I am afraid I have not given enough detail for you to “get it” based just on my comments. Often the phrases “resonance”, “density of states” and “impedance matching” are used as catch all terms for describing the situation, although these phrases obviously don’t themselves bring any understanding.
All three terms are describing the same thing in different words. “Impedance matching” is gesturing to the fact that when a wave moves into a material where it travels with a different speed their is a reflection at the interface, so shaping a cavity that effectively slows the sound waves down by making them ricochet reduces the amount of sound that the air bounces back into the string at that interface. Resonance is getting the same thing in the frequency picture. Density of states is saying the same thing again, this time using a Fourier transform to talk about the density of different possible waves in position instead of the speed of waves. (Essentially if the waves are walking on a monopoly board a slower speed implies a greater density of squares → more states. So something that likes putting sound counters into nearby squares will deposit more in the slow areas because their are more squares to put them in.)
I don’t get it yet. Thanks though! Might come back. (I’m probably not devoting enough attention to get it.)
I am afraid I have not given enough detail for you to “get it” based just on my comments. Often the phrases “resonance”, “density of states” and “impedance matching” are used as catch all terms for describing the situation, although these phrases obviously don’t themselves bring any understanding.
All three terms are describing the same thing in different words. “Impedance matching” is gesturing to the fact that when a wave moves into a material where it travels with a different speed their is a reflection at the interface, so shaping a cavity that effectively slows the sound waves down by making them ricochet reduces the amount of sound that the air bounces back into the string at that interface. Resonance is getting the same thing in the frequency picture. Density of states is saying the same thing again, this time using a Fourier transform to talk about the density of different possible waves in position instead of the speed of waves. (Essentially if the waves are walking on a monopoly board a slower speed implies a greater density of squares → more states. So something that likes putting sound counters into nearby squares will deposit more in the slow areas because their are more squares to put them in.)