At what speed should a source of sound move so that stationary observer finds the apparent frequency equal to half of the original frequency [RPMT 1996]

\frac{v}{2}

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2 v

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\frac{v}{4}

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v

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Solution

The correct option is D $v$
Frequency is decreasing (becomes half), it means source is going away from the observes. In this case frequency observed by the observer is
$n^{'} = n (\frac{v}{v + v_{s}}) \Rightarrow \frac{n}{2} = n (\frac{v}{v + v_{s}}) \Rightarrow v_{s} = v$

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At what speed should a source of sound move so that stationary observer finds the apparent frequency equal to half of the original frequency [RPMT 1996]

The correct option is D vFrequency is decreasing (becomes half), it means source is going away from the observes. In this case frequency observed by the observer isn′=n(vv+vs)⇒n2=n(vv+vs)⇒vs=v

The correct option is D $v$
Frequency is decreasing (becomes half), it means source is going away from the observes. In this case frequency observed by the observer is
$n^{'} = n (\frac{v}{v + v_{s}}) \Rightarrow \frac{n}{2} = n (\frac{v}{v + v_{s}}) \Rightarrow v_{s} = v$