Deriving Formula: f2 Frequency of Moving Object

[The Tutor]

Homework Statement

This is my first post, so it might not be that great... Anyways, I need help deriving the formula. This formula is pertaining to the doppler effect, and more specifically, to find the frequency of a sound made from an object moving toward/away from you.

f₂= f₁(v/v-v_s) or... f₁(v/v+v_s)

Where f₂ is the second frequency, f₁ is the first frequency, v is velocity, and v_s is the velocity of the source.

Homework Equations

v=(lambda)(frequency) (I don't know how to make any symbols =/)
v=d/t
beat frequency= absf₁-f₂endabs

The Attempt at a Solution

What I did was try to make every variable a frequency, and I had no idea what to substitute in for v_s...

 

[ideasrule]

I don't think you need the beat frequency formula.

Think about the problem like this. At a certain moment in time, a siren emits a crest (or trough; take your pick), and the energy spreads out in all directions at the same speed. After one period passes, it emits another crest, which again spreads out in all directions. If the siren's moving, this crest will be closer to the initial crest in the direction of motion and farther from it in the opposite direction. If you can find the distance between the two crests, that's your wavelength.

 

[The Tutor]

I don't think you need the beat frequency formula.

Think about the problem like this. At a certain moment in time, a siren emits a crest (or trough; take your pick), and the energy spreads out in all directions at the same speed. After one period passes, it emits another crest, which again spreads out in all directions. If the siren's moving, this crest will be closer to the initial crest in the direction of motion and farther from it in the opposite direction. If you can find the distance between the two crests, that's your wavelength.

I think I might've worded my question wrong; I'm trying to prove the formula itself, I don't need to find the wavelength; unless that is what I am suppose to do?

 

[The Tutor]

I don't think lambda was suppose to use in the original equation, was it? I forgot to add that part in my original question.