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A source of sound of frequency 600 Hz moves at 30 m s^-1 directly towards a large smooth vertical wall, while a stationary observer stands behind the…

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A source of sound of frequency

600\ \mathrm{Hz}

moves at

30\ \mathrm{m\,s^{-1}}

directly towards a large smooth vertical wall, while a stationary observer stands behind the source on the line joining the source and the wall. The speed of sound is

330\ \mathrm{m\,s^{-1}}

. The number of beats per second heard by the observer is

A. $55$
B. $60$
C. $110$
D. $120$

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Answer: (C) $110$

The source moves away from the observer, so the direct sound has

f_1=\dfrac{600\times330}{330+30}=550\ \mathrm{Hz}

. The wall receives and reflects the sound as a stationary reflector of the frequency heard by it,

f_2=\dfrac{600\times330}{330-30}=660\ \mathrm{Hz}

, and the stationary observer hears

660\ \mathrm{Hz}

. Beat frequency

=660-550=110\ \mathrm{Hz}

. Recognising that the wall, not the observer, sees the Doppler-shifted frequency is the key step.

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