VCE PHYSICS

1
VCE PHYSICS

• Unit 4
• Topic 3
• SOUND

2
UNIT OUTLINE

• To achieve this outcome students should
  demonstrate the knowledge and skills to
• explain sound as the transmission of
  energy via longitudinal pressure waves
• mathematically model the relationship between
  wavelength, frequency and speed of propagation of
  sound waves using v f?
• explain the difference between sound intensity
  (Wm-2) and sound intensity level (dB)
• calculate sound intensity at different distances
  from a source using an inverse square law.
• explain resonance in terms of superposition of a
  travelling sound wave and its reflection
• analyse, for strings and open and closed resonant
  tubes the fundamental as the 1st harmonic and
  subsequent harmonics
• explain qualitatively, in terms of electrical and
  electromagnetic effects the operation of
• microphones, including electret - condenser,
  crystal, dynamic and velocity microphones
• dynamic loudspeakers
• explain qualitatively the effects of baffles and
  enclosures for loudspeakers
• interpret frequency response curves of
  microphones, speakers, simple sound systems and
  hearing including loudness (phon)
• evaluate the fidelity of microphones and
  loudspeakers in terms of purpose, frequency
  response and qualitatively construction
• interpret qualitatively the directional spread of
  various frequencies in terms of different gap
  width or obstacle size including the significance
  of the magnitude of the ?/w ratio
• use safe and responsible practices when working
  with sound sources and sound equipment

3
Chapter 1

• Topics covered
• Wave nature of Sound.
• Transverse Waves.
• Longitudinal Waves.
• Sound Production, Transmission, Detection and
  Absorption

4
1.0 The Wave Nature of Sound

• Waves are a method of TRANSFERRING ENERGY from
  one place to another.
• Some waves (eg. Sound, Water Waves) need a MEDIUM
  through which to travel.
• The MEDIUM (eg. air, water), although disturbed
  by the passage of the waves, does NOT suffer any
  PERMANENT DISTORTION due to the waves movement
  through it.

Sound Waves require matter (either solid, liquid
or gas) as their medium This means, of course, no
one can hear you scream in space.
There are two basic types of waves TRANSVERSE
WAVES. LONGITUDINAL WAVES.
5
1.1 Transverse Waves

• Transverse waves are characterised by having the
  individual particles of the medium through which
  the wave travels, moving perpendicular to the
  direction of motion of the wave.

1.1 Transverse Waves
Notice the medium does not move along with the
wave. Pick a spot and follow its motion.
6
1.2 Longitudinal Waves

• LONGITUDINAL WAVES are characterised by having
  the individual particles which make up the medium
  through which the wave travels, moving parallel
  to the direction of motion of the wave.

Sound is a LONGITUDINAL WAVE.
Again, notice the medium does not move along
with the wave. Pick a spot and follow its motion.
7
Question 1 In the sentences below, options are
given within the brackets. Only one of the
options will be correct. Circle the best
option. A sound wave is a torsional /
transverse / longitudinal wave in which the air
particles move at right angles to / parallel to
/ by spiralling around the direction of
propagation of the wave. The wave transmits
energy / air particles / wave maxima from the
source to the receiver.
8
1.3 Sound Production
Sound is produced by making an object vibrate
(move backward and forward). As the object
vibrates back and forth, it pushes on the air
particles immediately next to it, creating a
series of COMPRESSIONS and RAREFACTIONS which
move outward from the source.
This moving chain of compressions and
rarefactions form a Sound Wave.
The faster the object vibrates, the higher the
frequency of the sound.
9
Consider a dust particle one metre in front of a
loudspeaker that is producing a constant tone
sound wave.
Question 2 Which one of the following statements
and diagrams (A to D below) best describes the
motion of the dust particle?
10
1.4 Sound Transmission

• Sound is transmitted from one place to another
  through a MEDIUM.
• The medium may be solid, liquid or gas.
• Generally the DENSER the medium the FASTER the
  speed of sound.
• Sound is transmitted through a medium by causing
  the particles of the medium to be disturbed from
  their mean or average positions as the wave
  passes by.
• The particles making up the medium DO NOT move
  along with the sound wave.
• The medium suffers no permanent effect from
  having a sound wave pass through it.

11
A particle of dust is floating at rest 10 cm
directly in front of a loudspeaker that is not
operating. The loudspeaker then emits sound of
frequency of 10 Hz and speed of 330 ms1.
Question 3 Which one of the following statements
best describes the motion of the dust
particle? A. It vibrates vertically up and down
at 10 Hz remaining on average 10 cm in front of
the loudspeaker. B. It vibrates horizontally
backwards and forwards at 10 Hz remaining on
average 10 cm in front of the loudspeaker. C. It
travels away from the loudspeaker at 330 ms1
while moving horizontally backwards and forwards
at 10 Hz. D. It remains at rest.
12
1.5 Sound Detection

• Sound is detected by making a receiver vibrate.
• Sound detection occurs in devices such as
  microphones where incoming sound waves cause the
  production of an electrical signal.
• Sound is detected by humans using our ears, in
  particular our Cochlea, a circular canal lined
  with clumps of hairs. Each hair clump is designed
  to react to a particular frequency.
• Sound Level Meters are used to measure Sound
  Intensity Levels, which are displayed in decibels
  (dB).
• The output from most sound level meters is
  adjusted to mirror the ears response by using
  the so called dB(A) scale. (see Slide 3.4 -
  Frequency Response Graphs)

13
1.6 Sound Absorption

• When a sound strikes a barrier, it is either
  reflected off, transmitted through or absorbed
  by, that barrier.
• The amount of reflection, transmission or
  absorption depends upon the nature of the
  barrier.
• The physical absorption of sound, as measured by
  the ABSORPTION COEFFICIENT (A.C.), occurs when
  the energy of the wave is transformed into other
  forms of energy (eg. Heat) within the absorbing
  material.
• The A.C. varies with frequency.
• Hard, rigid, non-porous materials have low A.C.s
• Soft, pliable, porous materials have high A.C.s

14
Chapter 2

• Topics covered
• Amplitude.
• Period.
• Frequency.
• Wavelength.
• Wave Speed.
• Sound Waves in Air.

