The difference between the apparent frequency of a source of sound as perceived by an observer during its approach and recession is $$2$$% of the natural frequency of the source. If the velocity of sound in air is $$300$$ $$m/$$$$sec$$, the velocity of the source is (It$$ is given that velocity of source

Question

The difference between the apparent frequency of a source of sound as perceived by an observer during its  approach and recession  is $$2$$% of the natural frequency of the source. If the velocity of sound in air is $$300$$ $$m/$$$$sec$$, the velocity of the source is (It$$ is given that velocity of source << velocity of $$sound)The$$ difference between the apparent frequency of a source of sound as perceived by an observer during its  approach and recession  is $$2$$% of the natural frequency of the source. If the velocity of sound in air is $$300$$ $$m/$$$$sec$$, the velocity of the source is $$(It$$ is given that velocity of source << velocity of $$sound)

Infinity Learn · Accepted Answer

When the source approaches the observer  Apparent frequency  n'$$=vv$$−vs.$$n=n11$$−$$vsv=$$  $$n1$$−vsv−$$1=n1+vsv(Neglecting$$ higher powers because vS << $$v)When$$ the source recedes the observed apparent frequency  n''$$=n1$$−vsvGiven n'−n''$$=2100n$$,  $$v=300$$ $$m/$$$$sec$$∴$$2100n=n1+vsv$$−$$n1$$−$$vsv=n2vsv$$⇒$$2100=2vsv$$⇒$$vs=v100=300100=3$$ $$m/$$$$sec$$

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