What sound frequencies can pass through a hole in a wall?

[S P]

TL;DR Summary

Hole in plate. What sound frequencies can pass through hole depending the hole diameter and length?

Hello,

First of all, I will try to overcome language barrier as this is not my native language and the more topic is scientific - the more chance for me to get lost in translation. Apologies for poor grammar in advance.

I marked it as Advanced post, so apologies if this has to be corrected by forum moderators.

The problem I am trying to solve is as follows:

There is hole in plate. On one side of the hole there is a sound source, playing music. On the other side is a listener. For the simplicity we can assume:

• The frequency range of the sound is the official hearing range of a human: 20Hz to 20kHz. Even for the sake of simplicity we can narrow it to the "telephone band" - 200Hz to 5000Hz.
• The source of the sound for the simplicity is a single point.
• There is just single hole.
• Sound transfer is simple air at 20 deg Celcius. Sound speed is 340m/s
• The distance from the hole to the sound source is lets say 1 meter (if that matters)
• The SPL (volume) of the sound is 90dB at the entrance of the hole. For simplicity.
• Hole axis and sound source is in line. You can visually see the sound source from other side of the plate.
• Plate is from some theoretically perfect material, non-resonant, fully absorbant, infinite dimensions, infinite mass, there is no reflections and refractions, sound transfer or other acoustic artefacts from the plate itself.
• Hole surface on the contrary is from real life material, lets assume simple plastic, wood or iron. Surface is perfectly smooth. Inner walls do not absorb or interfere with the sound passing through.
• Hole diameter R is something practical, like from 1mm to 10cm, in SI unit - from 0.001m to 0.1m.
• Hole length L is also something practical, like from 1cm to 10cm, in SI unit - from 0.01m to 0.1m.

The diagram of the "problem":

The question is:
What diameter and length hole will block what frequencies of the sound? Which percentage?
Is there some rule of thumb or simple formula or graph to calculate approx. values?

The simple answer could be that the hole diameter should be in the ballpark of the 1/2 or 1/4 or 1/8 of the wavelength to make some kind of filter for the sound but as I understand, that does not work for such frequencies, at least in 20-2000Hz range. Audio speaker industry has many "vented" type speaker and subwoofer boxes of bass reflex, bandpass, MLTL and other vented types and the vents can pass those frequencies while being even ~0.05m in diameter. The wavelength of 30Hz sound wave is ~11.5 meters, so 0.05m diameter vent can pass a wave that is 230 times the length. I have no idea how that changes in the higher region of 2000Hz 20kHz, ultrasound or even higher frequencies, but there has to be another mechanics which is involved.

Thank you in advance.

 

[Baluncore]

If there is just a simple hole in the wall, then why do you draw the green tube?
Is L the length of the tube, or is L the thickness of the wall?

There will NOT be a single frequency that will pass, it will be a harmonic comb.
There will be a transfer function for the audio spectrum.

 

[sophiecentaur]

it will be a harmonic comb.

Harmonic, with a tube that short and wide? Think of the end effect and then think of Overtones.

 

[Baluncore]

Harmonic, with a tube that short and wide?

The ratio of length to diameter will be important.
Should the search be for the acoustic transfer function of an "orifice plate" ?
Or is the hole better described as a short "organ pipe", open at both ends?

 

[Baluncore]

I would expect, for higher amplitude sound waves, an orifice may become nonlinear.

 

[S P]

If there is just a simple hole in the wall, then why do you draw the green tube?
Is L the length of the tube, or is L the thickness of the wall?

There will NOT be a single frequency that will pass, it will be a harmonic comb.
There will be a transfer function for the audio spectrum.

L - the length of the tube. It can be the same of larger than the thickness of the wall. Wall is acoustically a black hole, it absorbs everything. For the simplicity green tube is a hole, which is coated in real world material.

I do not think that there will be more than few % of difference because of diffraction from tube outside to the inside. I wanted the conditions to be simple. So the wall thickness and tube length is the same.

I do understand that there will be some spectrum that will pass, with most centered at one of multiple locations related to hole-tube L and R resonant frequencies or smth. If it is an exercise to find proper keyword then I am out of luck. Not much info on the web.

 

[S P]

Harmonic, with a tube that short and wide? Think of the end effect and then think of Overtones.

