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.

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