A whistle emitting a loud sound of frequency $540 \,Hz$ is whirled in a horizontal circle of radius $2 \,m$ and at a constant angular speed of $15 \,rad / s$. The speed of sound is $330 \,m / s$. The ratio of the highest to the lowest frequency heard by a listener standing at rest at a large distance from the centre of the circle is
KVPY 2014, Diffcult
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(c)
Given situation is as shown below.
Speed of approach of source
$=v_s=r \omega=30 \,ms ^{-1}$
Using formula for Doppler's effect,
Maximum frequency,
$f_{\max }=\left(\frac{v}{v-v_s}\right) \cdot f$
Minimum frequency,
$f_{\min }=\left(\frac{v}{v+v_s}\right) \cdot f$
So, ratio of
$\frac{f_{\max }}{f_{\min }}=\frac{v+v_s}{v-v_s}=\frac{330+30 }{330-30}$
$\Rightarrow f_{\max }=1.2$
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