Natural Science Forum / Physics / Acoustics / April 2005

A paper given by a Turkish presenter described renovations of a Mosque
where the walls were refinished, and reverberation became bad. It was
then realized that the small openings in the old walls that were covered
in the refinishing served a good purpose! They were the open mouth of
many jugs buried in the wall out of sight.

There is no doubt that sound of a certain frequency is captured and
intensified by the flask. But what percentage of that sound field was
captured? The absorption of the bottle is relatively low; it does not
take much energy to be built up in the bottle to give a pronounced
resonance within it.

If only little energy is taken from the space around the bottle, how
much do you expect it to affect the sound level around the bottle
opening. I have seen NO good analysis of this phenomenon.

Here's what I think should be done:

1- Measure the sound level in the vicinity of the flask opening, at all
frequencies, to such a precision that you feel you "should" see an
effect. Measure the sound level in the flask, also. I'll leave it up to
you to decide whether it should be in the neck, or SPL inside the bottle.

2- Place a small speaker in the bottle (you figure where to get it!).
Drive that speaker to produce the same SPL in the neck or interior.
Measure the sound field at various distances from the bottle, looking
for a square law fit to your data, if possible, but that is not important.

3- Compare the SPL exterior to, and various distances from, the flask as
follows: Calculate the change of external field, where the external
field is the same as that originally impinged on the flask. Figure two
cases for the summed sound; where the sound is additive to the field and
where the sound is subtracting from the field. I suspect that the change
will be extremely small in either case.

4- The next task is to develop an absorption prediction algorithm.

In considering absorbers in general, the perforated panel seems to be
the only useful manifestation of this Helmholtz effect, and such panels
are distributed over a wide area, hardly a flask or two, to get any
useful free field sound absorption.

5- I note finally that the "Conch shell effect" where a 'rush' is heard
as you hold its opening to you ear, is quite similar. One regular to
this group made a measurement of this phenomenon, and I believe that he
said he found 12 or 15 dB increase of SPL level inside the conch shell
as compared to the exterior free field. I further noted then that this
relate in turn to the "end effect" for ducts where it is known that
sound traveling in a duct will be reflected from an open end of the
duct. The reflection is quite large when the duct diameter is much less
than a sound wavelength, and diminishes as the sound wavelength gets
shorter (higher frequency) or the duct diameter becomes quite large.

6- So all someone here has to do is to codify all these random facts,
coupled with some sound theory (a pun!).

    Angelo Campanella

The effect of an absorber on spl will depend on what the sound was doing
before the resonator was introduced.  If the resonator is close to the
source of sound so that it is mainly in the direct field, most of the sound
energy would be going away and not coming back anyway, so I would not expect
to see any significant effect on spl.   If you had an intensity probe you
might be able to see that energy is going into the resonator.

The way to test absorption is to see the effect on reverberation.  You could
find something to act as a small reverberation chamber or have a tube that
has a resonance mode at the frequency you're interested in.  If you have
even a small chamber you will probably need quite a few bottles to have a
measurable effect.   You may need some damping such as lighweight fabric
stretched over the necks.

I'm surprised you saw much effect on spl in the neck, simple theory says
there will not be a significant pressure increase in the neck.   I wonder if
your microphone is really responding only to pressure.  If it is a genuine
Helmholtz effect you will certainly see a much larger spl increase in the
body of the flask.

Remember that Helmholtz resonators do not behave as simple theory indicates.
Depending on the shape, the dimensions of the device may not be small enough
to be neglected in comparison with the wavelength of the sound at the
Helmholtz resonance frequency, and there will be lots of higher resonance
modes as well.

A grossly over-simplified model of the situation is that of a pressure
divider with the pressure source being the free field pressure.   The
source impedance is the acoustic radiation impedance looking outward at the
plane of the neck opening and the load impedance is the acoustic input
inpedance at the plane of the neck opening looking into the resonator. I
did a quick back of the envelope calculation of the impedances and the
expected pressure division at resonance for a resonator having a 10cm long
neck, a resonant frequency 100 Hz and a Q of 30, and came up with the
result that the pressure at the entrance of the resonator would be
approximately 11dB lower than the free field pressure.  

