An engine moving away from a vertical cliff blows a horn at a frequency $f$. Its speed is $0.5 \%$ of the speed of sound in air. The frequency of the reflected sound received at the engine is ............ $f$
KVPY 2013, Advanced
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(a)
Frequency of sound received at cliff is let $f_1$.
By Doppler's formula, we have
$f_1 =\left(\frac{v}{v-v_s}\right) \cdot f$
$=\frac{v}{v-0.5 v} f=2 f \quad\left[\therefore v_s=0.5 \,v\right]$
Now, reflected sound is observed on a moving engine.
Let observed frequency is $f_2$, then
$f_2=\left(\frac{v-v_0}{v}\right) f_1=\frac{1}{2} f_1=\frac{1}{2} \times 2 f$
$\therefore \quad f_2 \approx 0.990 f$
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