Acoustics
Reflection, Diffraction, Refraction,
Diffusion
Reflection of Sound


If a sound is activated
in a room, sound
travels radially in all
directions. As the
sound waves
encounter obstacles or
surfaces, such as
walls, their direction
of travel is changed,
i.e., they are reflected.
The diagram shows
the reflection of waves
from a sound source
from a rigid, plane
wall surface.
Reflections from Flat Surfaces
Like a mirror, the reflected wavefronts act as
though they originated from a sound image.
 The image source is located the same distance
behind the wall as the real source is in front of
the wall.
 Below 300 – 400 Hz, sound is best considered
as waves. Sound above 300 – 400 Hz is best
considered as traveling in rays.
 The mid/high audible frequencies have been
called the specular frequencies because sound
in this range acts like light rays on a mirror.

Angle of Reflection
Sound follows the
same rule as light:
the angle of incidence
is equal to the angle
of reflection.
 The pressure at the
face of a perfectly
reflecting surface is
twice that of a
perfectly absorbing
surface.

Reflections from Convex Surfaces
Reflection of plane
wavefronts of sound
from a solid convex
surface tends to
scatter the sound
energy in many
directions.
 This amounts to a
diffusion of the
impinging sound.

Reflections from Concave Surfaces
Plane wavefronts
of sound striking
a concave surface
tend to be
focused to a
point.
 The precision
with which sound
is focused is
determined by
the shape of the
concave surface.

Reflections from Parabolic Surfaces
A parabola has the
characteristic of
focusing sound
precisely to a point.
 This concept is used
in microphone design
to create highly
directional
microphones known
as parabolic mics.

Standing Waves

The concept of standing waves is directly
dependent on the reflection of sound.

A standing wave is a resonance condition
in an enclosed space in which sound
waves traveling in one direction interact
with those traveling in the opposite
direction, resulting in a stable condition.
Reflection of Sound from
Impedance Irregularities

Mismatches in impedance give rise to reflections,
which cause numerous undesirable effects, but
can sometimes be desirable effects instead.

Example: when a sound wave (noise) traveling
in an air conditioning duct suddenly encounters
the large open space of the room, the
impedance mismatch reflects a significant
portion of the sound back toward the source.
This is considered a desirable effect due to the
fact that the air conditioning noise is reduced.
Diffraction of Sound

Wavefronts and rays of sound travel in
straight lines, except when something gets
in the way.

Obstacles can cause sound to be changed
in its direction from its original path.

The process by which this change of
direction takes place is called diffraction.
Diffraction and Wavelength
Obstacles capable of diffracting (bending)
sound must be large compared to the
wavelength of the sound involved.
 The effectiveness of an obstacle in
diffracting sound is determined by the
acoustical size of the obstacle.
 Acoustical size is measured in terms of the
wavelength of the sound.

Some Examples of Diffraction

In figure A, the upper edge of the
wall acts as a new, virtual source
sending sound energy into the
“shadow” zone behind the wall.

In figure B, most of the sound
energy is reflected from the wall
surface, but that small portion
going through the hole acts as a
virtual point source, radiating a
hemisphere of sound into the
“shadow” zone behind the wall by
diffraction.
Diffraction by Large and Small Apertures

In figure A,
the arrows
indicate that
some of the
energy in the
main beam is
diverted into
the shadow
zone.
Diffraction of Sound by Obstacles

In figure A
the obstacle
is so small
compared to
the
wavelength
that it has no
appreciable
effect on the
passage of
sound.
Diffraction by Acoustic Lens
Diffraction around the Human Head
For frequencies
1 – 6 kHz
arriving from
the front,
sound pressure
changes around
the head.
 At frequencies
below 1 kHz,
sound pressure
change is
negligible.

Refraction of Sound

Diffraction is changing the direction of
travel of sound by encountering sharp
edges and physical obstructions.

Refraction changes the direction of travel
of the sound by differences in the velocity
of propagation.
Refraction of Light

The visual
distortion that
occurs when an
object is placed
in the water at
an angle is due
to refraction of
the light waves
in the denser
medium.
Refraction of Sound in Solids

Sound waves
traveling
through
materials at an
angle will bend
when they
encounter a
different
material of
greater or lesser
density.
Speed of Sound

Some
examples of
the speed of
sound based
on density.
Refraction of Sound in the
Atmosphere
The atmosphere
is anything but
a stable,
uniform medium
for the
propagation of
sound.
 The diagram
shows refraction
due to
temperature
gradients.

Another Example

This diagram
shows refraction
of sound
radiated
upwards.

