Where do pure tones occur in nature, besides harmonics? When you sound a tuning fork, you hear an pure tone/sine wave of usually 440Hz. Yesterday, I tried hitting a table knife made entirely from stainless steel against a grapefruit. When I held it up to my ear, I heard a frequency of roughly 698Hz, working nearly exactly like a regular tuning fork, but with a slightly less sustained tone. It got me wondering; what are the conditions for a pure tone like this to occur?
I'm going to assume that the tones from a tuning fork (and my table knife) aren't entirely pure. I know there are some upper frequencies that ring out aswell, and possibly some other stuff. But some objects make an entirely different sound all together, with much clearer overtones and a more specific timbre. In contrast to those, I think it's safe to say that tuning forks essentially sound a relatively pure tone.
But what are the conditions for a pure tone like this to occur? I know they can be picked out as overtones from a note with harmonics. But what makes a tuning fork not sound a standalone tone with no harmonics, or at least rather inaudible ones? What are the actual, physical conditions for something like this to occur? And how can one possibly recreate it?
Apologies if I've missed anything obvious or formatted anything badly, this is my first post on this site. Thank you in advance!
 A: This is a very broad question, and the most complete answer would just be a copy of an acoustics textbook. In general, though, we can say that several factors are important for determining the way a vibrating object sounds, such as:


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*Material properties such as stiffness, tension, the speed of sound inside the material, the homogeneity of the material, etc.

*Geometry, which changes the number and frequency of the available normal modes;

*How the oscillations are created, as different driving forces will excite different normal modes;

*Properties of the air, which can attenuate and distort an audio signal non-uniformly as a function of frequency; and

*The response of the ear, which is both non-uniform and non-linear as a function of frequency.
The tuning fork has a particular geometry that, given its material properties, makes one normal mode much more prominent than others for the proper driving force (namely, a moderately sharp, but not too sharp, tap on a soft object. Hitting it too hard will excite the upper harmonics as well), making the air vibrate at a frequency that 1) is not attenuated too much by the air over the distance from the tuning fork to your ear, and 2) is in the range where the ear's response can register a sound of that intensity and frequency.
If you change any one of these factors, then the sound may be quite different. Making the tuning fork out of a different material will influence the vibrations that the fork makes in response to a tap, and may excite more than one normal mode (especially if defects are present, as vibrations can reflect off of them). Making a tuning fork of a different shape will change the presence and/or frequency of the normal modes. Making a tuning fork vibrate by a different method (for example, hitting it too hard against a hard object, or hooking it up to a mechanical oscillator tuned to resonate with a higher normal mode) will change the normal modes that are excited. Making the tuning fork vibrate in conditions where the air preferentially absorbs the desired normal mode will change the sound. And hearing the tuning fork vibrate with an ear (or a microphone) that has a different response curve will also change the perceived sound.