Real world scenario: the hole in wall is something you can drill - 5mm diameter R and 20mm length L. Ratio 1 to 4. Hole inside is 100% reflective. Music or pink noise plays on the other side of the wall. Which range from 200Hz to 5kHz will transfer best?

 

[sophiecentaur]

Real world scenario: the hole in wall is something you can drill - 5mm diameter R and 20mm length L. Ratio 1 to 4. Hole inside is 100% reflective. Music or pink noise plays on the other side of the wall. Which range from 200Hz to 5kHz will transfer best?

The numbers totally rule here - well done to inject some sense. A 200mm hole corresponds to one wavelength at 1.5kHz so @Baluncore ‘s “comb” of modes / overtones is very relevant. Transmission will be very low at some frequencies (nulls) and high at frequencies in between. Those sweet spots will transmit about 50dB less than an open window. (based on the hole area)That is a really annoying level in an otherwise quiet room.

 

[Baluncore]

Energy radiated from an isotropic point source, that then passes through an aperture, will be attenuated by the aperture. It will then be attenuated again by the inverse square law before it reaches the sensor beyond the aperture.
Where r is the radius of the hole, and d is the distance of the source beyond the hole.
Spherical surface area = 4πd² ; Aperture area = πr² ;
Power or Energy transmission coefficient = πr² / 4πd² = r² / 4d² ;
Pressure or amplitude transmission coefficient = r / 2d ;

For low frequencies, with λ > r, the energy passing through the hole will appear to re-radiate from a point source at the centre of the hole.

For higher frequencies, where the wavelength of the sound is λ ≤ r, the radiation pattern from the hole, will become progressively more complex, with nulls and side lobes.

Longer holes will have an impedance mismatch at each end, while they also form resonators.

 

[S P]

The numbers totally rule here - well done to inject some sense. A 200mm hole corresponds to one wavelength at 1.5kHz so @Baluncore ‘s “comb” of modes / overtones is very relevant. Transmission will be very low at some frequencies (nulls) and high at frequencies in between. Those sweet spots will transmit about 50dB less than an open window. (based on the hole area)That is a really annoying level in an otherwise quiet room.

Hole is 20mm length and 5mm width. There is an example of subwoofers playing very low notes of massively longer wavelengths through small holes. Your example is of another scenario

 

[Vanadium 50]

Subwoofers?

Let's back up a bit. Sound waves are longitudinal waves. They are not restricted by the aperture because the wavelength "doesn't fit inside". They are restricted because the waves need to satisfy the boundary conditions imposed by the aperture.

 

[hutchphd]

Let's back up a bit. Sound waves are longitudinal waves.

I don't really understand why this is important , although I agree with the rest. The boundary conditions are not really simply predicated on this are they? The details will surely matter either way.

 

[Vanadium 50]

I don't really understand why this is important

A longitudinal plane wave (i.e. from infinity) will pass through the aperture, attenuated only by the ratio of areas of the aperture and the wall, independent of frequency. That's an idealization, of course, but understanding the right limiting behavior is too.

 

[hutchphd]

This is not also equally true for a transverse (plane) wave? Say a water wave ito a "pocket" harbor opening (in 2D). I don't see what the "longitudunal " has to do with it. Scalar waves allso give a similar result .
I need to go look at the optical theorem....

 

[sophiecentaur]

Hole is 20mm length and 5mm width. There is an example of subwoofers playing very low notes of massively longer wavelengths through small holes. Your example is of another scenario

Which goes to show that an initial description of the actual scenario is very helpful and more potentially fruitful. Context is essential.

 

[sophiecentaur]

They are not restricted by the aperture because the wavelength "doesn't fit inside".

Although very long wavelength EM waves can travel along very small feeders as long as the boundary conditions support them. For instance, co-ax cables can work down to DC but many wave guide shapes have a cut-off wavelength below which the 'doesn't fit' problem arises.

Say a water wave ito a "pocket" harbor

Thing is, water waves are not simple longitudinal waves. They have a transverse and longitudinal components. A particle of dust below the surface of a sea wave travels in an oval path; back and forth and up and down so water in your harbour will also move as a result of very long waves out at sea.

 

[hutchphd]

Yes. But that is not really the point of my question. Assume the waves are in deep water......or just take a generic scalar wave. My objection is to ascribe the effect in question to longitudinal waves. The rest is complication and not relevant (to me).
Don't get me wrong water waves are fascinating and wonderfully complicated. At one time surface waves (in solids mostly) were my primary research interest.

