A source of sonic oscillations with frequency n $$=$$ $$1700$$ Hz and a receiver are located on the same normal to a wall. Both the source and receiver are stationary, and the wall recedes from the source with velocity u $$=$$ $$6.0$$ $$cm/s$$. Find the beat frequency (in$$ $$Hz) registered by the receiver. The velocity of sound is equal to v $$=$$ $$340$$ $$m/s$$.

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Infinity Learn · Accepted Answer

In this case the observer will notice two frequencies. One, direct through the source and second, through the reflection by moving wall.As both source and receiver are at rest the frequency of sound waves which directly reach to receiver, will be $$1700$$ Hz.Hence ndirect $$=1700Hz$$. The frequency of sound which wall will receive as a moving observer $$isn1=n0v$$−uv−$$0=n0v$$−uv                    …$$(i)The$$ wall now behaves as a moving source of frequency $$n1$$ which when received by receiver, the frequency observed is $$n2=n1v$$−$$0v$$−$$($$−$$u)=n1vv+u=n0v$$−$$uv+u$$                …$$(ii)=1700340$$−$$0.06340+0.06=1700$$×$$339.94340.06=1699.4HzThus$$, beat frequency received by detector is Δ$$n=1700$$−$$1699.4=0.6Hz$$

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