## Doppler Effect

Consider a pedestrian is standing on the sidewalk when an emergency vehicle approaches at 30 m/s with its sirens blasting at a perceived 400 Hz frequency. After the vehicle drives past, what is the new frequency the pedestrian hears? Assume the speed of sound is 340 m/s. Expand Hint
The doppler effect:
$$f=\frac{s}{s+v}f_0$$$where $$f$$ is the new frequency, $$s$$ is the speed of sound, $$v$$ is the velocity of the moving sound emitting object, and $$f_0$$ is the initial sound frequency. Hint 2 When the vehicle is driving towards the pedestrian, the velocity is negative. The doppler effect: $$f=\frac{s}{s+v}f_0$$$
where $$f$$ is the new frequency, $$s$$ is the speed of sound, $$v$$ is the velocity of the moving sound emitting object, and $$f_0$$ is the initial sound frequency.
$$400=\frac{340m/s}{340m/s-30m/s}f_0$$$Note that the velocity is negative because the vehicle is approaching the pedestrian. $$400=\frac{340}{310}f_0\rightarrow f_0=\frac{400\times 310}{340}=365\:Hz$$$
When the vehicle is driving away, the scenario can be described with a positive velocity:
$$f=\frac{340m/s}{340m/s+30m/s}\times 365=\frac{340}{370}\times 365=335\:Hz$$\$
335 Hz