An observer is riding on a bicycle and moving towards a hill at...

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

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

Correct answer

Step-by-step solution

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, ${f}_{beat} = 650 - 630 = 20Hz$

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