 

[S P]

So, if the sound waves are longitudinal then more or less the amount of sound energy passing is just related to the size of the hole, correct?
Still the filter thing is real for really small holes - 200-1000x smaller diameter than sound wave?

 

[sophiecentaur]

So, if the sound waves are longitudinal then more or less the amount of sound energy passing is just related to the size of the hole, correct?
Still the filter thing is real for really small holes - 200-1000x smaller diameter than sound wave?

This is correct as long as the 'room' on both sides is very large. If the impedance of the cavity on one side is included then the impedance of the hole to incoming sound is affected and incident energy can be totally reflected, for instance.

Have we actually been told the precise scenario yet? A sub-woofer (a ported cavity?) was quoted in the thread. If the volume on one side of the hole is small, we are in the realms of a Helmholtz resonator but this is a subset of problems.

 

[sophiecentaur]

So, if the sound waves are longitudinal then more or less the amount of sound energy passing is just related to the size of the hole, correct?
Still the filter thing is real for really small holes - 200-1000x smaller diameter than sound wave?

That's probably too much of a simplificaton for a detailed prediction. It's right for long wavelengths but, when the hole has modes with , say a half wavelength or greater (high frequency sound), your model falls down and you can get enhanced propagation sometimes - 'positive gain' because of the different impedances. The effective speed of sound in a pipe is affected by the width and the effective length will vary with frequency, so it's modes and not simple harmonics that count. Near resonances, the matching of the tube to the impedances at each end can greatly affect the throughput. The tiniest hole through a thick brick wall can allow unpleasant levels of squeaky, upper register chidren's voices. The better sound-proofed the wall, the worse the effect of small levels of breakthrough.

 

[Vanadium 50]

That's probably too much of a simplificaton

Perhaps, but if we don't have the actual problem with actual dimensions and an actual drawing, it is hard to tell, isn't it? People are coming up with all sorts of models with differing idealizations and limiting cases. They can't all be applicable, but which are which?

 

[sophiecentaur]

Which goes to show that an initial description of the actual scenario is very helpful and more potentially fruitful. Context is essential.

 

[Vanadium 50]

I agree.

There seems to be a growing trend of "Help me with this problem" "OK, what is it?" "I'm not going to tell you."

 

[S P]

This is correct as long as the 'room' on both sides is very large. If the impedance of the cavity on one side is included then the impedance of the hole to incoming sound is affected and incident energy can be totally reflected, for instance.

Have we actually been told the precise scenario yet? A sub-woofer (a ported cavity?) was quoted in the thread. If the volume on one side of the hole is small, we are in the realms of a Helmholtz resonator but this is a subset of problems.

Nope. This is not sub-woofer building. The precise scenario is the sound filtering panel, which theoretically can be used to "filter" some frequencies more than others. The so called "panel" can be of different shape and different thickness.

Sub-woofer or any other bass-reflex type audio speaker was just an example of how relatively very small hole lets through very long wavelength waves. But the fact that sound is longitudinal waves kinda explains that in simple terms.

That's probably too much of a simplificaton for a detailed prediction. It's right for long wavelengths but, when the hole has modes with , say a half wavelength or greater (high frequency sound), your model falls down and you can get enhanced propagation sometimes - 'positive gain' because of the different impedances. The effective speed of sound in a pipe is affected by the width and the effective length will vary with frequency, so it's modes and not simple harmonics that count. Near resonances, the matching of the tube to the impedances at each end can greatly affect the throughput. The tiniest hole through a thick brick wall can allow unpleasant levels of squeaky, upper register chidren's voices. The better sound-proofed the wall, the worse the effect of small levels of breakthrough.

I thought to "solve" this by the very simple solution: the smaller the hole - the smaller the frequencies that can go through. But Helmholtz resonator thing is a separate problem. Yes, I already understood that this is complex problem: wave length, hole diameter, hole length and hole air mass/volume. And that is before we get to multiple holes and diffraction

Perhaps, but if we don't have the actual problem with actual dimensions and an actual drawing, it is hard to tell, isn't it? People are coming up with all sorts of models with differing idealizations and limiting cases. They can't all be applicable, but which are which?

