two Doppler shifts...

endeavor

A stationary source directs an 800-Hz sound wave toward an approaching object moving with a speed of 25.0 m/s. What is the frequency shift of the reflected wave if the air temperature is 20ºC? (Hint: There are two Doppler shifts here. Why?)

f = 800Hz
the speed of sound = v = 331 + 0.6T_c = 343 m/s
the speed of the object = v_o = 25.0 m/s
For the first doppler shift,
f₁ = (v + v_o)/v * f
f₁ = 858 Hz
For the second doppler shift, I'm guessing that we use the object moving as the source of the sound and the original sound source as the observer:
f₂ = v/(v - v_o) * f₁
f₂ = 925 Hz

But the answer is 126 Hz!

Curious3141

The shift in frequency is the difference between the final frequency and the initial one, so your answer is actually correct. (925 - 800 = 125 Hz, which is close enough to the expected answer).

robphy

the Google calculator says:
(((343 + 25) / (343 - 25)) * 800) - 800 = 125.786164
Sometimes it's best to get an algebraic answer in terms of the given variables, then plug in the numbers. Otherwise, intermediate numerical values can introduce round-off errors.

endeavor

Yeah, my value of 125 Hz comes from the fact that I used f₁ = 858 Hz, when I think it should've been 858.3xxxxxxx.... I get it now. Thanks.