Note the “sound
shadow” due to
refraction near
the ground.
Wind Gradients

Outdoors,
wind
usually
plays a
bigger
role in
refraction
of sound.
Diffusion of Sound

Sound diffusion is the spreading out or
scattering of sound waves or rays in many
different directions.

Diffusion problems are most troublesome
in smaller rooms and at the lower audio
frequencies.

The problem with small spaces is that
modal spacings below 300 Hz guarantee a
sound field far from diffuse.
The Perfectly Diffuse Sound Field

Even though unattainable, it is instructive to
consider the characteristics of a diffuse sound
field. Randall and Ward have given us a list of
these characteristics:
– The frequency and spatial irregularities
obtained from steady state measurements
must be negligible
– Beats in the decay characteristic must be
negligible
– Decays must be perfectly exponential
(straight lines on a logarithmic scale)
The Perfectly Diffuse Sound Field
– Reverberation time will be the same at
all positions in the room
– The characteristic of the decay will be
essentially the same for different
frequencies
– The characteristic of the decay will be
independent of the directional
characteristics of the measuring
microphone
Evaluating Diffusion in a Room

The
loudspeaker
and
microphone
were placed in
opposing
corners
because all
room modes
terminate in
the corners.

The
fluctuations in
this response
cover a range
of about 35 dB.
Decay Beats

As discussed
earlier, decay
beats induced
by closely
spaced modes
cause
irregularities in
decay,
especially at
low
frequencies.
Exponential Decay
A truly
exponential
decay is a
straight line on a
level vs. time
plot.
 This decay shape
is probably a
mode or group
of modes
encountering low
absorption.

Another Example

This decay
shape is due to
an acoustically
coupled space.
Adjustable Acoustics

The inconsistency
of decay time at
lower frequencies
indicates a nondiffuse condition.
Room Shape

The popularity of rectangular rooms is due
in part to economy of construction, but it
has its acoustical advantages.

The relative proportioning of length,
width, and height of a sound sensitive
room is most important.

Some shapes, like parabola, can be
eliminated because they focus sound,
which is the opposite of diffusion.
Optimal Room Proportions

This table
shows
several
“optimal”
room
ratios as
proposed
by four
different
studies.
Optimal Room Proportions

Another study shows
ideal room ratios. This
study was done by
Bolt and is referred to
as the “Bolt Area.”
Nonrectangular Rooms

Splaying one or two walls of a sound-sensitive
room does not eliminate modal problems,
although it might shift them slightly and produce
somewhat better diffusion.

Flutter echoes definitely can be controlled by
canting one of two opposing walls. The amount
of splaying is usually between 1 foot in 20 feet
and 1 foot in 10 feet.

Making the sound field asymmetrical by splaying
walls only introduces unpredictability in listening
room and studio situations.
Geometrical Irregularities

Many studies have been made on what type of
wall diffusors provide the best diffusing effect.

Geometrical diffusors must be at least 1/7th of a
wavelength before their effect is noticed.

Studies have shown that the straight sides of the
rectangular shaped diffusor provide the greatest
effect for both steady-state and transient
phenomena.
Rectangular Wall
Panels

Rectangular sound
absorbing panels with
wood edges are an
inexpensive way to
achieve both
absorption and
diffusion.
Convex vs. Concave Surfaces
The Poly vs. Planar Diffusion

Favorable
reflection,
absorption, and
reradiation
characteristics
favor the use of
the cylindrical
surface over the
planar surface.
The Schroeder Diffusor
Manfred
Schroeder
pioneered the
concept of
acoustic
diffusors.
 The diagram
shows his
first design.

Commercial Diffusors

There are many companies now
manufacturing various types of diffusors,
available through pro audio stores, mail
order, or on-line sales.

The best diffusors are made by companies
with years of research and experience
backing their product.

Choosing a product will depend on budget
and specific diffusion needs.
Types of Diffusors

The most common types of commercially
available diffusors are:
– Reflection Phase-Grating (RPG)
– Quadratic-Residue (QRD)
– Diffractal (DFR)
QuadraticResidue
Diffusors

RPG Diffusor
Systems, Inc. is a
leading
manufacturer of
diffusion devices.
Dispersion Pattern

The hemidisc
pattern is
shown here.
More RPG
Products

Three different types
of diffusors are shown
here.
Diffractal
Diffusion

This design utilizes
three different
frequency ranges of
diffusion.
Diffractal
Diffusion

Another
example
Diffusion in Three Dimensions

Hemicylindrical and Hemispherical diffusion.