15
2.0 Amplitude
Amplitude is a measure of the size of a
disturbance above or below a mean or average
value. In sound wave representations, the
amplitude is measured as a variation in air
pressure (?P), above or below the normal
atmospheric pressure.
This method allows sound to be presented as a
transverse rather than a longitudinal wave.
The unit for ?P is the PASCAL (1 Pa 1 Nm-2).
Human ears interpret Amplitude as the Loudness
of a sound Large amplitude loud sound, Small
amplitude soft sound
16
2.1 Frequency

• Frequency (symbol f ) is most generally defined
  as the number of events which occur during a time
  interval.
• In terms of Sound Waves it represents the number
  of complete sound waves passing a given point in
  a given time.
• In the SI system, frequency is defined as the
  number of events or cycles per second.
• The UNIT for frequency is the HERTZ (Hz), where 1
  Hz 1 cycle per second

Human ears interpret frequency as the pitch of
a sound High frequency high pitch, Low
frequency low pitch
17
2.2 Period

• Period (symbol T) is defined as the time it takes
  for one event to occur.
• It is the time it takes for one complete sound
  wave to pass a given point.
• Period is the measure of a time interval, thus
  has the unit seconds (s).
• Period and frequency are the inverse of one
  another thus

Period (T) 0.02 s f 1/T
1/0.02 50 Hz
Thus, a wave of period 0.02 s has a frequency of
50 Hz
18
2.3 Wavelength

• Wavelength, (symbol ?, Greek Letter LAMBDA), is
  a measure of the distance between two adjacent
  points on a wave undergoing similar motions.
• Thus the distance between two adjacent
  compressions or two adjacent rarefactions would
  be 1 wavelength.

Wavelength is a distance measure, hence the unit
for ? is metres (m).
19
Rachel and Bruce have assembled some laboratory
equipment and are planning a series of
sound-related experiments.
An audio-signal generator is used to drive a
small loudspeaker, which emits sound uniformally
in all directions. The audio power from the
loudspeaker is kept constant at all frequencies
used in the experiments. A sound level meter is
used to measure sound intensity. This is shown in
Figure 2.
Initially, the frequency of the signal generator
is set to 476 Hz. The speed of sound at the time
of the experiment was 340 ms-1. Question
4 Calculate the wavelength of the 476 Hz sound
wave. Include a unit in your answer.
? v/f 340/476 0.71 m
20
2.4 Wave Speed
The relation is summarised in the so called WAVE
EQUATION, v f?
Wave Speed (symbol v) is a measure of how
quickly a wave train is moving.
where v Speed (ms-1),
f Frequency (Hz) ?
Wavelength (m).
The wave speed is dependent on the frequency and
wavelength of the wavetrain.
The speed of Sound in Air is temperature
dependent and is approx 340 ms-1 at 200C
Sound travels faster through denser mediums
21
Roger, an instrument maker, is constructing and
testing pipes for a pipe organ. He measures the
speed of sound in air at the time of the test to
be 333 ms1. Question 5 One pipe is designed to
produce the note middle C (256 Hz). Which one of
the following best gives the wavelength
corresponding to middle C? A. 0.38 m B. 0.77 m C.
1.3 m D. 2.6 m
22
2.5 Sound Waves in Air
This means the air particles must vibrate back
and forth around their MEAN, AVERAGE or CENTRAL
POSITION.
In air, the passage of a sound wave causes a
series of COMPRESSIONS and RAREFACTIONS
In areas of above average air pressure
(Compressions), the particles are packed CLOSE
TOGETHER. So only small scale vibrations are
needed for them to transfer their information
(sound wave energy), to adjacent particles.
In areas of below average air pressure
(Rarefactions) the particles are SPREAD APART. So
large scale vibrations are needed for information
to be transferred to adjacent particles.
The energy lost per transfer is high and so sound
travels a lesser distance than at normal air
pressure.
Energy lost per transfer is low and the sound
travels a greater distance than at normal air
pressure
23
Chapter 3

• Topics covered
• Sound Intensity.
• Sound Intensity Level.
• The Decibel Scale.
• Frequency Response Graphs.
• Sound Intensity versus Distance
• Human Response

24
3.0 Sound Intensity

• The INTENSITY of a sound is DEFINED as THE RATE
  OF FLOW OF ENERGY through an area perpendicular
  to the direction of travel of the sound wave.

The rate of flow of energy is the definition of
POWER. In this case the power is ACOUSTICAL
POWER. Thus SOUND INTENSITY is defined as
POWER/AREA.

