Answer to Question #164335 in Optics for Carol

Question

A car sounding an alarm at a frequency of 512Hz is approaching a listener at a speed of 8ms-1, The

         reflected sound from the listener awakes a passenger of the car who was sleeping.

         (a.) Determine the apparent frequency of the horn as perceived by the listener and that of the

         reflected sound as perceived by the awakened passenger under the following cases:

         (i.) the listener is stationary, (ii.) the listener is approaching the car at 2ms-1, (iii.) the listener is

         moving away from the approaching car at 3ms-1.

         (b.) Explain why in all the above cases, the listener has the impression that the frequency of the

         sound heard is varying. 

Answer 1

a) i)

$$f_|=\frac{340}{340-8}512=524.34\ Hz\\ f_P=\frac{340+8}{340}524.34=536.68\ Hz$$

ii)

$$f_|=\frac{340+2}{340-8}512=527.42\ Hz\\ f_P=\frac{340+8}{340-2}527.42=543.02\ Hz$$

iii)

$$f_|=\frac{340-3}{340-8}512=519.71\ Hz\\ f_P=\frac{340+8}{340+3}519.71=527.29\ Hz$$

b) It is the consequence of the Doppler effect.