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
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