Answer to Question #161981 in Optics for Carty

Question

An ambulance moving at 42m/s sounds its siren whose frequency is 450 Hz. A car is moving in the same direction as the ambulance at 25m/s. What frequency does a person in the car hear;

(a) as the ambulance approached the car?

(b) After the ambulance passes the the car?

[Take v= 340m/s]

Answer 1

(a)

$$f_o=f_s(\dfrac{v-v_o}{v-v_s}),$$ $$f_o=450\ Hz\cdot(\dfrac{340\ \dfrac{m}{s}-25\ \dfrac{m}{s}}{340\ \dfrac{m}{s}-42\ \dfrac{m}{s}})=476\ Hz.$$

(b)

$$f_o=f_s(\dfrac{v+v_o}{v+v_s}),$$ $$f_o=450\ Hz\cdot(\dfrac{340\ \dfrac{m}{s}+25\ \dfrac{m}{s}}{340\ \dfrac{m}{s}+42\ \dfrac{m}{s}})=430\ Hz.$$