Two sources of sound $$S1$$ and $$S2$$ are at some distance apart. A person is at some point between $$S1$$ and $$S2$$ on the line joining them. Each of the sources emits sound with frequency $$f0$$. The source $$S1$$ starts moving away from the person with velocity vn and the source $$S2$$ starts moving towards the listener with velocityvn. If velocity of sound in air is V, find the beat frequency heard by the person.

Question

Two sources of sound $$S1$$   and   $$S2$$ are at some distance apart. A person is at some point between $$S1$$   and   $$S2$$  on the line joining them. Each of the sources emits sound with frequency  $$f0$$. The source  $$S1$$ starts moving away from the person with velocity vn  and the source  $$S2$$ starts moving towards the listener with velocityvn.  If velocity of sound in air is V, find the beat frequency heard by the person.

Infinity Learn · Accepted Answer

$$f1$$ $$=$$ Apparent frequency heard by the person due to the sound emitted by $$S1=f01+v/nv$$  $$=$$  $$nf0n+1f2$$  $$=$$ Apparent frequency heard by the person due to the sound emitted by  $$S2=f01-v/nv$$  $$=$$  $$nf0n$$−$$1$$∴$$fb=$$ Beat frequency $$=$$ $$f2$$−$$f1=$$ $$nf0n$$−$$1$$−$$nf0n+1=2nf0n2$$−$$1$$

Detailed Solution

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