In brevity, our ears react to a pressure differential between the inside of the eardrum and the outside. The tympanic cavity slowly equalizes to atmospheric pressure via the eustachian tube, so without a sound being present, the pressure on both sides of the eardrum will be roughly equal.
The force acting on the eardrum is only dependent on sound pressure, not atmospheric pressure because atmospheric pressure acts from both the tympanic cavity as well as from the ear canal, which results in zero net force.
Consequently, the only pressure having any bearing on the power received by the ear is the sound pressure, because the eustachian tube acts as a low pass and will not allow pressure to equalize quickly enough.
There are other factors playing into our sense of loudness, some of them do depend on speed of sound, which for example changes the resonance frequency of the ear canal (subtly). However, these are more than offset by the ability of our brain to modulate the sensitivity of the hearing apparatus (the so-called stapedius reflex).
As Iāve mentioned in one of my previous posts, the more likely cause for things sounding unusually muffled is a steep temperature gradient of the air. This is not uncommon when the sun heats the ground while the surrounding air is cold and there is no wind mixing the air. The temperature gradient will lead to a higher speed of sound close to the surface as opposed to further up, leading to sound energy being propagated away from the surface up into the air (where you wonāt be able to pick it up). A steady tailwind blowing from you towards the source can have a similar effect.
is that similar to how sound travels in water causing the Sonar convergence zonesā¦
where the pressure and density of the water effects the way the sound pressure wave moves through it
Yes these are all effects caused by a change in propagation speed.
You also see this in the reflection/refraction effects when looking at a water surface from above or below. The speed of light is vastly different in air vs. in water.
Thanks for that very detailed answer!
But I feel I need to follow upā¦
Wonāt the density of the atmosphere in which the the pressure differences (waves) propagate, affect the sound wave in any wayā¦?
where Ī¾ is the particle displacement, Ļ the frequency, c the speed of sound and Ļ the density of the medium.
What does this mean?
Youāre in a room where the pressure is lower (and so the density of air is also lower). Say that your sound source (string, speaker or whatever) is vibrating with the same amplitude and frequency, so Ī¾ and Ļdonāt change. The speed of sound is roughly independent of the pressure. So your sound intensity will be roughly proportional to the density of the air, or proportional to the pressure.
This sounds (a little pun intended ) to me like high density air = high perceived volume.
But Iāll take your word over a nameless source on the web any day. Just wanted you to know my reasoning.
But seriously: If youāre riding a bycicle and pulling a trailer, and I double the weight in your trailer, can you still achieve the same amount of acceleration?
If we assume we keep amplitude and speed of sound the same, then yes, a denser medium will mean a higher intensity. But suddenly we have to put more energy in at the source to achieve that.
You completely disregard the fact that we are operating in a system where energy can not be won or lost. The source radiates a certain amount of sonic energy (there are dependencies on sound radiation wrt impedance coupling, but I donāt have the patience to get into that now). When you increase the density of the medium, what will happen to amplitude?
It will go down, just the right amount so the laws of energy conservation are met. And we still measure the same intensity at the receiver.
Iām sorry if Iām testing your patience.
And let me just say that I canāt be disregarding something I do not know. Itās not a willful act on my behalf.
What then explains this phenomenon of muffled sound at altitude? Surely you must have noticed it too?
I have offered multiple explanations for what Chris described to the best of my ability, Iām done repeating them. If you donāt trust my expertise or I didnāt explain them well enough, please read a textbook on acoustics.
@sobek, Iām sorry if I have offended you or your knowledge here. That was never my intention. Itās not easy to ask the correct questions, especially when one is not versed in the terminology.
Unfortunately I am no closer to understanding this muffled sound phenomenon. Since you say you havenāt experienced it I wonder if it may have something to do with ear pressure equalization after flight? I must ask my AME.
Failure to equalize will have a strong effect on your hearing curve, but at that point you would definitely feel discomfort.
Exposure to a loud environment will trigger your stapedius reflex and make everything sound muffled, but that should pass quickly, unless we are talking outside of the jet while itās running sound pressure levels.
The air at altitude is generally colder, which means high frequency sound doesnāt propagate as far, but you would only notice that for very distant sources, not up close. If you are flying from moderate humid to high cold places with very low humidity, that could explain it.
Oh yes. Been there, done that. But I have also had instances where I feel about like when I get water trapped in the ear. Not painful, but like I have an earful of cottonā¦ It goes away after a while.
You talk about humidity. The bleed air condition system produces rather dry air in the pressurized cabin of the aircraft. The cabin altitude is typically 5-8000 ft.
Could flying into an airfield with pretty much the same air pressure as the dry air airplane cabin you flew in on, have caused it?
That could be a partially blocked Eustachian tube
I sometimes get muffled hearing and and have to clear it by blocking my nose and sniffing, the blockage slows the pressure equalisation
Yes, thatās the issue on those occasions but it rarely affect both ears simultaneously, in my case.
I went back to the thread where this discussion started and saw @komemiuteās edit.
That seems like a good, low level, explanation.
When googling this the google AI will come up with this reply:
Yes, air density does affect the perceived volume of sound, though not in a simple, direct way. While sound intensity, which is related to volume, is roughly proportional to air density, the relationship is more complex.
Now, Google AI will also tell you that thereās no water in the swimming pool on the Titanic. So I guess that should serve as a caution. But following a link that Google used for the answer, I read this:
Quote from the article:
So in the scenario youāre describing, if T is taken as constant, then the speed of sound doesnāt change, but its intensity does, as the density of the air is much lower on top of mountains, rough approximation for the intensity would be
IāpvāĻĀ²cĻ
Where v is the speed of air molecules, Ļ sound frequency. So one thing is for sure, you will need to shout much louder on a mountain, for people further ahead to be able to hear you.
Thereās also a reply debating this in what I think is more along @sobekās explanations.
Reading further I come to think about the sounds @BeachAV8R heardā¦ Engines with propellers and fans. Would speed of sound explain the muffled sounds? Itās colder at altitude, so SoS is lower. Are shockwaves forming on the tips of the propeller or fan blades, altering the sound image? Chris has heard more than an occasional aircraft engine in his career and Iām guessing that most of them are at warmer temperaturesā¦?
The first reply on stackexchange makes the same error interpreting the formula. You canāt change density and expect velocity to remain the same, unless you change the energy emitted by the source.
The second answer is much better, it touches on the changes in coupling of the mechanical and acoustic domains when the density of the acoustic medium changes.
Donāt please. In the most friendly way possible never ever bring up AI in any discussion of this sort. Not worthy of your time, not worthy of my time.
Sorry if it offends you.
I just mentioned it since Google will automatically give you an AI TL;DR of the results of your Google search. I shows how easy it is to interpret the information that is easily comprehended, when the detailed answer is hidden. And as I also wrote, it served as a caution. We can turn a blind eye on AI as much as we want, but it is starting to dictate the knowledge that we are presented with. You really need to assess the information in the sources that is used. Itās sort of becoming a matter of considering the source of the sourceā¦
) to me like high density air = high perceived volume.