• Mathematically
  I P/A Where,
• I Sound Intensity (Wm-2)
• P Total Acoustical Power (W)
• A Area (m2)

25
It is a cold, windless morning and three hot-air
balloons hover above a park. Each balloon is
stationary and in direct line of sight, with no
obstacles near them, as shown in Figure 3.
Balloon A is equipped with a 100 W siren, which
emits a 2000 Hz tone uniformally in all
directions. On board balloons B and C are
students with sound measuring equipment.
Question 6 Which of the following is the best
estimate of the sound intensity of the siren as
measured at balloon B? A. 0.5 Wm-2 B. 2.5 10-2
Wm-2 C. 8.0 10-4 Wm-2 D. 2.5 10-5 Wm-2
100 W spread over a sphere of radius 100 m gives
a sound intensity of 100/(4p(100)2) 8.0 x 10-4
Wm-2
26
3.1 Bels
The Bel (symbol B) is a unit of measurement of
ratios, such as power levels and voltage levels.
It is mostly used in telecommunications,
electronics and acoustics.
It was invented by engineers at the Bell
Telephone Laboratory to quantify (give a number
to) the reduction in audio level over a 1 mile
length of standard telephone cable. It was named
in honour of Alexander Graham Bell.
The bel was too large for everyday use, so the
decibel (dB), equal to 0.1 Bel, became the more
commonly used unit.
27
3.2 Decibels
We could use scientific notation, but a
comparison between 2.3 x 101 and 4.7 x 1012 is
still awkward. For convenience, we find the
RATIO between the two numbers and convert that
into a logarithm.
The decibel is not a unit in the sense that a
metre or a kilogram is. Metres and kilograms are
defined quantities of distance and mass. They
never change. A decibel is a RELATIONSHIP
between two values of POWER.
11.3 B
Decibels are designed for talking about numbers
of vastly different magnitudes, eg., 23 Watts vs.
4,700,000,000,000 Watts. With such vast
differences, the most difficult problem is
getting the number of zeros right.
To make life a little easier, we can get rid of
the decimal by multiplying the result by 10, so
So comparing the numbers above on this basis, you
find that the larger number is 113dB bigger than
the smaller number.
28
3.3 Sound Intensity Level

• Sound Intensity measured in Wm-2 and Sound
  Intensity Level measured in decibels (dB) are NOT
  the same.
• Sound Intensity Level is DEFINED as the Logarithm
  of the ratio of the intensity of a sound to that
  of a reference sound.
• The intensity of the reference sound has a value
  of 1 x 10-12 Wm-2, and is the minimum audible
  sound intensity at 3000 Hz. Corresponds to
  displacement of air particles by 100 billionth
  of a metre.
• The decibel scale ranges from 0 dB (the softest
  audible sound) to approx 140 dB (sound causing
  pain/ear damage)

Mathematically S.I.L. 10 Log
I
Io
where S.I.L.
Sound Intensity Level (dB) I
Sound Intensity (Wm-2) Io
1 x 10-12 Wm-2
29
An isolated siren emits sound of 3000 Hz
uniformly in all directions. At a point 20 m from
the siren, the sound intensity is measured to be
1.0 103 Wm2. Question 7 Which one of the
following best gives the sound intensity level
(in dB) at this point? A. 1.0 103 dB B. 9.0
dB C. 90 dB D. 100 dB The sound intensity is
measured at a distance of 60 m from the
siren. Question 8 Which one of the following
best gives the sound intensity (in Wm2) at 60
m? A. 3.3 103 Wm2 B. 1.1 104 Wm2 C. 3.0
102 Wm2 D. 9.0 103 Wm2
30
3.4 Comparing Sound Intensity Levels

• The Sound Intensity Level formula can also be
  used to determine CHANGES in dB levels between
  two intensities labelled I1 and I2.
• Thus the equation becomes
• SIL 10 Log I2/I1
• When used in this form, the reference term (Io)
  is not used, and I1 and I2 are the two sound
  intensities being compared.

Let I1 1 Wm-2 and I2 10 Wm-2 S.I.L. 10
Log I2/I1 10 Log 10/1 10 dB
This 10 dB increase in S.I.L. is perceived by the
Human Ear as a Doubling in the LOUDNESS of the
sound. In fact, every 10 dB increase leads to a
doubling of the loudness. So an 80 dB sound will
be perceived as twice as loud as a 70 dB sound
NOTE Loudness is a subjective, non measurable
quantity, used by humans to characterise and
compare sounds.
31
3.5 The Decibel Scale
Remember when comparing S.I.Ls we use SIL 10
Log I2/I1

• The decibel scale is used for a number of
  reasons
• 1. The human ear responds to a vast range of
  sound intensities (from 10-12 Wm-2 to 102 Wm-2 -
  a range of 1014 or one hundred thousand billion
  units).
• 2. In order to bring this range to a more
  manageable size, the log of intensities is used,
  so the range now becomes 0 dB to 140 dB.
• 3. Luckily the ear also responds to sound
  intensities in a logarithmic rather than a linear
  fashion, as shown in last section.

Let I1 100 Wm-2 and I2 200 Wm-2 S.I.L.
10 Log I2/I1 10 Log 200/100 3 dB
Thus, if the sound intensity doubles, this leads
to a 3 dB increase in S.I.L. This is about the
smallest change in S.I.L. detectable by the human
ear.
So, if you replace your 100 W speakers with far
more expensive 200 W ones, you will barely notice
any difference !!!!!!
32
Question 9 By how many decibels will the sound
intensity level at balloon C be lower than at
balloon B?
Doubling the distance quartered the intensity.
Each time the intensity was halved the sound
level reduced by 3 dB, so the total reduction was
6 dB.
Balloons B and C move so that they are at equal
distances from balloon A. The sound intensity at
balloon C is now measured as 1.0 10-2 Wm-2.
Question 10 What is the sound intensity level
(dB) at balloon B?
SIL 10 log I/Io 10 log (1.0 10-2 )/(1.0
10-12) 100 dB
33
3.6 Frequency Response Graphs

