A bat emits a sound at a frequency of 30.0 kHz as it approaches a wall. The bat detects a beat frequency of 700 Hz. The speed of the bat is

Question

A bat emits a sound at a frequency of 30.0 kHz as it approaches a wall. The bat detects a beat frequency of 700 Hz. The speed of the bat is closest to

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Huyền Thanh 5 years 2021-07-31T06:58:12+00:00 1 Answers 39 views 0

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  1. RobertKer
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    2021-07-31T07:00:04+00:00
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    Answer:

    3.948m/s

    Explanation:

    To solve this we need to apply Doppler effect theory

    So

    To find the frequency received by insect will be gotten when the Source and observer both are moving in same direction which is given by

    f1 = f0 x (V – Vo)/(V – Vs)

    f0 = 30.0 kHz

    V = 344 m/s

    Vs will now be the speed of the bat and

    Vo will be the speed of the object which is = 0 m/s

    So substituting we have

    f1 = 30 x 10^3 x (344- 0)/(344- Vs)

    Next to find the frequency reflected by wall we use

    f2 = f1 x (V + Vs)/(V + Vo)

    So substituting the value of f1 calculated above we have

    f2 = 30 x 10^3 x (344 + Vs) x (344 – 0)/[(344 – Vs) x (344 + 0)]

    f2 = 30 x 10^3 x (344 + Vs)/(344- Vs)

    But the beat frequency detected by bat is 700 Hz,

    So we say

    f2 – f0 = 700 Hz

    30 x 10^3 x (344+ Vs)/(344 – Vs) – 30x 10^3 = 700

    (344 + Vs)/(344 – Vs) = 1 + 700/30000 = 1.023

    344 + Vs = 344 x 1.023 – Vs x 1.0233

    Vs = 344 x ( 1.023 – 1)/(1 + 1.023)

    So finally

    Vs = Speed of source that is the bat is = 3.949m/s

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