Verb to cause one to listen, as in "show" means to cause one to see

In cases where you're having the person listen to an audio recording or something musical, the verb play is appropriate.

For example,

May I play you my favorite composition by Debussy?

would be fitting if you want to either play a recording of the piece, or if you're sitting at a piano and want to play it yourself. This phrasing works for any audio recording, since starting the playback of a recording is just "playing" it - you could "play someone a speech", "play someone a recording of birdsong", or "play someone the sound of a motorcycle", so long as they are all recorded sounds.

For things that are not recordings or musical, "play" doesn't fit. If you want to show off the sound of your new motorcycle in person, for example, you don't "play someone the sound of the motorcycle". In this case, show could be used for non-visual stimuli, as "show" most generally just means "display or allow to be perceived". One could show their anger through the tone of their voice or the words they choose, even if they are speaking over the telephone, so "show" does not strictly imply a visual phenomenon. So, you could say:

I'd like to show you the sound of my new motorcycle.

although this does sound a little odd to me. Other phrasings with "show" sound a bit more natural, such as:

Let me show you what my motorcycle sounds like at full throttle.

perhaps because it doesn't have the unusual phrasing of "showing a sound", but instead "shows what it sounds like". At any rate, you can't go wrong by rephrasing to use a more auditory-oriented verb, such as:

I'd like you to hear my new motorcycle.