point Z is moving at a steady speed. The pattern of the
emitted wavefronts is shown.

Which row describes the frequencies of the sound heard by stationary observers at X and Y?

Solution:
Answer: C
Let v be the speed of sound in air. A source of sound has a frequency F and wavelength λ. The source moves towards an observer at a speed v_s.

The period of oscillation of the source of sound is T (= 1/F). In the time of one oscillation the source moves towards the observer X a distance v_sT. Hence the wavelength is shortened by this distance. The wavelength of the sound received by the observer is λ − v_sT.

Hence the frequency observed f_o = v / (λ - v_s T)

                                         = v / [(v/F)-(v_s / F) ]

                                         = (Fv/(v-v_s))

The source would move away from a stationary observer at position Y on the right-hand side. The observed wavelengths would lengthen.

For a source of sound moving away from an observer the observed frequency can be shown to be           f_o = Fv/(v + v_s)

*The frequency is increased when the source moves towards the observer and the frequency is decreased when the source moves away from the observer.

Reference: PYQ - Oct/Nov 2017 Paper 13 Q25