Doppler effect on a police car?

AI Thread Summary
The discussion centers on the Doppler effect as it applies to a police car's siren moving away from a stationary observer. The initial calculation suggests that the frequency decreases to 51.4 Hz, leading to a wavelength of 5.8 meters. However, the book states the frequency increases to 70 Hz using a different formula. This discrepancy raises questions about the correct application of the Doppler effect equations. Ultimately, the confusion highlights the importance of understanding how the motion of the source affects perceived frequency.
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A police car's siren emits a wave with a frequency of 60 Hz. The speed of sound is 300 m/s and the car is moving 50 m/s. "what is the wavelength of the wave behind the car"

So, the answer seems pretty easy. The observer is a stationary point behind the car, and the source is moving away from the observer, which means frequency should decrease:

f = 60 (300+0)/(300+50) = 51.4 Hz
wavelength = 300/51.4 = 5.8

Is this logic correct?

However, the answer in the book states that the final frequency is 70 Hz, by this equation:
f = 60 (300+50)/(300+0) = 70 Hz

Which one is correct?
 
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An increase in the frequency would indeed make no sense at all. :)
 
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