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23 January, 07:31

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? Assume the room temperature is 20°C.

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  1. 23 January, 10:58
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    f_h = 620 Hz

    f_l = 580 Hz

    Explanation:

    Given:

    - Length of the rope L = 1.0 m

    - Rotational speed N = 100 rpm

    - Frequency of source f_s = 600 Hz

    - Velocity of sound in air v = 343 m/s

    - Angular Frequency : f = N / 60

    Find:

    What are the highest and lowest frequencies heard by a student in the classroom?

    Solution:

    - Calculate the linear speed of the source v_s:

    v_s = L * (2*pi*f)

    - Plug values in:

    v_s = L * (2*pi*N / 60) = 1*2*pi*100 / 60

    v_s = 10.47 m/s

    - The highest frequency can now be calculated using Doppler's effect equation:

    f_h = f_s / (1 - v_s / v)

    - Plug the values in:

    f_h = 600 / (1 - 10.47/343)

    f_h = 620 Hz

    - Similarly, compute for the lowest frequency using Doppler's effect equation:

    f_l = f_s / (1 + v_s / v)

    - Plug the values in:

    f_l = 600 / (1 + 10.47/343)

    f_l = 580 Hz

    - The highest frequency is f_h = 620 Hz

    - The lowest frequency is f_l = 580 Hz
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