Question 102: Waves

Question

An observer is riding on a bicycle and moving towards a hill at $$18 \,\mathrm{kmh}^{-1}$$. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is $$640 \mathrm{~Hz}$$ and velocity of the sound in air is $$320 \mathrm{~m} / \mathrm{s}$$, the beat frequency between the two sounds heard by observer will be _____________ $$\mathrm{Hz}$$.

Accepted Answer

$${f_1} = {f_0}\left( {{{320 - 5} \over {320}}} \right) = 640\left( {{{315} \over {320}}} \right)$$
$$ = 630$$ Hz
$${f_3} = {f_0}$$ [No relative motion]
$${f_2} = {f_0}\left[ {{{320 + 5} \over {320}}} \right] = 640\left( {{{325} \over {320}}} \right)$$
$$ = 650$$
Beat frequency $$ = {f_2} - {f_1}$$
$$ = 650 - 630 = 20$$ Hz

Waves

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