• The Human Ear and various Musical/Electrical
  devices (eg. Microphones) respond to different
  Audible Frequencies in different ways.
• We dont hear each frequency with equal loudness.
• In order for the Ear to perceive various
  frequencies at the SAME LOUDNESS, they must be
  played at VARYING SOUND INTENSITY LEVELS.
• This is best shown on a Frequency Response Graph

Thus a 20 Hz sound needs to be played at 25 dB
for the ear to hear it
at the same loudness as a 4000 Hz sound played at
1 dB
The ear is most sensitive at the lowest point
on the graph in this case 4000 Hz.
34
3.7 Sound Intensity vs Distance
If a sound source is small (a so called POINT
SOURCE), the sound it produces radiates out
equally in all directions. This has the effect
of producing an expanding sphere of sound. (NB.
The surface area of a Sphere 4?r2)
If the source is operating at a fixed power
level, the sound intensity/unit area will
decrease as the area (of the expanding sphere)
increases. The rate at which the intensity drops
off is inversely proportional to the square of
the distance from the source Mathematically I
? 1/r2
So doubling the distance from the source leads to
the intensity dropping in to ¼ of its original
value.
35
At a distance of 4.0 m from a loudspeaker, a
sound intensity of 1.25 x 10-4 Wm-2 is detected.
Question 11 What sound intensity would be
detected at 1.0 m from the source?
I ? 1/r2, therefore, decreasing distance to one
quarter increases intensity by a factor of 16. 16
x 1.25 x 10-4 2.0 x 10-3 Wm-2
Question 12 What sound intensity level would be
detected at 1.0 m from the source?
SIL 10 log I/IO 10 log (2.0 x 10-3)/(1.0 x
10-12) 93 dB
36
3.8 Human Response
The human ear responds to sound in the range from
about 20 Hz to 20 kHz.
The ear is most sensitive at about 4 kHz and has
the lowest threshold of pain at the same
frequency
The distance between the red and green lines
represents the range of audible sound for each
frequency
37
3.9 Phons
The ear is not equally responsive to all
frequencies.
The curves represent equal loudness as perceived
by the average human ear
The Phon is defined as a unit of apparent
loudness, equal in number to the intensity in dB
of a 1 kHz tone judged to be as loud as the sound
being measured.
The ear is less sensitive to low frequencies and
this discrimination against lows becomes steeper
for softer sounds
Sound intensity in dB does not reflect changes
in the ears sensitivity with frequency and sound
level
Curve for the threshold of hearing
Thus 50 phon means as loud as a 50 dB, 1kHz
tone
and 100 phon means as loud as a 100 dB, 1 kHz
tone
38
The graph in Figure 1 shows the relationship
between sound intensity level (dB), frequency
(Hz) and loudness.
Sound intensity level (dB) of a note of 10 000 Hz
is measured by a sound meter to be 60
dB. Question 13 Which one of the values below
best gives the loudness in phon at this point? A.
20 phon B. 40 phon C. 60 phon D 80 phon
Question 14 The loudness scale (phon)
specifically takes account of which one of the
following factors? A. Intensity of sound, as
perceived by human hearing, is inversely
proportional to distance from the source. B. The
perception of sound by human hearing is
logarithmic, rather than linear, compared to
sound intensity. C. The perception of the
intensity of sound by human hearing varies with
frequency. D. Human hearing has a very limited
range of frequencies that it can hear.
39
Chapter 4.

• Topics covered
• Reflection.
• Refraction
• Diffraction.
• Superposition.
• Interference.

40
4.0 Reflection

• Sound (like any other wave) undergoes reflection
  when it strikes a wall or barrier.
• It will follow the laws of reflection
  ? i ?r
• where ?i is measured between the direction of the
  incoming wave train and the Normal and ?r is
  measured between the Normal and the direction of
  the reflected sound waves.

41
Two physicists are discussing the design of a new
theatre for use by a school choir. The design
requirement is for good acoustic properties in
particular, for even distribution of sound over
the whole frequency range throughout the
theatre. A plan of the theatre to be used is
shown in Figure 2.
One of the physicists wants to line the walls of
the audience area of the theatre with heavy
sound-absorbing curtains. Question 15 Which one
of the following states why this is a good
idea? A. The curtains will reduce the effect of
diffraction through the stage opening, hence
producing better quality sound. B. Without the
curtains, different frequencies will reflect
differently from the walls, causing distortion
due to diffraction effects. C. Without the
curtains, different frequencies will reflect
differently from the walls, causing distortion
due to interference effects. D. Without the
curtains, there would be multiple paths from the
speaker to each member of the audience, thus
causing distortion and sound loss due to
interference effects in some parts of the theatre.
42
4.1 Refraction
Refraction is the bending of waves when they
enter a medium where their speed is different
More Dense Medium
Sound waves, unlike light waves, travel faster in
denser materials, such as solids and liquids,
than they travel in air.
When sound waves leave a solid, their velocity
and wavelength decrease and they are bent
towards the normal to the surface of the solid.
Less Dense Medium
For sound waves in air, their speed is
temperature dependent. (v 331 0.6T)
During a temperature inversion, the sound will
refract back toward the ground.
For normal conditions sound will refract away
from the ground, producing a sound shadow as shown
43
4.2 Diffraction
For visible light, ? is about 550 nm or 5.5 x
10-7 m, so it needs to pass through a VERY NARROW
gap to produce a diffraction effect.
Diffraction is a phenomenon demonstrated by all
waves and is best described as the bending of
waves as they pass around objects or through
gaps or openings.
The extent of diffraction depends on the ratio
between the wavelength of the wave and the size
of the object, gap or opening. This is called the
?/w ratio
Diffraction is rarely seen or experienced in the
visual world but is part of everyday experience
in the aural (hearing) world.
For sound of frequency 4000 Hz (when the ear is
at its most sensitive), ? 8.75 cm, so sound
can (and does) diffract around everyday objects.
44
4.3 Diffraction Around Corners

• Since sound waves have wavelengths in the
  centimetre to metre range, sound can, and does,
  suffer diffraction in the world in which we live.

