Acoustics week 7

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Acoustics week 7

• Key points you should learn from today's lecture
• Room modes ( critical frequency)
• acoustic treatment
• control of low frequencies in rooms

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• reminder
• The absorption coefficient of materials is
  frequency dependent. Therefore the RT60 and the
  critical distance of a room is frequency
  dependent.

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Room Modes

• In any room their exists the opportunity for
  standing waves to be set up
• consider two parallel walls in a room
• where two reflections meet, at a specific
  frequency superposition may occur and a standing
  wave be set up.

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The diagram shows the first mode of how standing
waves can be set up between two parallel
walls this would be the first harmonic or
fundamental
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if there is a fundamental frequency there must be
the possibility of a second harmonic and then
also a third harmonic and so on through all the
harmonics.
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The diagram in shows the second mode of how a
standing wave can be set up between two parallel
wallsI.e the second harmonic
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This is how standing waves operate between
parallel surfaces, in a rectangular room. The
proper terminology for these standing waves are
eigentones, room resonances or most commonly,
modes. In this case the modes are called Axial
modes.
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The frequency for the fundamental is given by
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It therefore follows that the frequency for 2nd
harmonic 2xf03rd harmonic 3xf04th
harmonic 4xf0etc
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act in all three directions (axis) (axial)
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The situation, however is much more complex than
this in practisethere are two more methods of
resonance in a room. The tangential mode, where
sound can reflect off four walls, The oblique
mode, where sound can reflect off all six walls.
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Tangential modes only have half the energy of the
axial modesOblique modes only have a fourth
the energy of the axial modes for this course
we will neglect the effect of tangential and
oblique modes
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Analysis

• We must look for frequencies which are very close
  together
• look in the difference column and spot any
  differences of zero
• This means that at least two of the three axes
  have a modal resonance at the same frequency
• This can result in a significant increase in
  sound intensity at this frequency

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Analysis

• Another thing to look for is large gaps between
  frequencies in the difference column
• look in the differences column for any gaps above
  25Hz (approximately)
• this would indicate a possible 'dead spot' in the
  frequency response of the room.

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Modes tend to affect the acoustics of a room only
at lower frequenciesmodes still exist at higher
frequencies, but become much more densely packed
and even therefore less of a problemthere is a
critical frequency below which they become
dominant
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One of the problems with modal frequencies is
that they are position dependant they vary
depending on where you are in the roomwhich
means that the room no longer supports a diffuse
sound field Hence any RT60 calculations that
have been done could be invalid below this
critical frequency.
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Critical frequency is calculated as follows
where c speed of sound v room volume s
room surface area.
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Calculate the critical frequency for the room we
previously calculated RT60 times for i.e. room
dimensions 6m x 5m x 3m
Which gives a critical frequency of 180 Hz
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which indicates that for this particular room
frequencies below 180Hz should be analysed using
modal analysis in preference to RT60 decay time
calculations. Hence for the previous example
we need only to run the axial analysis up to
approximately 180Hz.
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We now know how to analyse our room, but how can
we fix any possible problems?
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We have all but answered this for the RT60 decay
curves in the mid to higher frequency range
there are many materials which absorb sound energy
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The rock wool panels in the Studio 1 (E2
finishing room E1 pro tools rooms) are an aid to
sound absorptionwhich will be absorbing more in
the mid to higher frequencies
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The industry standard type of open cell foam
(remember it is surface area that counts in
absorption) absorbent tiles are made by SONEX. A
typical graph of absorption coefficient is shown
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Rock wool

• Also very commonly used is high density semi
  rigid rock wool
• rock wool rw3 60kg/m3
• Rock wool rwa45 45kg/m3
• Different thicknesses

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On many occasions, improved diffusion may be an
alternative to increased absorption to solve
troublesome problems at certain frequencies.
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If we already have a perfect RT60 time for a room
then we do not want to increase or decrease
absorption for any surface so an increase in
diffusion may be the answer to our problems.
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Flutter echo

