Answer to Question #342339 in Mechanics | Relativity for Anonymous005

Question

A fire truck is emitting a 450 Hz signal passes by a stationary detector. The difference in frequency measured by the detector is 58 Hz. If the speed of sound is 345 m/s, how fast is the truck moving? (ans: 22m/s)

Answer 1

The Doppler's effect says

$$f=f_0\frac{c\pm v_r}{c\pm v_s}$$ $$f=f_0\frac{c}{c+ v_s}$$ $$v_s=c(f_0/f-1)\\ =345(450/(450-58/2)-1)=24\:\rm m/s$$