Two Doppler Shifts: 800Hz to 126Hz

[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]

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.

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.