An ambulance has just passed by your home. You detect that the frequency of thereceding siren is 900.0 Hz. If you know that the frequency of the ambulance’s sirenis 950.0 Hz, how fast is the ambulance moving? The speed of sound in this case is335 m/s.
Question
An ambulance has just passed by your home. You detect that the frequency of thereceding siren is 900.0 Hz. If you know that the frequency of the ambulance’s sirenis 950.0 Hz, how fast is the ambulance moving? The speed of sound in this case is335 m/s.
Solution
This problem can be solved using the Doppler effect formula for sound. The Doppler effect refers to the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source.
The formula for the Doppler effect when the source is moving away from the observer is:
f' = f * (v / (v + vs))
where:
- f' is the observed frequency (900 Hz in this case),
- f is the actual frequency of the sound (950 Hz in this case),
- v is the speed of sound (335 m/s in this case), and
- vs is the speed of the source (the ambulance, which we're trying to find).
We can rearrange the formula to solve for vs:
vs = v * ((f / f') - 1)
Substituting the given values:
vs = 335 m/s * ((950 Hz / 900 Hz) - 1)
vs = 335 m/s * (1.05555555556 - 1)
vs = 335 m/s * 0.05555555556
vs = 18.6 m/s
So, the ambulance is moving at a speed of approximately 18.6 m/s.
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