• simple method of removing flutter echo from
  parallel surfaces is to place absorbent material
  on one of the walls
• However this may not be desirable in terms of its
  effect on the RT60 of a room
• another method of removing flutter echo may be to
  increase diffusion of sound from the problem
  surfaces so that the energy is diffusely
  reflected in all directions

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Controlling the lower frequencies specifically
below the critical frequency is much more
difficult than the mid to higher frequencies.
The lower frequency diffusion should first be
designed into a room by selecting the correct
room sizes
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Certain 'golden ratios' are often employed to
ensure the correct sized rooms. 1.14 1.39 1 1
.28 1.54 1 1.60 2.33 1Hence if a room is
built according to any of these size ratios, then
modal problems should be reduced, i.e. the
resonant modes should be evenly spaced and the
low frequency response of the room should be
fairly smooth.
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the 'bass trap' a deep box filled with absorbent
material and with a lid of semi-rigid glass fibre
is mounted usually in a wall or ceiling. The
depth of the box is related to the frequency at
which it absorbs Since it is the velocity
component of the waveform that interacts with a
porous absorber and the position of highest
velocity actually occurs 1/4? away from the hard
surface. I.e. the highest interaction with an
absorbent surface is at the top of the bass
trap.
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Calculating the depth of a bass trap (simply
using vf?) It can be shown that the depth needs
to be large to absorb very low frequencies e.g.
1/4? at 100 Hz is 85cm. This can make the bass
trap rather unwieldy
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Another low frequency absorber is the panel
absorber A thin plywood panel supported by a
frame. This will work as a diaphragm, vibrating
with a specific resonance depending on its size,
mass, density and depth of air gap.
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Where M is the mass of the panel (kgm-2)And
d is the depth of the airspace (m)Hence if
a 6.25mm plywood panel has an air gap of 100mm
and a density of 3.6kg/m2 the frequency of
resonance will be 100Hz.
The formula for frequency of resonance is
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If the air gap is left empty, then there will be
a sharp peak of absorption at the resonant
frequency if the gap is filled with fibreglass
then the peak is wider and flatter .This is a
lower Q factor
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Another form of resonant absorber uses the
principle of the Helmholtz resonator, named after
a German physicist Hermann von Helmholtz
(1821-1894) the principle of which is shown
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The principle of operation is as follows, blowing
across the top of the narrow neck of the bottle
creates a lower pressure in the neck, drawing air
from it. The main volume of air inside the
bottle is analogous to a spring, whilst the
"plug" of air in the neck acts as an attached
mass, hence sustained oscillation beginsThe
resonant frequency of which is given by another
equation
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constructed in a similar fashion to the panel
absorber but with the front membrane perforated
with many small holes each hole acts as a
Helmholtz resonator. These panels can absorb
efficiently at lower frequencies without taking
up so much space as a standard bass trap.
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Where c is the speed of sound in air p is the
perforation percentage i.e. the hole area divided
by the panel area 100 d is the depth of air
gap m t is the length of the hole in metres
taking into account the ends correction
formula(Panel thickness 0.8 hole ?)
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• Previous bass traps are narrow band (tuned)
  resonators (absorbers).
• There is much evidence to suggest that broadband
  bass absorbers should be used in preference to
  tuned (narrow band) absorbers
• This will smooth out the bass response more
  evenly and (hopefully) negate any holes in the
  sound field

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wide band absorber, which combines the effects of
a porous absorber with a helmholtz perforated
resonator.
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Superchunks
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Absorption figures
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Further work

• Work through the examples in last 2 weeks notes
• Reverb time (try with Excel)
• Reverb modified with curtains
• Try modifying using rock wool rw3 60kg/m3
• Critical distance calculate at different
  frequencies and different speaker directivity (Q)
• Try low frequency analysis with critical
  frequency calculations
• Remember the important difference between
  listening rooms and performance spaces