• This is because the houses we live in, and the
  objects we surround ourselves with, have similar
  dimensions to the wavelengths of sound.

He can hear what the ladies are talking about
without being able to see them
We can hear mum shouting to turn down the stereo
in part because her sound waves are diffracted
around the house.
45
4.4 Diffraction through Gaps
When a series of straight waves approaches a gap,
such as a doorway, those waves will suffer a
change in direction in passing through the gap,
ie. they will suffer diffraction.
The EXTENT OF DIFFRACTION depends upon the ratio
of wavelength (?) to the gap width (w). If the
wavelength and gap are about the same size,
appreciable diffraction will occur.
If ? is very much bigger (or smaller) than w, no
diffraction effects will occur. Thus 1. Maximum
diffraction occurs when ?/w is between about 0.1
and 50 2. No diffraction effects occur when ?/w
?? 1 or ?/w ?? 1
46
Question 16 In the paragraph below, options to
complete each sentence are given within the
brackets. Circle the correct option in each
case. Jamie is listening to the sound of an
orchestra through a small gap in a partly open
sliding door. When the sound wave travels through
the gap,constructive interference /
destructive interference / diffraction occurs
and spreading of the wave results. High pitched
(frequency) instruments such as flutes
experience more / the same / less spreading
than lower pitched instruments. As the size of
the gap decreases, the angle of spreading will
increase / not change / decrease.
47
4.5 Diffraction Effects
An observer at A will hear both high and low
frequency sounds
Band
An observer at B will hear low frequency sound
ONLY
High Frequency sounds suffering less diffraction
are said to be much more directional or line
of sight. This is one of reasons we can hear the
low frequency (bass) sounds but not hear the high
frequency (treble) sounds coming from a party a
few streets away on a Saturday night.
Since wavelength and frequency are so closely
related, the extent of diffraction for sound can
be thought of in terms of the frequency of
sound. Low Frequency (Bass) sounds are generally
diffracted by a greater amount than High
Frequency (Treble) sounds.
48
Question 17 A Speaker system uses a single,
wide-frequency response speaker. Explain why the
quality (fidelity) will deteriorate as the
listener moves off the centreline. Hence explain
why a multiple-loudspeaker system, as shown in
Figure 1, would be more satisfactory.
The amount of diffraction depends on the ratio
?/w. For a single speaker, the high frequencies
would not diffract away from the centre line as
much as the low frequencies. Using different
speaker sizes for different frequency ranges
would ensure that comparable spreading will occur
for all frequencies.
49
Chapter 5

• Topics Covered
• Superposition
• Standing Waves
• Standing Waves on Strings.
• Standing Waves in Open and Closed Pipes.
• Overtones Harmonics.
• Resonance.

50
5.0 Superposition
Two or more waves occupying the same space will
interact to form a single, composite or total
wave which reflects the size and orientation of
the individual waves making it up.
This addition process is called SUPERPOSITION.
Superposition is a VECTOR addition process, so
wave orientation as well as amplitude are
important
Destructive Superposition
Constructive Superposition
DESTRUCTIVE SUPERPOSITION occurs when two waves
with opposite orientations add.
CONSTRUCTIVE SUPERPOSITION occurs when two waves
with similar orientations add.
51
5.1 Standing Waves
Standing waves are produced when two identical
wave trains travelling in opposite directions
interact with one another (undergo Superposition)
to produce a so called Standing Wave Pattern.
The whole pattern remains fixed in space as
long as the frequencies of the two travelling
wave trains remain constant.
Adjacent Nodes N in a Standing Wave Pattern are
½? apart. Similarly Antinodes A are also ½?
apart.
This then makes an adjacent Node and Antinode ¼?
apart.
52
Two speakers facing each other are connected to
the same signal generator/amplifier and are
producing 340 Hz.
Question 18 Assume the speed of sound is 340
ms-1. Mary stands in the centre, equidistant to
speakers A and B. She then moves towards speaker
B and experiences a sequence of loud and quiet
regions. She stops at the second region of
quietness experienced. How far is she from
speaker B? Explain your reasoning.
Being connected to a common source, the speakers
will be in phase, ensuring the midpoint is an
antinode or a region of loudness. The distance
between successive antinodes is ?/2, and ?/4
between an antinode and an adjacent node.
Accordingly, Mary has moved 3?/4 from the
central antinode to the second node. Since ?
1.0 m, she has moved 0.75 m toward B and
therefore is 5.0 0.75 or 4.25 m from B
53
5.2 Standing Waves - Strings
2. First Overtone
1. Fundamental Frequency
For a string FIXED AT BOTH ENDS
Simplest Standing Wave Pattern for a string fixed
at both ends Length of string L ?/2 Thus ? 2L
and from v f ? we get f v/2L This is
the Fundamental Frequency (f1)
Now, L ? Thus, f v/L 2f1 and 1st overtone
2f1
1. All OVERTONES exist
2. Nth Overtone (N 1) x Fundamental Freq.
4. Third Overtone
3. Second Overtone
L 2? Thus, f 2V/L 4f1 3rd Overtone 4f1
Now L 3?/2 Thus, f 3V/2L 3f1 So, 2nd
Overtone 3f1
54
5.3 Standing Waves - Open Pipes
FUNDAMENTAL FREQUENCY

• Simplest Standing Wave in an open pipe.
• Pressure node at each end, pressure antinode in
  middle.
• Length of pipe, L ?/2
• Thus ? 2L, and from v f ? we get f
  v/2L
• This is called The Fundamental Frequency (f1)
  for this pipe.

