How will the frequency of the sound differ as it travels through air when compared to its frequency as it travels through water?

It will NOT differ. The speed at which the sound travels will be affected, but the frequency will not be any different.

Why? The frequency is what really defines a wave. Let’s take our voice as an example. Our voice is composed of many overlapping frequencies. Stand on the other side of a door and try to talk to someone on the other side. When you speak, can the person recognize your voice? Can you recognize their voice? Yes and Yes.

The wave has changed mediums as it travels from you to the person on the other side. But you can still recognize each other because the frequencies of your voice have remained the same. If they have changed, then you might not be able to recognize the person’s voice as they talk through the door. The door would act as a voice changer which we know does not happen.

Hopefully this answers your question.