Root canal apex locator

While strapped to the dentist's chair yesterday, having a conversation with him which went mostly "Hmmm Mmmm Ummmm Ggg" (and that was him talking, I was much worse) I learned about a new tool he had bought recently that was designed to determine the depth of a tooth's root, for root canal surgery.

What they do is drill out most of the canal, then insert a pin-like drill as far up as they can go, which has an Ohmmeter clipped to one end. This fancy expensive Ohmmeter is calibrated to work out the resistance through the remaining tooth and from that they guess how deep the root canal must be.

While listening to this explanation and making "grrrrrg" noises by way of keeping the conversation going, I had a thought that an alternative way to determine the length of a hollow tube might be to simply tap it and listen for the reverb. A root canal is almost a hollow tube (actually it's a slightly tapered cone, but that doesn't affect the idea much) and I'm pretty sure that it ought to be possible to make it chime. Either by a simple tap, or maybe by holding something like a variable frequency tuning fork against it. Or a white noise generator on a stick.

Whether it would be any more accurate or less unpleasant than the current system I've no idea, but there's definitely a student project in here somewhere for dentists - or maybe an engineer with a good collection of stolen teeth.

Obviously there would be some maths involved in converting from the received harmonic note to a length, and it might involve needing to know the width of the channel from an X-Ray, but if lucky it would be a function of only the length. (I'm not a musician, I don't know the theory of producing notes well enough to give you the formula that would be needed here.)

The root pre-drilling is not hollow, but the density of what is in that tube compared to a tooth is much lower, so I'm hoping that is enough to allow it to resonate like a cavity.

By the way the reason they can't just measure it from the X-Ray is that X-Ray's frequently underestimate the length of the root canal. The dentists distinguish between what they call the True Apex and the Radiological Apex. It sounded a lot like what engineers would refer to as a 'fudge factor'. (A notion that even Einstein had to rely on once, with his "cosmological constant" - the biggest fudge factor in the Universe...)

G