An ambulance is generating a siren sound at a frequency of 2,400 Hz. The speed of sound is 345.0 m/s. The observer is traveling at a velocity of 24.00 m/s toward the ambulance and the ambulance is traveling at a velocity of 24.00 m/s away the observer. What is the frequency of the siren perceived by the observer?
Question
An ambulance is generating a siren sound at a frequency of 2,400 Hz. The speed of sound is 345.0 m/s. The observer is traveling at a velocity of 24.00 m/s toward the ambulance and the ambulance is traveling at a velocity of 24.00 m/s away the observer. What is the frequency of the siren perceived by the observer?
Solution
To solve this problem, we need to use the Doppler effect formula for sound:
f' = f * (v + vo) / (v + vs)
where: f' is the observed frequency, f is the source frequency, v is the speed of sound, vo is the speed of the observer, vs is the speed of the source.
Given: f = 2400 Hz, v = 345 m/s, vo = 24 m/s (towards the source, so it's positive), vs = 24 m/s (away from the observer, so it's positive).
Substituting these values into the formula, we get:
f' = 2400 Hz * (345 m/s + 24 m/s) / (345 m/s + 24 m/s)
Solving this equation will give us the observed frequency.
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