An ambulance is generating a siren sound at a frequency of 2,400 Hz. The speed of sound is 345.0 m/s. If the observer is traveling at a velocity of 24.00 m/s away from the stationary ambulance, then 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. If the observer is traveling at a velocity of 24.00 m/s away from the stationary ambulance, then 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. 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 stationary and the observer is moving away from the source is:
f' = f * (v / (v + vo))
where:
- f' is the observed frequency,
- f is the source frequency,
- v is the speed of sound, and
- vo is the speed of the observer.
Substituting the given values into the formula:
f' = 2400 Hz * (345.0 m/s / (345.0 m/s + 24.00 m/s))
Now, perform the calculation inside the parentheses:
f' = 2400 Hz * (345.0 m/s / 369.0 m/s)
Then, divide 345.0 m/s by 369.0 m/s:
f' = 2400 Hz * 0.935
Finally, multiply 2400 Hz by 0.935 to find the observed frequency:
f' = 2244 Hz
So, the frequency of the siren perceived by the observer is 2244 Hz.
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