Question 116 of 142

An observer is riding on a bicycle and moving towards a hill at $18km{h}^{-1}$. 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 $640Hz$ and velocity of the sound in air is $320m{s}^{-1}$, the beat frequency between the two sounds heard by observer will be _____ $Hz$.

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Answer: 20

Here, ${V}_{S}=0,{V}_{ob}=18\left(\dfrac{5}{18}\right)=5{ms}^{-1}$
Frequency, ${f}_{direct}=\left(\dfrac{320-5}{320}\right)640=630Hz$
${f}_{reflected}=\left(\dfrac{320+5}{320}\right)640=650Hz$
Thus, beat frequency, ${f}_{beat}=650-630=20Hz$