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an apparent change in the frequency of a wave because the observer and source are moving is called the

If the observer and the source are getting closer together OR getting farther apart, the observer will hear a sound with a different frequency compared to the sound that's actually coming out of the source.

An Austrian physicist and mathematician named Christian Doppler studied this effect, and he worked out the math that tells how much the frequency will change, depending on how fast the source and observer are moving, and whether they're moving together or apart.

After Doppler worked it out other scientists debated and argued for several years what they wanted to CALL this effect.  

Some wanted to call it the "Freaky-Shifty Effect", because when the motion is there, the frequency of the source gets shifted.

Other scientists noticed that if the observer moves back and forth and back and forth, the frequency he hears goes up and down and up and down, and it sounds something like "OOWAH-EEYOO OOWAH-EEYOO", so THEY wanted to call it the "Y-U Effect".

After years of disagreement and debate, the cooler scientists found the best way to displease everyone.  They just pointed out that it was Doppler who explained the whole thing and worked out all the math, and it would actually be nice to give him some credit for it.  So everybody just cooled off and agreed to call it the Doppler Effect .

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