Acoustics sound propagation and interaction

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Acoustics - sound propagation and interaction

• Key points you should learn by the end of today's
  lecture
• refraction
• diffraction
• reflection
• diffusion
• Reverberation ??
• Absorption ??

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Refraction of Sound

• sound travels in straight lines
• refraction can occur when a sound wave travels
  between two mediums
• Speed of sound will be different in each of the
  two mediums
• Refraction will also occur at sharp edges and
  boundaries of obstructions.

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Refraction at a boundary
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Medium Speed in m/s Air 344 Sea
water 1,500 Wood, Pine (along grain)
3,800 Mild Steel bar 5,050 Plasterboard 6,8
00Typical speed of sound
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Refraction in the Atmosphere

• The atmosphere of the earth is not uniform
• Temperature
• Humidity
• Density
• refraction effects can be heard, and demonstrated
  in the atmosphere.

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Diffraction of Sound

• Subtly different from refraction
• diffraction is the effect of sound bending around
  corners and obstacles
• diffraction is the change in direction of the
  sound travel by encountering sharp edges and
  physical obstructions. The shorter the
  wavelength, the less dominant the diffraction
  effect is. Obstacles capable of diffraction must
  be larger than the wavelength

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Diffraction around a small object
Diffraction around a large object
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• If Obstacle is small compared to the wavelength
  it may have no effect whatsoever,
• A larger object in relation to the wavelength
  will cause a shadow behind it.
• Any diffracted wavefront can then act as a new
  point source of sound
• All points p on the diffracted wavefronts may
  act as point sources of sound radiation.

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Diffraction by apertures.

• Since the diffraction is dependant on the size of
  the obstacle and the wavelength of the sound
  wave, it is the same for apertures.

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Diffraction through a large aperture
Diffraction through a small aperture
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• We can see that for a larger aperture the sound
  can pass through with little disturbance, again
  with the wavefronts acting as point sources
  radiating into the shadow zones
• For smaller apertures (compared to the
  wavelength) the wavefronts can not pass through
  the hole but will act like point sources

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when sound hits a barrier, the point becomes
another effective point source of sound which
(depending on wavelength) can lessen the effect
of the sound shadow created.
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Reflection of Sound
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• Reflected wavefronts act as though they originate
  from a sound images, located behind the wall.
• In a room 6 walls exist and the effect of all the
  6 images must be considered
• Images of images exist

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• Mid and high audible frequencies are called
  specular as they reflect off flat reflective
  surfaces
• the angle of incidence aI is equal to the angle
  of reflection ar

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Reflection at Curved Surfaces

• Reflection of plane wavefronts of sound from a
  solid convex surface tends to scatter sound
  energy in many directions.
• This amounts to diffusion of sound

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A concave surface can concentrate sound waves
Reflection at Curved Surfaces
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EchoObjects can be located by sending out a
pulse of sound and noting the time it takes for
the reflected echo to return. Bats use this
principle to hunt navigate in the dark.
Humans use it to obtain the depth of oceans.
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Echo

• Object location
• Precedence effect
• Flutter echo caused by two opposing parallel
  reflective surfaces
• generate a series of echoes reflecting
  alternately from each wall
• usually at a distinctive frequency
• distortion of sound in that frequency range.
• sound energy will not decay in a smooth line, but
  will have peaks in the decay.

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Diffusion of Sound

• Most of the theory that follows is dependant on
  the sound field in a room being diffuse
• That is that the sound is fairly evenly
  distributed throughout the room (after it has had
  time to propagate)

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• In a totally homogeneous sound field a highly
  directional microphone pointed in any direction
  should pick up a constant signal.
• room shape and size has a large effect on the
  level of diffusion and can be used to design
  suitable acoustics.
• mid to higher frequencies - make the walls less
  flat, which is to say more uneven or rough (to
  achieve diffusion)
• avoid specular reflection
• reflection in many and random directions.

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• Diffusion relies on reflection of sound to
  achieve it's aim
• Objects will only reflect sound depending on the
  size of the object in relation to the wavelength
  of the sound
• Normal treatment of walls is only going to help
  for mid to high frequencies
• Diffusion at lower frequencies can only really be
  achieved by choosing correct room proportions.

