Understanding Doppler Effect

[Waz]

Homework Statement

Two trumpet players are both playing with a pitch of 440 Hz, corresponding to the musical pitch A above middle C. However, one of the trumpet players is marching away from you so that your hear a beat frequency of 4 Hz from the two trumpets. With what speed is the departing trumpet player moving away from you? (The speed of sound in air is 340 m/s)

Homework Equations

f' = f(V+-Vo/V-+Vs)

f2 - f1 = beat frequency

The Attempt at a Solution

How I approached the question was the following:

f' = f(V/V+Vs)
f(V/V+Vs) - f1 = beat

so
440(340/340+Vs) - 440 = 4
which solves to Vs = 3.06 m/s

However, looking at the answer (3.12 m/s) It seems I should have set the equation up as:

440 - 440(340/340+Vs) = 4
which goes to 3.119 m/s

So conceptually speaking, how am I supposed to know how to set up the equation? Is it just what yields a positive answer? or is there something I'm not thinking of. I couldn't find anything specific online. Thanks for the help.

 

[Mickey Tee]

How I thought of it is, the player is moving away, so the apparent frequency of the sound from his trumpet should be less than 440.
We know that the difference, or lowering of the frequency, is 4Hz, so f' is 436.
To have a frequency lower than the original, the denominator term of the velocity ratio should be greater. So we add the speed of air and the speed at which he is moving away.