I don't want actual calculations. This is the very general problem, right now on the theoretical level. I am not strong in this area, but sometimes you have to do things which are out of your knowledge in some parts of it. I thought there is low hanging fruit where someone made exact or very similar research which is publicly available and not protected intellectual property but I cannot find it.

I agree.

There seems to be a growing trend of "Help me with this problem" "OK, what is it?" "I'm not going to tell you."

This is a generalization. I am a very rare visitor there, so cannot talk about the overall atmosphere. I almost never go into explaining myself, but my personal experience is as follows:
1. I never ever go into personal emotional stuff. I do not intend to offend somebody or opposite - be emotionally pleasant to someone. If I somehow offended someone - my apologies. After the first post of "This forum is/gets/became (pick any reason)" or "You are/did/didn't (pick any) do that by the rules... " - your thread is gone...
2a. By explaining problem too broadly that thread is a target for different trolls to hijack. This is a dream for discussion board owners as they get free original content. After the first post with the words "...when I used to work/teach/learn/sell X Y Z at A B C we used to do K L M" your thread is gone...
2b. By giving too much info you can get helpful answers which are useful, but unrelated. The very clear examples are of the problem, which can have multiple solutions, but the OP want info about the particular one, like: "My apartment neighbors are playing music too loud. How to soundproof wall cheaply?" will get many answers of "Call police" which are right, but not what was asked by OP. I do not want info about how to make smooth holes, or critique how the hole somehow is drawn non-perfectly or smth else.
3. It is hard to make complex conversation in non-native written language about the complex things you barely understand. That locks me into simple things
4. My evil minds want free knowledge from the poor smart geniuses lurking here to make God-level patent and rule entire galaxy enslaving everyone else . But you destroyed my plans

 

[hutchphd]

If you ask a bad question you will get useless answers. Garbage in / garbage out, as in all things transactional. You may consider this "garbage out".

 

[S P]

If you ask a bad question you will get useless answers. Garbage in / garbage out, as in all things transactional. You may consider this "garbage out".

What is wrong in my question?

 

[Baluncore]

What is wrong in my question?

You assumed you knew enough, to reduce the question to the case of a single hole. An array of holes has a different response to a single hole.

If you had identified the application, you could have avoided wasting my time, and I would not have unwatched this thread.

 

[S P]

You assumed you knew enough, to reduce the question to the case of a single hole. An array of holes has a different response to a single hole.

Lets simplify it to single hole.

If you had identified the application, you could have avoided wasting my time, and I would not have unwatched this thread.

My apologies.

 

[sophiecentaur]

the smaller the frequencies that can go through.

This is not the correct way round; it's higher frequency sound that is attenuated least through small holes. It is not a 'go-no go' thing. It's all to do with impedance and geometry. Hand waving doesn;t take you far.
I repeat the point that others have made. A summary of your basic problem is essential if you want not to waste people's time and to get the most useful answers fast.

Your post #24 really doesn't help. Whenever you are on line you risk bad experiences but PF is rather a haven of politeness and good sense. This is due to the tight rules we work to and everyone is a winner that way. Trolls and the like don't get much change here so you are comparatively safe because most contributors know their stuff and nonsense tends to get filtered out.

 

[S P]

Sophiecentaur,

I am not a troll. The task I am solving sounds exactly like that: a possibility to selectively "filter" some frequencies of sound coming from 1 side of the panel (some sort of a board to the other, by drilling holes of the exact diameter and/or length. Of course there is a limitation of the panel thickness, but this is another problem. Also another problem is the amount of holes, and interaction between them, but I want now assume that this is just a 1 hole in total. That is all. The question is if there is some kind of formula or some measurements already done.

 

[sophiecentaur]

I am not a troll. The task I am solving sounds exactly like that

No. Not at all. Your basic problem is almost universal for building design.

Thing is, you would be far better off doing a Google search to find more precisely what you need. My first Google hit was this link which provides "some kind of formula". There were many others and I suggest you go down the same path.
When you find something that looks the right level, ask PF again to clear up particular problems. you find there. Otherwise, it can turn out to be too open ended for PF to help.

 

[ProfRob]

I am very new here....and yet I found the question interesting. I have been wondering the same thing myself. Another approach to the problem might be to ask, "what theories come into play" with this problem? If we knew the major theories involved, we should be able to learn and solve the problem on our own. Please don't give up on the question, keep it very simple - at the theoretical level. Thanks you, Rob