Answer to Question #164236 in Optics for Gasty

Question

A car travelling at 10ms^-1 sounds its horn, which has a frequency of 500 Hz, and this is heard in

      another car which is travelling behind the first car, in the opposite direction, with a velocity of

      20ms^-1. The sound can also be heard in the second car by reflection from a bridge ahead, in the

      direction of the first car. What frequencies will the driver in the second car hear?

Answer 1

(a)Let's first find the frequency that the driver in the second car hear when the sound of the horn is directly coming to the second car:

$$f_o=f_s(\dfrac{v-v_o}{v+v_s}),$$ $$f_o=500\ Hz\cdot(\dfrac{340\ \dfrac{m}{s}-20\ \dfrac{m}{s}}{340\ \dfrac{m}{s}+10\ \dfrac{m}{s}})=457\ Hz.$$

(b) Let's first calculate the frequency at the bridge:

$$f_{o,b}=f_s(\dfrac{v}{v-v_s}),$$ $$f_{o,b}=500\ Hz\cdot(\dfrac{340\ \dfrac{m}{s}}{340\ \dfrac{m}{s}-10\ \dfrac{m}{s}})=515.1\ Hz.$$

Finally, we can find the frequency of the reflected sound:

$$f_{o,r}=f_{s,b}(\dfrac{v-v_o}{v-v_s}),$$ $$f_o=515.1\ Hz\cdot(\dfrac{340\ \dfrac{m}{s}-20\ \dfrac{m}{s}}{340\ \dfrac{m}{s}-10\ \dfrac{m}{s}})=500\ Hz.$$