In real life, a tuning fork is an instrument that when tapped against a sturdy object, makes a sound at a consistent key. Usually that's at 440hz, known as the key of A in music talk. I imagine the tuning fork makes a noise in the same "key" as the plane. Otherwise, I think they would have used a different word for the intended use of the object.
The original detail on which key for which fork applies to which plane is from Dragon Magazine 120 pages 42 & 43 in an article titled Plane Speaking: Tuning in to the Outer Planes by Jeff Grubb. There's reason to take this as plausibly canon information: Ed Greenwood, the chief designer of the Forgotten Realms, was one of the editors, and Grubb has worked with Ed Greenwood before in the Forgotten Realms setting. Grubb was in charge of the original Manual of the Planes which this is directly related to, and also had a lot to do with Spelljammer back when it was TSR and not Wizards of the Coast.
The article has an entire list on the subject at hand, the materials, and tuning of the tuning fork, or "forked rod," which is exactly a tuning fork. This is old lore, and may not be relevant in 5e, but it provides the kind of detail that you might want to add to your campaign. For example the first layer of Carceri (né Tarterus) needed an E flat iron fork. (@HeyICanChan)
