I’ve always wondered how striking a tuning fork and holding the Struck fork next to a cylindrical body with an adjustable length can yield an ideal length of that body which produces the loudest sound. I saw this in a Julius Sumner Miller lesson and was curious about why a specific length yielded a specific loudness of a given frequency. His attitude of “letting you think about that” raised a couple of questions. 1. How does sound travel through a hollow body/vessel? Is there an ideal face shape for that vessel that sound travels about best? For instance would sound travel more efficiently through a cylindrical vessel than through a vessel with more edges? 2. In addition what makes the sound the loudest from the audiences perspective? Is it possible that the frequencies traveling through this body are intercepting directly at the point where the end of a certain point of the face the body meets atmospheric air? ex. For example, if the frequencies from the tuning fork travelled through the body, and met at their respective points on the face of the the vessel where it meets atmospheric air, there’s a specific length of that adjustable vessel that would allow for the frequency to intercept with itself at that exact point. If any of these questions could be answered that would be great. And if my last question is even comprehendible or can be further educated with some critiques or enlightenment of my knowledge of sound, that would be greatly appreciated. Thank you.
$\begingroup$ The general answer to your question is related to "standing waves in tubes". If you look it up you will find out how the length of the tube is related to the frequency. Unfortunately I don't undertsand your other questions so I cannot answer them. $\endgroup$– nasuDec 12, 2020 at 1:22
Hollow body: sound travels by bending the shell, in most cases you imagine. Especially if wavelength is significantly longer than the shell thickness. Best shape is the one with significant stiffness, that is usually provided by two axis bending, like a sphere or a saddle. Flat shape is worse because it is usually poorly supported and tension changes along the body, making it harder for the sound to move through all sections of the body with different stifnesses. Each body's part can be imagined as a mass-spring system. Each body part must have the same resonant frequency for a single wave to travel further. Flat body almost always is tensioned unevenly, making spring-mass model have different resonating frequency, thus no particular frequency can travel this system well. Cylinder is a bit better than flat sheet but worse than a sphere. Any edges are worse than even a flat sheet. Just imagine the object as a thoudand tiny mass on springs, and that each is a filter to one frequency. Edges would be much more stiff than the surroundings for example, making them pass very different frequencies.
Sound attenuation: sound can be seen as power, and more power you add, more sound you get, just as with electricity. Nothing stops you from just using lots of power to make much louder noise. Another point is human's ear sensitivity to particular frequency. We can hear 20hz-20khz. But our sensitivity is stronger within 300hz-3khz. And maximum sensitivity is about 1khz. So spending same power at 1khz than at 10khz, a human will hear the sound much louder, about 10 to 100 times, depending on age. Older people decrease in high frequency sound sensitivity. Depending on transfer medium you can also lose some frequency. In particular high frequencies are lost faster in almost all cases. If your source of sound is far away, high frequencies will attenuate much more. 100Khz drops in power 10 times every few meters for example. So if a bat uses echolocation at this frequencies, it cant see further than a few dozen meters. On the other hand whales use very low frequencies for their echolocation, and their sound goes without much attenuation for many kilometers. Sound does get lost on a larger area, but it power is delivered to the target almost fully. If a bat would try to echolocate something a kilometer away, its sound power will simply be lost as heat into the air, with next to nothing reaching the target. Same rules applie to almost all barriers that force sound to convert it power to heat. Same applies to bone conductivity headphones, they lose high frequency in the bone as heat. But they are bad with the bass to begin with, so it cancels out. Some rough numbers, 1w of sound power is similar to a person screaming, so overheating from sound is very unlikely. Unless ultrasound with many kw of power is used, like in ultrasound plastic sealers. Regarding mundane conditions, ear and few meters of air - there is no significant loss of sound power, so there is no significant change in what frequencies pass unaffected either. They all do about the same.
TLDR: each sound frequency carries a bit of power. Any obstacle is more likely to turn to heat high frequency sound easier. Sound frequencies are not interacting with each other. Sound travels with the maximum speed it can all the time. Springy objects may pass one specific frequency but block all other. For sound going through springy objects imagine each part of object as a spring and mass that can wobble. Springy objects with different resonant frequencies along it body will end up blocking all frequencies. High quality ringers have all of their shell parts designed to pass the same frequency.
p.s. the title - 1khz sound wavelength is 0.3m in air or 5m in metal. Sound takes atleast this much space. Sound goes as full volume if it can. It can also travel as surface wave on thinner object, like string or a flat sheet. In springy object with surface wave spring-mass analogy is better than imagining that sound is a blob 5m in diameter.