How does win affect the Doppler effect?

[thebillsfan]

Would I be understanding this correctly if I said:

Wind doesn't increase the relative speed btw source and observer, but rather increases the effective sound of speed in air. that's why you need to use the FULL equation for Doppler's effect instead of the shortened EK (change f/f = relative speed/speed of sound) version of the equation if you have wind.

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[Hemichordate]

As an addendum, what are the "easy to memorize" formulas for each of the situations involving the Doppler Effect? Like if you are moving toward or away from a stationary observer, do you get a +v or -v in the numerator and denominator? What if you are stationary and the observer is moving?