For a pipe OPEN AT BOTH ENDS 1. All OVERTONES
exist 2. Nth Overtone (N 1) x Fundamental
Freq. 3. The Fundamental and ALL Overtones can
exist in the pipe AT THE SAME TIME.
55
Question 19 The fundamental of a bugle is 88 Hz.
Other notes easily produced by a bugle have
frequencies of 264 Hz, 352 Hz and 440 Hz. Should
the bugle be modelled as an open or a closed
pipe? Justify your answer. Take the speed of
sound in air as 340 ms-1 .
The fundamental frequency for the bugle f1
88Hz. The other easily produced notes are 264Hz
3f1, 352Hz 4f1 440Hz 5 f1 and hence the
bugle is an open pipe since there is an even
harmonic produced.
Question 20 Calculate the length of the air
column in the bugle. You may neglect any end
correction.
For the fundamental freq L ?/2 ? v/f
340/88 3.86 m L ?/2 3.86/2 1.93 m
F
56
Sarah is planning to buy some plastic pipe from a
hardware store. To measure the length of the
pipe, she intends to blow across one end of the
pipe and measure the frequency of the resonance
produced. The shop owner questions this method,
but in the end agrees to let her perform the
measurements. Sarah takes a section of pipe open
at both ends, and performs the measurements. A
clear resonance of 200 Hz can be heard. Question
21 Use this information to determine the length
of the pipe. Show your working/reasoning. (speed
of sound 340 ms-1)
v f? ? ? v/f 340/200 1.7 m
An open/open pipe has L ?/2 ? L 1.7/2 0.85
m
57
Question 22 At which one or more of the following
frequencies could Sarahs pipe also resonate? A.
300 Hz B. 400 Hz C. 500 Hz D. 600 Hz
Question 23 Briefly explain resonance in terms of
the behaviour of the sound waves in a tube open
at both ends.
Since the pipe was open at both ends, all
harmonics were possible. Resonance is the
matching of frequency between the natural
frequency of the tube and the frequency within
the source of the excitation, the blowing across
the tube. (1) At an open end there is a
pressure node, the distance between adjacent
nodes is half a wavelength, (1) so this
determines the natural frequency of the tube.
(1).
58
5.4 Standing Waves - Closed Pipes

• Simplest Standing Wave pattern in a Closed Pipe.
  Pressure antinode at closed end, node at open
  end.
• Length of pipe, L ?/4
• Thus ? 4L and from v f ? we get
  f v/4L
• This is called the Fundamental Frequency (f1)
  for this pipe.

FOR A PIPE CLOSED AT ONE END. 1. Only ODD
overtones exist. 2. The Nth Overtone (2N 1) x
Fund. Freq. 3. The Fundamental and all ODD
OVERTONES can exist in the pipe AT THE SAME TIME.
59
Roger, an instrument maker, is constructing and
testing pipes for a pipe organ. The pipes can be
considered to be uniform tubes open at one end
and closed at the other. Roger tests the pipe by
placing a loudspeaker attached to a very precise
audio signal generator at the open end of the
pipe, and gradually increases the frequency. He
finds that in addition to the resonance at 256
Hz, there is a higher resonance (the second
harmonic). Question 24 At which one of the
following frequencies will this second harmonic
be observed? A. 128 Hz B. 512 Hz C. 768 Hz D.
1024 Hz
60
Question 25 Which one of the following statements
best describes how Roger was able to identify
this second harmonic? A. At the frequency of this
second harmonic a standing wave is set up in the
tube. This absorbs sound energy, hence the volume
heard by Roger decreases. B. At the frequency of
this second harmonic the first harmonic is also
heard, so when Roger hears this as well, he knows
the signal generator is at a harmonic. C. At the
frequency of this second harmonic a standing wave
is set up in the tube. This causes the volume
heard by Roger to increase. D. At the frequency
of this second harmonic the fidelity (quality) of
the note changes, and Roger is able to identify
this.
Question 26 Roger is later designing a different
pipe to give a wavelength of 0.325 m. Which one
of the following lengths should Roger make the
pipe? A. 0.081 m B 0.325 m C. 0.65 m D. 1.30 m
61
5.5 Standing WavesOvertones vs Harmonics

• Overtones and Harmonics are two terms used to
  describe the same effect - standing wave
  patterns which are whole number multiples of a
  Fundamental Frequency.
• Overtones are numbered AFTER the Fundamental
  Frequency.
• Harmonics are numbered to INCLUDE the Fundamental
  Frequency

