HELP asap please?

Question

The siren of a fire engine that is driving northward at 30.0m/s emits a sound of frequency 2000 Hz. A truck in front of this fire engine is moving northward at 20.0m/s.
a) What is the frequency of the siren's sound that the fire engine's driver hears reflected form the back of the truck?

b) What wavelength would this driver measure for these reflected sound waves?

Answer 1

doppler effect: apparent freq (n') of actual freq (n)

n ' = n [v-vo] / [v-vs]
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in this formula, all v, (sound spped), vo (observer) and source (vs) are necesarily moving in the same direction (say + x). if one is not in + x, then is will be resolved therein.
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v=343 m/s (+x), vs = 30 m/s (+x), v0 = 20 m/s (+x)
all in same direction
the apparent freq to trucker
n ' = 2000 [343 - 20] / [343 - 30] = 2063.90 Hz
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this n' is reflected and trucker becomes a virtual source
vs = 20 (+x) , vo (engine) = 30 (+x)
but sound is now directed from truck to engine, so resolved as v = - 343 (+x)
n '' (apparent to engine) = n ' [- v - vo] / [- v - vs]
n '' = n ' [v+vo] / [ v+vs]
n '' = 2063.90 [343 +30] / [343 + 20]
n '' = 2120.75 Hz
this is what fire engine driver will hear as reflected freq
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wavelength = v /n'' = 343 / 2120.75 = 0.1617 meter
wavelength = 16.17 cm

Answer 2

LOL! I'm sorry, but I've really forgotten how to do all that long ago. If you ask me, however, I would say the frequency of the siren would be heard by the driver at the frequency it is emitting since the driver is sitting directly underneath it and can't possibly hear what is reflected off of another moving vehicle. Therefore, the wave length of what he is hearing is the same as if there were NO vehicle in front of him.

Would you please send me an email as to what the correct answer is once you find out?