A physics professor demonstrates the Doppler effect by tying a 600 Hz sound generator to a 1.0-m-long rope and whirling it around her head i

Question

A physics professor demonstrates the Doppler effect by tying a 600 Hz sound generator to a 1.0-m-long rope and whirling it around her head in a horizontal circle at 100 rpm. What are the highest and lowest frequencies heard by a student in the classroom

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niczorrrr 2 months 2021-08-15T07:52:27+00:00 1 Answers 10 views 0

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    2021-08-15T07:54:16+00:00

    Answer:

    619.2 Hz and 582.5Hz

    Explanation:

    Given that

    Frequency of the generator, F(s) = 600 Hz

    Length if the rope, r = 1 m

    Speed of whirling, w = 100 rpm

    For starters, we find the speed of the generator, v(g)

    v(g) = r.w

    It should be noted, however, that we are to convert the speed of whirling from rpm to rad/s, thus

    100 rpm = 100 * 2π/60 rad/s

    100 rpm = 200π/60

    100 rpm = 620.4 / 60

    100 rpm = 10.47 rad/s

    Now, we use this to find the speed of the generator

    v(g) = r.w

    v(g) = 1 * 10.47

    v(g) = 10.47 m/s

    When approaching the generator, the frequency is calculated as

    F(a) = F(s) / [1 – (v(g)/v)]

    F(a) = 600 / [1 – (10.47/343)]

    F(a) = 600 / 0.969

    F(a) = 619.2 Hz

    On the other hand, the receding generator frequency is

    F(r) = F(s) / [1 + (v(g)/v)]

    F(r) = 600 / [1 + (10.47/343)]

    F(r) = 600 / 1.030

    F(r) = 582.5 Hz

    Therefore, we can conclude that the highest and lowest frequency is 619.2 Hz and 582.5 Hz respectively

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