# absorber distance from wall

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### absorber distance from wall

Hi,
I need to put up some absorption in a piano room. Research tells me that having a gap between a panel and the wall helps with reducing lower frequencies.

What is confusing me is everyone saying that this is due to velocity. I was under the impression that sound changed speed at different temperatures and the medium it is travelling through. I can understand velocity being at zero where it touches a wall but what makes sound slow down as it approaches a wall and then accelerate away from it?

I know people have done tests and proved a gap makes a difference but surely it has nothing to do with the speed of sound.

Could one of you kind people explain what I'm missing?
SteveKD
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### Re: absorber distance from wall

SteveKD wrote:Research tells me that having a gap between a panel and the wall helps with reducing lower frequencies.

Kind of... But not quite. Moving the panel away from the wall helps to extend the absorption frequency range downwards, but the lowest frequency to which a panel is effective is also related to the overall depth of the panel.

What is confusing me is everyone saying that this is due to velocity.

Again, kind of. Conventional porous absorber panels made of foam or mineral wool (etc) work by channelling the sound waves through labyrinth-like structures in the material, losing energy as they progress through friction, thus converting acoustic energy into heat.

This process therefore requires the air particles to be moving -- having some velocity. For a soundwave arriving at a fixed boundary, the sound wave pressure is at a maximum at the surface, while the particle velocity is zero (there's nowhere for the air to go).

However, the air particle velocity is at a maximum at the quarter-wavelength point, and consequently a porous absorber is most effective when centered around the quarter-wavelength point. Following on from that, a handy rule of thumb is that the absorber is maximally efficient to the lowest working frequency if spaced from the boundary wall by the same distance as its thickness. That maximises the lowest extent of the frequency range over which absorption is useful.

I was under the impression that sound changed speed at different temperatures and the medium it is travelling through.

True, but neither fact is particularly relevant in this context.

I can understand velocity being at zero where it touches a wall but what makes sound slow down as it approaches a wall and then accelerate away from it?

Physics, innit! ;-) This is fundamental longitudinal-wave-motion physics. It might help to remember that the individual air particles aren't travelling anywhere. They are just oscillating backwards and forwards around their nominal position. And the particle velocity is always 90 degrees out of phase to the air pressure.

I know people have done tests and proved a gap makes a difference but surely it has nothing to do with the speed of sound.

Correct, nothing at all.

Could one of you kind people explain what I'm missing?

Hopefully the above has pointed you in the right direction...

Hugh Robjohns
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### Re: absorber distance from wall

Meh, wrote an answer but Hugh has written a better one quicker.

blinddrew
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### Re: absorber distance from wall

He's good in't he :D I believe he gets paid to do it :D

Sam Spoons
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### Re: absorber distance from wall

Must be worth a pay rise, surely? :lol:

Hugh Robjohns
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### Re: absorber distance from wall

To be fair, i was watching an episode of the mandalorian at the time. ;)

blinddrew
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### Re: absorber distance from wall

blinddrew wrote:To be fair, i was watching an episode of the mandalorian at the time. ;)

Thus proving that men can't multi-task? :silent:

Martin

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### Re: absorber distance from wall

Hugh Robjohns wrote:
I know people have done tests and proved a gap makes a difference but surely it has nothing to do with the speed of sound.

Correct, nothing at all.

In a practical sense the variation in the speed of sound due to temperature, air pressure, altitude, has no effect but you may notice the speed of sound featuring in explanations / calculations regarding the relationship of panel gap to wall vs effective lower working frequency. As Hugh has said, the velocity of the air molecules at the wall is zero, so the absorber has no effect. The maximum velocity of the air molecules occurs at a point one quarter wavelength away from the wall. This is the point at which the absorber is most effective. Lower frequencies have longer wavelengths therefore gapping the panel from the wall (or having a thicker panel) improves the effectiveness.

Where the speed of sound comes into play is in the relationship between frequency and wavelength;

Speed of Sound = Frequency x Wavelength

To give you a feel for the numbers the Quarter Wavelength distance for a 100Hz wave is approx. 850mm. That doesn’t mean that a thinner panels have absolutely no effect at lower frequencies, they are just less effective.

Music Wolf
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### Re: absorber distance from wall

As Hugh has said, the velocity of the air molecules at the wall is zero, so the absorber has no effect. The maximum velocity of the air molecules occurs at a point one quarter wavelength away from the wall.

This is where my lack of physics catches up with me.

Am I right to think velocity of air molecules = speed of sound?
Why does it accelerate as it moves from the wall? I thought other than temperature the speed of sound through the air was a constant.
I take it I'm wrong comparing to a ball bouncing off a wall?

thanks for the assistance guys, much appreciated.
SteveKD
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### Re: absorber distance from wall

Music Wolf wrote:To give you a feel for the numbers the Quarter Wavelength distance for a 100Hz wave is approx. 850mm. That doesn’t mean that a thinner panels have absolutely no effect at lower frequencies, they are just less effective.

Which also serves to illustrate why effective bass traps need to be big and why fitting them into corners increase their effectiveness as the reflected wave has two surfaces to bounce off between entering and emerging.