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Reverberation in enclosed spaces

• Music or sound is generally listened to in a room
  of some description, and therefore is influenced
  by the boundaries of that space.
• The are three main stages through which a
  radiated sound passes

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Direct Sound

• Sound which travels directly from the source to
  the listener i.e. unaffected by any boundaries
  in the room, the delay between the sound
  generation and the listener hearing it. is simply
  linked to the distance between them

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• Under free field conditions all sound energy is
  radiated directly away from the source, so the
  sound received at any point, is governed by the
  inverse square law.
• The free field is also often referred to as the
  near field, (it is common in recording studios to
  make use of near field monitors)
• It is the area where direct sound predominates
  over any reflected sound effects from the room.

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• After the direct sound is heard, a short time
  later early reflections are heard, these are
  reflections of the original sound reflected once
  from the surfaces of the room
• The early reflections are separated both in time
  and direction from the original.

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• The intensity levels of these reflections depends
  on the distance travelled and the surface from
  which they have reflected
• The reflections will be predictably smaller in
  amplitude due to the inverse square law (since
  these reflections have travelled a greater
  distance)
• Most surfaces will absorb some energy, hence
  making these reflections weaker still

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Sometime after the early reflections the sound
has been reflected many times off all surfaces
and in all directions, a denser set of
reverberations reach the listener, this is
reverberation.
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The amount of time it takes for a sound to die
away is called the reverberation timeIt
depends on the size of the space and the amount
of absorption by the surfaces of each reflection
of the sound.
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Reverberation time

• The amount of reverb required in a room depends
  entirely on the application and size of the room
• Speech may require a reverberation time of less
  than one second
• If for pop music then nearly a second or over may
  be more appropriate.
• For classical music more than 2 seconds may be
  appropriate
• Reverb times for recording spaces and mixing
  rooms often need to be different

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• Reverberation time
• The amount of time required for the sound field
  in a space to decay by 60dB (one millionth of the
  original power)
• Reverberation time is important
• it can affect how well you understand speech
• it can change the way music sounds

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Every absorbent material has a Sound absorption
coefficient which is a useful measure of how much
sound it will absorb.This is a number between 0
and 1 where0 indicates no absorption (total
reflection)1 would indicate total absorption.
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• Remember
• All surfaces will
• Absorb some of the sound energy
• Allow some sound energy to pass through
• Reflect some sound energy
• Or most likely, a combination of all three

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• NOTE when a longitudinal sound wave is reflected
  from a hard surface, at the point of reflection
  the VELOCITY of the wave must be zero, but since
  it still has energy, all that energy at that
  point is in the compression of the air i.e. the
  PRESSURE. (Strictly speaking the pressure
  component is twice as large as normal)(high
  potential energy)
• 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. Therefore
  porous absorbers work well when they are either
  at least 1/4? in width or are 1/4? away from the
  hard surface. (high kinetic energy)

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• The unit of sound absorption is the Sabine and is
  equivalent to one square metre of perfect
  absorber (i.e. ?1)
• named after Wallace Clement Sabine (1868- 1919)
• i.e. 1 Sabine 1 m2 of material for which ?
  1.0
• hence we can calculate the absorption of any
  material in Sabines for which we know ? and size

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• for a heavy carpet with heavy underlay 4m x 3m
  with an ?0.5 (at 500 Hz)
• 4 x 3 x 0.5 6 Sabines
• for a heavy carpet with heavy underlay 4m x 3m
  with an ?0.15 (at 125 Hz)
• 4 x 3 x 0.15 1.8 Sabines
• for a vinyl floor 3m x 5m with an ?0.05 (at 500
  Hz)
• 3 x 5 x 0.05 0.75 Sabines

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• We are now in a position to calculate the
  reverberation time (RT60) for a room using
  Sabine's formula, which is
• Reverberation time 0.161x total volume of the
  room
• Total number of Sabines
• RT600.161V
• n

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• where n (total number of Sabines) can be found by
  multiplying the area a of each type of surface by
  its absorption coefficient ? , and then summing
  them all together. In mathematical terms, this is
• n ?ai?i
• which when expanded becomes
• n (a1?1 a2?2 a3?3 .. ai?i)

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• http//www.bkla.com/reverb.htmReverb20Demos
• http//hyperphysics.phy-astr.gsu.edu/hbase/hframe.
  html
• Look under sound and hearing
• http//www.customaudiodesigns.co.uk/diffusers.htm
• Or any book on the reading list