A car on a road parallel to and right next to a railroad track is approaching a

Question

A car on a road parallel to and right next to a railroad track is approaching a train. The car is traveling eastward at 30.0 m/s while the train is going westward at 50.0 m/s. There is no wind, and the speed of sound is 344 m/s. The car honks its horn at a frequency of 1.00 kHz as the train toots its whistle at a frequency of 1.50 kHz.


The wavelength of the sound from the train's whistle, as measured by the driver of the car, is closest to:

0.263 m
0.180 m
0.196 m
0.229 m
0.249 m

using the doppler equation and plugging in the numbers, i got 0.438 m, which is incorrect. Here's what i did:

d = s ( v -/+ vs ) / (v ± vd)   

i put the car's numbers in for d and vd as it is detecting the sound, and the train's numbers in for s and vs as it is the source. i subtracted in the numerator and added in the denominator since both vehicles are moving toward each other.

so all in all here's what i did: d = 344 m/s / 1000 Hz = 0.344 m

0.344 m = s ( 344 - 50 ) / (344 + 30) so that s = 0.438, which isn't any of the possible answer choices. what am i doing wrong?

Explanation / Answer

Car speed v ' = 30 m/s Train speed v = 50 m/s Speed of sound V = 344 m / s Frequency of the train whistle f = 1.5 kHz                                                  = 1500 Hz Apperent frequency f ' = [ (V+v ') /(V-v) ] f                                    = 1.272 f                                    = 1908.16 Hz The wavelength of the sound from the train's whistle, as measured by the driver of the car, is closest to ' = V / f '          = 0.1802 m          ~0.180 m

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