Doppler shift equation...?

[m25]

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I came across this equation:
Δλ/λ = v/c
for doppler shift shift, in which Δλ is change in wavelength, λ is original wavelength, v is the speed of the object emitting the sound, and c is the velocity of the medium in which sound travels.
But looking at the classic doppler equation:

I really don't understand how the above equation could be derived. Anyone got ideas?

 

[techfan]

I think about it this way, if you are in a batting cage and a pitching machine is throwing out pitches at a certain speed (in your equation that's c) then the amount of times you get hit with each pitch is f. If you start moving towards the machine you get hit more quickly and you would think that the pitching machine is throwing at a faster pace so you have to add the speed you are running at the machine at to c in order to see what you perceive the frequency to be.

Unless you are simply looking for the v=fλ relationship to find how f and λ are related. In that case look at the units of f which is 1/s and the units of λ which is m in SI (nm for most practical purposes) and then if you multiply 1/s*m you get m/s which is velocity and HOT DAMN there's the wave equation.

 

[Hadi7183]

The equation "Δλ/λ = v/c" is derived from a special case of Doppler equation in which (based on your convention) "vr" is zero; that is, f=(c/c+vs)*f0. If you do the math, you will easily arrive at the same equation.

 

[m25]

The equation "Δλ/λ = v/c" is derived from a special case of Doppler equation in which (based on your convention) "vr" is zero; that is, f=(c/c+vs)*f0. If you do the math, you will easily arrive at the same equation.

Ok so I tried to do the math, but it's not working. How do you do it?
I ended up at
Δf/f=v/(c+v)

 

[Hadi7183]

I hope this helps!

 

[m25]

I hope this helps!

Ahhh, this makes so much sense. Thank you!