Since you did not see any effect in your experiment, I decided to repeat
it.  I  fabricated a Helmholtz resonator using a plexiglass tube and a
glass bottle.  I made my measurements using a 4134 mic capsule on a 2639
preamp which was plugged into a 2032 FFT analyzer.  Random noise
bandlimited to 400Hz from the analyzer was applied to a power amplifier and
then to a bookshelf speaker which provided the excitation.  The
measurements were made with the microphone at a distance of 12 inches from
the speaker and with the microphone at 90 degrees relative to the incident
sound.  The analyzer was set for Hanning weighting and 256 linear averages.  
Three measurements were made: 1) resonator absent, 2) resonator present and
at 0 degrees sound incidence, and 3) resonator present and at 90 degrees
sound incidence.  In the latter two cases the microphone capsule was at the
center of the resonator opening and perpendicular to the plane of the
opening.  

The results of my measurements are as follows.  The resonant frequency of
the resonator, as determined by the frequency of sound produced when
blowing across the neck was 144.5Hz.  For zero degree sound incidence,
there was an 5.6dB increase in spectral level at 145 Hz and an 8.6dB
decrease in spectral level at 149.5Hz.  For 90 degree sound incidence,
there was 6.4dB increase in spectral level at 144.5Hz and a 9,7dB decrease
in spectral level at 149Hz.  The increases and decreases were measured
relative to the spectral level that was measured in absence of the
resonator.  Spectral levels at frequencies above and below the range from
140-150Hz did not change by more than 1dB when the resonator was inserted
into the sound field.

Aside from the discrepancy between your experimental results and mine,
there is the issue that an undamped Helmholtz resonator will not absorb any
energy.  So, unless you have a theoretical interest in Helmholtz
resonators, you may be starting at the wrong place.  If you put a Helmholtz
resonator on an impedance tube, you will find that the maximum absorption
(minimum reflection) will occur when the resonator is damped and that real
part of the input impedance of the resonator is equal to the characteristic
impedance of the tube.  Consequently, if your interest is in sound
absorption, investingating the behavior of an undamped Helmholtz resonator
is not, in my opinion, the proper starting point.  

 

     

 

Robert,

Helmholtz resonators have a long history of use where narrow band absorption is
required. Due to a number of unknowns in the design some final tuning is required.

I used to live in the steel city of Newcastle (Australia) where the coke oven
exhaust stack (~5 metre diameter) was fitted with an array of helmholtz
absorbers at the base of the stack in a hot, corrosive, dust-laden gas flow.

Every 6 months or so, the whole city knew when cleaning was required on the
absorbers, as dust build-up in the helmholtz absorbers caused them to drift off
the exhaust fan blade pass frequency.

The maintenance people would have to bring the coke plant off line, wait for the
stack to cool and unscrew the backs off all of the resonators to scrape out the
dust. The dust, until compacted, acted to broaden the absorption peak, but once
it compacted the whole system would mis-tune.

What application are you looking at ?

Brian

PS On a much larger scale, the river mouth to the ocean had breakwaters and
partially enclosed beaches, that apparently acted as quarter wave branches to
attenuated incoming ocean waves that would have impacted on the port facilities
just inside the river mouth.

< SNIP >

snip......snip


Here are a couple of white papaers by Trevor Cox who appears to be an
authority on the matter.  

http://www.rpginc.com/whitepapers/Clearsorber-White-Paper.pdf

http://www.acoustics.salford.ac.uk/student_area/bsc3/room_acoustics/absorpt
ion.pdf

I understand that there is detailed info in the book Acoustic "Absorbers
and Diffusers:Theory,Design and Application" by Trevor Cox and Peter
D'Antonio, but I can't say for sure because I don't have the book.