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

Answer 1

619.2 Hz and 582.5Hz

Step-by-step 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