Question

A physics professor demonstrates the Doppler effect by tying a 650 Hz sound generator to a 1.0-m-long rope and whirling it around her head in a horizontal circle at 100 rpm.

b. What is the difference between the highest frequency heard by a student in the classroom and the initial frequency of the sound generator?

a.What is the difference between the lowest frequency heard by a student in the classroom and the initial frequency of the sound generator?

Answer 1

First we have -

100 rpm = 100 / 60 = 1.67 rps  

The rope has a length of 1.0 meters so the circumference of the orbit is 2*pi

This means the velocity of the sound generator is:

2*pi*1.67 = 10.47 m/s  

Use Doppler effect -

The new frequency is:

((V(sound)/(V(sound)+V(source))*F(0)= F

The speed of sound is 340m/s

(340/(340+10.47))*650 = 631 Hz

This is when the sound generator is moving away from the class. When it is moving towards the class it is:

(340/(340-10.47))*650 = 671 Hz

(b) Difference between highest frequency and the initial frequency = 671 - 650 = 21 Hz

(a) Difference between lowest frequency and the initial frequency = 650 - 631 = 19 Hz