A driver travels northbound on a highway at aspeed of 30.0 m/s. A police car, tr

Question

A driver travels northbound on a highway at aspeed of 30.0 m/s. A police car, travelling southbound at a speed of 39.0 m/s, approaches with its siren producing sound at a frequency of 2450 Hz. What frequency does the driver observe as the police car approaches?__________ Hz What frequency does the driver detect after the police car passes him?____________ Hz Repeat parts (a) and (b) for the case when the police car is traveling northbound. while police car overtakes__________ Hz after police car passes___________ Hz

Explanation / Answer

Assuming temperature is 20*C and speed of sound in the air is 343 m/s:

f' = f * (343 +/- vo) / (343 -/+ vs )

When deciding whether to use + or -, just think about it logically. If the observer is moving opposite the directions of the waves, then the observer will run into more waves, making the frequency higher, so use + for vo. If the observer is in the trail the source (in other words, behind the source), then the observer will run into fewer waves, so use + for vs.

a) The driver sees an approaching source and he is also an approaching detector. The detected frequency will be

f' = 2450 * (343 + 30) / (343 - 39) = 3006.1 Hz

b) The driver sees a receding source and he is also a receding detector. The detected frequency will be

f' = 2450 * (343 - 30) / (343 + 39) = 2007.5 Hz

c)
If the source is traveling northbound:

i) The driver sees an approaching source and he is a receding detector. The detected frequency will be

f' = 2450 * (343 - 30) / (343 - 39) = 2522.5 Hz

ii) The driver sees a receding source and he is an approaching detector. The detected frequency will be

f' = 2450 * (343 + 30) / (343 + 39) = 2392.3 Hz

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