Answer to Question #161989 in Optics for friedel craft

Question

Standing at a crosswalk, you hear a frequency of 560Hz from the siren of an approaching ambulance. After the ambulance passes, the observed frequency of the siren is 480Hz. Determine the ambulance speed from these observations.

(V = 340m/s)

Answer 1

Initially, the ambulance approaching the person, so we can write:

$$f_1=f(\dfrac{v}{v-v_s}).$$

Then, the ambulance moves away from the person, therefore, we can write:

$$f_2=f(\dfrac{v}{v+v_s}).$$

Let's divide the first eqution by the second one, we get:

$$\dfrac{f_1}{f_2}=\dfrac{v+v_s}{v-v_s},$$ $$\dfrac{560}{480}=\dfrac{v+v_s}{v-v_s},$$ $$480(v+v_s)=560(v-v_s),$$ $$80v=1040v_s,$$ $$v_s=\dfrac{80v}{1040}=\dfrac{80\cdot340\ \dfrac{m}{s}}{1040}=26.15\ \dfrac{m}{s}.$$