Overtones on a String. Fixed at both ends. Let
Fundamental Frequency 256 Hz Then 1st overtone
2 x 256 512 Hz 2nd overtone 3 x 256 768
Hz 3rd overtone 4 x 256 1024 Hz
Harmonics on a String. Fixed at both ends. Let
fundamental frequency 256 Hz Then 1st
Harmonic 256 Hz 2nd Harmonic 512 Hz 3rd
Harmonic 768 Hz 4th Harmonic 1024 Hz
62
5.6 Timbre
So an accordion, playing the same note, has a
different timbre to
Music, played on any musical instrument, has a
depth and resonance beyond the simple note or
tone played.
Not only that, but the same note can be played on
different instruments and sound completely
different.
Instruments all have very different qualities to
their sounds which make them distinctive these
qualities are often referred to as the
instrument's timbre.
a trumpet
The timbre for an instruments is determined by
its fundamental frequency and overtones/harmonics
all of which exist at the same time. It is the
unique combination of fundamental and harmonics
that give each musical instrument its unique
sound.
63
5.7 Resonance

• Every known object has a so called Natural
  Frequency of Vibration.
• This is the frequency with which the object
  would wish to vibrate if it has to.
• If the object is attached to an external source
  which vibrates at the objects natural frequency
  of vibration, the object will vibrate with an
  amplitude much larger than expected.
• This is because a standing wave pattern is
  set up within the object producing the large
  amplitudes observed.
• This is known as RESONANCE.

Examples of this phenomenon are The opera
singer breaking the glass.
and the Tacoma Narrows Bridge collapse in the USA
in 1940.
64
5.8 Tacoma Narrows
The bridge earned the nickname "Galloping Gertie"
from its rolling, undulating behaviour.
Motorists crossing the 2,800-foot centre span
sometimes felt as though they were travelling on
a giant roller coaster, watching the cars ahead
disappear completely for a few moments as if they
had been dropped into the trough of a large wave.
The original, 5,939 ft (1810 m) long Tacoma
Narrows Bridge opened to traffic on July 1, 1940
after two years of construction, linking Tacoma
and Gig Harbour in Washington State, USA. It
collapsed just four months later during a 68 km/h
wind storm on Nov. 7, 1940.
65
Chapter 6

