A physics professor demonstrates the Doppler effect by tying

A physics professor demonstrates the Doppler effect by tying a 520.47Hz sound generator to a 0.55-m-long rope and whirling it around her head in a horizontal circle at 79.34 rpm. Assume the room temperature is 18.56^oC. What is the highest frequency heard by a student in the classroom?

Solution

c = sqrt (1.40 * 8.314 * (273.15+18.56) / 0.02896)

= 342.41 m/s

The sound generator moves on a circular with tangential velocity v_t = w r = 2 pi n r

= 2 pi * 79.34 * 0.55

= 274.18 ,m/min

= 4.57 m/s

Highest frequency is observed, when generator moves with maximum velocity towards the student

v = v_t

f = f₀ / (1 - v_t / c )

= 520.47 / (1 - (4.57 / 342.41)

= 527.5 Hz