Sam Spoons
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### Re: absorber distance from wall

The Speed of Sound thing also related to stuffing in speakers. I understand there is an optimum density/volume that lowers the speed of sound* and thus makes the system resonance lower than the box dimensions would suggest? Maybe the information OP read was mixed up with speakers?

*The words "adiabatic" and "isothermal" seem to ring a bell but it has been a LONG time since I knew this stuff!

Dave.
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### Re: absorber distance from wall

SteveKD wrote:Am I right to think velocity of air molecules = speed of sound?

No.

The sound wave itself -- the transfer of sound energy through the longitudinal wave -- moves at the speed of sound from its source to your ear. Roughly 760mph across your studio, or roughly one foot every millisecond.

But the movement of the individual air particles back and forth about their nominal resting position occurs at the frequency of the sound being conveyed.

Why does it accelerate as it moves from the wall?

It doesn't. Nothing is moving away from the wall. We are just talking about what's happening at different distances from the wall.

This is a simplified view, but at a wall itself we can consider the air pressure to be at a maximum value simply because there is nowhere for the sound wave energy to go.

The physics of a longitudinal wave means that the air particle velocity is at a maximum where the air pressure is zero, and vice versa -- and the phase angle between the peak and the zero line is 90 degrees or a quarter of the full wave cycle.

So the maximum air particle velocity occurs a quarter of a wavelength away from the boundary surface where the pressure is at the maximum, and so that quarter-wavelength distance is the region where a porous absorber is going to be most efficient and effective.

The problem comes in the fact that different frequencies have different wavelengths (the formula for calculating one from the other does involve knowing the speed of sound in the relevant medium -- air in this case), and whereas the wavelength at high frequencies is very small, it quickly becomes very large for lower frequencies.

At 1kHz the wavelength is 0.34 meters, or about 1.1 feet, but at 10kHz it's just 3.4cm (1.3 inches) and at 100Hz its 3.43 metres (about 11.2 feet).

The corresponding quarter-wavelength figures -- which are relevant to deciding panel thickness and wall spacing come out at 8.5cm (3.3 inches) for 1kHz, and 86cm (2.8 feet) for 100Hz.

So, the lower the frequency you want to absorb with a porous absorber, the thicker (deeper) the panel needs to be and the larger the gap between it and the wall. Clearly, a porous absorber is impractical for dealing with very low frequencies at it would need to be so large you'd have no space left inside the studio!, but for frequencies above about 500Hz it's a very simple and cost-effective solution. (A four inch panel placed up to four inches from the wall is often manageable. Smaller spacings will raise the lowest effective absorption frequency, as will thinner panels).

As I mentioned before, to understand this you really need a grasp of the underlying physics and associated maths of longitudinal waves. There is a very good explanation with some helpful graphic animations here which may help:

https://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html

I thought other than temperature the speed of sound through the air was a constant.

It is. But 'the speed of sound' refers to the passing of acoustic energy along the longitudinal wave, not the speed at which the individual air particles are moving back and forth.

I take it I'm wrong comparing to a ball bouncing off a wall?

The bouncing ball can be related to the way the energy of a sound wave is reflected from some surfaces... but that's not relevant to the way a porous sound absorber works.

Hugh Robjohns
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### Re: absorber distance from wall

The whole Wave Motion thing can seem a bit confusing at first. The way my Physics teacher described it was to imagine a duck floating on the surface of a lake. There's a wind blowing which is creating waves, these waves are travelling across the lake (with a certain speed) yet the duck is just bobbing up and down. The duck doesn't go anywhere.

This is what is happening with a sound (or any kind of) wave. The air molecules (the duck) are just oscilating back and to (i.e. bobbing up and down) whilst the wave is travelling across the room at the speed of sound.

Music Wolf
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### Re: absorber distance from wall

This animation might help, as it shows the particle motion in the longitudinal wave with a nice accompanying sine wave - you can see that the "particles" aren't really going anywhere other than a small distance back and forth (see the red particles used to illustrate this) - they're just bumping into each other, and the "wave" moves by conveying this bumping motion along a series of particles.

The accompanying sine wave shows the pressure, and the top of this wave (highest pressure) correlates with the regions of the wave where the particles are most heavily squashed together.
If you focus on one of the red dots and pay attention to the speed with which it moves, you can also see that this is fastest at the point where the line on the graph crosses the x-axis behind each peak as it moves along - this is 1/4 of a wavelength different to (i.e. out of phase with) the points where the pressure is highest, nicely illustrating the phase relationship between the pressure and velocity.
Logarhythm
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### Re: absorber distance from wall

Thank you everyone. I obviously need to do more reading on this. So please forgive if this is a stupid question before doing that.

It seems that we are trying to get the absorber as near as possible to where maximum number of particles are moving (high pressure) rather than how fast those particles are moving.

Even though a porous absorber works by velocity, its best placement is determined by pressure.

Hope I haven't caused you to bang your heads against the nearest wall. I'll do some reading later this week!
SteveKD
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