• Topics covered
• Microphones
• Speakers

66
6.0 Microphones
A microphone is a device that converts sound into
an electrical signal. Microphones are used in
many applications such as telephones, tape
recorders, hearing aids, motion picture
production and in radio and television
broadcasting.
In all microphones, sound waves (sound pressure)
are translated into mechanical vibrations in a
thin, flexible diaphragm. These sound vibrations
are then converted by various methods into an
electrical signal which varies in voltage
amplitude and frequency in an analogue of the
original sound.
For this reason, a microphone is an acoustic wave
to voltage modulation transducer.
Many types of microphones exist as can be seen
67
6.1 Electret Microphones
An electret is a dielectric material that has
been permanently electrically charged or
polarised.
Capacitor microphones can be expensive and
require a power supply, but give a high-quality
sound signal and are used in laboratory and
studio recording applications.
In a capacitor microphone, also known as an
electret - condenser microphone, the diaphragm
acts as one plate of a capacitor, and the
distance changing sound vibrations produce
changes in a voltage maintained across the
capacitor plates.
Sound information exists as patterns of air
pressure the microphone changes this information
into patterns of electric current. Fidelity is
the term used for the accuracy of this
transformation, and a flat response is the most
sought after property of a microphone.
68
Question 27 Which one of the following (A to D
below) best describes the physical operating
principle of the electret-condensor
microphone? A. electromagnetic induction B.
piezo-electric effect C. capacitance D.
electrical resistance
The diagram represents a particular
microphone. Question 28 Identify the type of
microphone this diagram represents.
electret-condensor microphone?
Question 29 Describe how this microphone detects
the wave and produces the signal output.
The sound wave vibrates the diaphragm which is
permanently charged (polarised). The diaphragm
is effectively one side of a capacitor. As the
capacitance changes, a tiny current is induced
and hence a signal voltage appears across the
resistor.
69
6.2 Crystal Microphones
These microphones utilises the piezoelectric
effect. Piezo (Greek for Push) electric solids
produce a voltage between surfaces when a
mechanical stress is applied.
Sound waves cause the diaphragm to move which in
turn communicates the resulting vibration to an
attached piezo electric crystal.  Charges and
hence voltages are proportional to the crystals
bending.
Crystal microphones tend to be used for low
quality audio applications such as telephone
handsets since they dont require phantom
powering or amplification and are cheap to
produce.
The frequency response of crystal microphones is
often limited to a relatively narrow band
restricting their application.
70
6.3 Dynamic Microphones
In the dynamic microphone a small movable
induction coil, positioned in the magnetic field
of a permanent magnet, is attached to the
diaphragm.
When the diaphragm vibrates, the coil moves in
the magnetic field, producing a varying current
in the coil. Dynamic microphones are robust and
relatively inexpensive, and are used in a wide
variety of applications.
However the inertia of the coil reduces high
frequency response.
It is important to remember that current is
produced by the motion of the diaphragm, and that
the amount of current is determined by the speed
of that motion. So this type of microphone is
also known as a velocity microphone
Hence they are NOT best suited to studio
applications where quality and subtlety are
important such as high quality vocal recording or
acoustic instrument micking.
71
Question 30 Explain the operation of a dynamic
microphone.
A dynamic microphone consists of a coil of wire
inside a magnetic field. (1) The coil is made to
vibrate backwards and forwards by sound waves.
This movement within the magnetic field produces
an induced voltage that matches the variation in
sound pressure. (1)
Figure 2 shows the frequency response curve for a
dynamic microphone.
Question 31 From the data on the graph, what
makes this microphone particularly suitable for
use by a singer?
The microphone is suitable because it has a
linear response over the frequency range of the
singer.
72
6.4 Ribbon Microphones
Ribbon microphones employ electromagnetic
induction to convert sound to voltage.
A long thin strip of conductive foil moves within
a magnetic field to generate a current hence
voltage.
The foils lower mass when compared to a moving
coil gives it a smoother and higher frequency
response.
However the relatively low output requires a step
up transformer.
Ribbon microphones are good for quality studio
recording of acoustic instruments though can be
delicate, for instance you wouldnt want to put
one in front of a bass cabinet.
73
Three types of microphone are
electret-condenser crystal dynamic. The
physical properties on which the operation of
these microphones depend are listed below (not in
order).
Question 32 Which one of the boxes correctly
matches the microphone type to the relevant
physical property?
74
6.4 Loudspeakers
The loudspeakers are almost always the limiting
element on the quality of a reproduced sound.
A loudspeaker without an enclosure does a very
poor job of producing sounds whose wavelengths
are longer than the diameter of the loudspeaker.
Once you have chosen a good loudspeaker from a
reputable manufacturer and paid good money for
it, you might presume that you would get good
sound reproduction from it. But you won't -- not
without a good enclosure or cabinet. The
enclosure is an essential part of sound
reproduction.
These wavelengths are prone to generate
interference patterns (through the process shown
below) which particularly affect the lower
frequency or bass aspects of the music
75
6.5 Speaker Enclosures
The enclosure increases the effective size of the
loudspeaker.
The ideal (but impractical) mount for a
loudspeaker would be a flat board (flat baffle)
of infinite size with infinite space behind it.
Thus the rear sound waves cannot cancel the
front sound waves.
The bass-reflex enclosure (baffle) makes use of a
tuned port which projects some of the sound
energy from the back of the loudspeaker, energy
which is lost in a sealed enclosure. But care
must be taken to avoid the back-to-front
cancellation of low frequencies which
characterizes unenclosed loudspeakers.
76
Question 33 In the paragraph below, options to
complete each sentence are given within the
brackets. Circle the correct option in each
case. A loudspeaker is removed from its
enclosure box. When an audio signal is
connected, the loudspeaker produces sound waves
at both its front and rear surfaces. The sound
waves from the front of the loudspeaker are
in phase with / out of phase with / of much
higher intensity than the waves from the rear.
For a listener in front of the speaker the
waves from the front interfere constructively
/ interfere destructively / diffract
destructively with those generated from the
rear surface. This affects the frequency /
intensity / directional spread of the
resulting sound.
77
A high fidelity loudspeaker system comprising
individual speakers mounted on a baffle board is
shown in the diagram in Figure 1.
Question 34 Explain the role of the baffle board
in improving the performance of the loudspeaker
system above.
Sound from the back and front of the speaker was
out of phase. The baffle prevented these from
meeting and interfering.
78
6.6 Multiple Speakers
Even with a good enclosure, a single loudspeaker
cannot be expected to deliver optimally balanced
sound over the full audible sound spectrum. For
the production of high frequencies, the driving
element should be small and light to be able to
respond rapidly to the applied signal. Such high
frequency speakers are called "tweeters".
On the other hand, a bass speaker should be large
to efficiently impedance match to the air. Such
speakers, called "woofers", must also be supplied
with more power since the signal must drive a
larger mass.
79
6.7 Enclosure Problems
Enclosures play a significant role in the sound
production, adding resonances, diffraction, and
other unwanted effects. Problems with resonance
are usually reduced by increasing enclosure
rigidity, added internal damping and increasing
the enclosure mass.
Diffraction problems are addressed in the shape
of the enclosure avoiding sharp corners on the
front of the enclosure for instance.
Sometimes the differences in reaction time of the
different size drivers (speakers) is addressed by
setting the smaller drivers further back in the
enclosure, so that the resulting wavefront from
all drivers is coherent when it reaches the
listener.
80
6.8 Frequency Response
Frequency Response attempts to describe the range
of frequencies or musical tones a speaker can
reproduce, measured in Hertz. The range of human
hearing is generally regarded as being from 20Hz,
through to 20kHz. Presumably a speaker that
could reproduce that range would sound lifelike.
Alas, it is no guarantee. The most important
determinant of a speaker's frequency performance
is not its width or range, but whether it's
capable of reproducing all the audible
frequencies at the same volume at which they were
recorded.
The relatively flat line on the graph indicates
that the speaker is "flat. This means that it
will treat all sounds equally. It won't impose
its will on the music but will allow you to hear
the music as it was recorded. Flat is good.
Flat response means that the speaker reproduces
sound accurately.
Remember that the ear is barely able to discern
changes of 3 dB in SILs, so flat 3 dB is flat
to our ear.
81
The response curve for a loudspeaker is shown
opposite Question 35 State the frequency range
where the speaker performs well.
50 Hz to 1 kHz
The speaker is used in a speaker box with
crossover circuits to supply separate speakers
within the box. Question 36 What specific
application would this speaker perform within the
system?
This speaker is a low frequency speaker (or
woofer or bass speaker).
82
The frequency response curve for one of the
speakers in the system shown in Figure 1 is shown
in Figure 2 above. Question 37 Which type of
speaker is most likely to have a response curve
similar to that shown in Figure 2? A.
sub-woofer B. woofer C. mid-range speaker D.
tweeter
83
6.8 Crossover Networks
Most loudspeakers use multiple drivers and employ
crossover networks to route the appropriate
frequency ranges to the different drivers.
84

• The End

Ollie Leitl 2005