This is a good example of one of those things that you don't really need to know for the MCAT - if you can remember conservation of energy as a way to remember that light has a constant frequency, and then remember that this applies to all waves, you're good to go for test day.
But, "it just works that way" isn't very satisfying.
Remember that for any wave, you're going to have a series of crests and troughs. So when the crest of the wave hits the boundary, it's going to transmit a "crest" into the new medium. And then when the trough of the wave hits the boundary, it's going to transmit the trough into the new medium. Since those crests and troughs are coming at a certain frequency and have to "line up" with each other at the boundary, you're not going to get a change in frequency.