2.5.pdf

Module 2
Licence Category
B1 and B2
Physics
2.5 Wave Motion and Sound
For Training Purposes Only

5-2 Module 2.5 Wave Motion and Sound
ST Aerospace Ltd
© Copyright 2012
Use and/or disclosure is
governed by the statement
on page 2 of this chapter.
Intentionally Blank

5-3
Module 2.5 Wave Motion and Sound
on page 2 of this chapter. ST Aerospace Ltd
© Copyright 2012
Copyright Notice
© Copyright. All worldwide rights reserved. No part of this publication may be reproduced,
stored in a retrieval system or transmitted in any form by any other means whatsoever: i.e.
photocopy, electronic, mechanical recording or otherwise without the prior written permission of
ST Aerospace Ltd.
Knowledge Levels — Category A, B1, B2, B3 and C Aircraft Maintenance
Licence
Basic knowledge for categories A, B1, B2 and B3 are indicated by the allocation of knowledge levels indicators (1,
2 or 3) against each applicable subject. Category C applicants must meet either the category B1 or the category B2
basic knowledge levels.
The knowledge level indicators are defined as follows:
LEVEL 1
• A familiarisation with the principal elements of the subject.
Objectives:
• The applicant should be familiar with the basic elements of the subject.
• The applicant should be able to give a simple description of the whole subject, using common words and
examples.
• The applicant should be able to use typical terms.
LEVEL 2
• A general knowledge of the theoretical and practical aspects of the subject.
• An ability to apply that knowledge.
Objectives:
• The applicant should be able to understand the theoretical fundamentals of the subject.
• The applicant should be able to give a general description of the subject using, as appropriate, typical
examples.
• The applicant should be able to use mathematical formulae in conjunction with physical laws describing the
subject.
• The applicant should be able to read and understand sketches, drawings and schematics describing the
subject.
• The applicant should be able to apply his knowledge in a practical manner using detailed procedures.
LEVEL 3
• A detailed knowledge of the theoretical and practical aspects of the subject.
• A capacity to combine and apply the separate elements of knowledge in a logical and comprehensive
manner.
Objectives:
• The applicant should know the theory of the subject and interrelationships with other subjects.
• The applicant should be able to give a detailed description of the subject using theoretical fundamentals
and specific examples.
• The applicant should understand and be able to use mathematical formulae related to the subject.
• The applicant should be able to read, understand and prepare sketches, simple drawings and schematics
describing the subject.
• The applicant should be able to apply his knowledge in a practical manner using manufacturer's
instructions.
• The applicant should be able to interpret results from various sources and measurements and apply
corrective action where appropriate.

ST Aerospace Ltd
© Copyright 2012
Intentionally Blank

5-5
© Copyright 2012
Table of Contents
Module 2.5 Wave Motion and Sound____________________________________________9
Wave Motion ____________________________________________________________9
Resonance_____________________________________________________________13
Sound ________________________________________________________________19
Supersonic Speed and Mach Number ________________________________________27
The Doppler Effect_______________________________________________________27

ST Aerospace Ltd
© Copyright 2012
Intentionally Blank

5-7
© Copyright 2012
Module 2.5 Enabling Objectives and Certification Statement
Certification Statement
These Study Notes comply with the syllabus of Singapore Airworthiness Requirements Part 66 -
Aircraft Maintenance Licensing:
Objective
SAR-66
Reference
Licence Category
B1 B2
Wave Motion and Sound 2.5 2 2
Wave motion; mechanical waves, sinusoidal
wave motion, interference phenomena,
standing waves
Sound: speed of sound, production of sound,
intensity, pitch and quality, Doppler effect
:

ST Aerospace Ltd
© Copyright 2012
Intentionally Blank

5-9
© Copyright 2012
Wave Motion
Transverse and Longitudinal Waves
Mechanical waves can be classified as transverse or longitudinal according to how they
travel. Both types of wave can be demonstrated using a slinky (a long steel spring). The
transverse wave occurs when the coils move at right angles to the direction of motion of the
wave, with the motion along the length of the slinky. To produce a transverse wave, the slinky is
rested on a flat surface and one end is moved from side to side, setting up the oscillation and
hence the traveling wave.
The end of the slinky can also be moved in and out along its axis. The coils undergo
compression, followed by rarefaction when the coils open out. Displacement of the coils is
now along the axis of the spring.
Figure 5.1: Transverse and longitudinal waves produced on a slinky

5-10
ST Aerospace Ltd
© Copyright 2012
Progressive and Stationary Waves
When we start a wave in the slinky, either transve
one end to the other. Because it progresses along the slinky it is called a progressive wave.
However, if the far end of the slinky is fixed, waves are reflected back.
the next waves which are traveling forwards. At the right combination of frequency and speed,
the waves traveling in opposite directions can produce a
we shall consider both types.
The Wave Formula
There are many types of waves: light waves, sound waves, radio waves, cosmic rays, x
communication waves, waves on cords, etc. In our first discussion of waves, we will deal with
that type which is called just “wave”, that is, a water wave.
Let us assume that a stone is thrown into
the middle of a large, calm pond on a day
when there is no wind. If there is a
perpendicular plane surface cutting the
water surface through a point where the
stone hits the water, an observer would
see the water surface disturbed in such a
way that a curve would be visible. This curve
would have a shape as shown in figure
In figure 5.2 it is important to note that the
pattern of crests and troughs is moving. If the stone hits th
pattern is moving to the right in the diagram above. Of course, the entire pattern is moving out
from point (P) in all directions, but we are looking in only one direction. We should also note that
the pattern is moving with a definite speed, called the wave speed (v).
The amplitude (A) of the wave is the greatest displacement from the rest position. The
amplitude is shown in figure 5.2.
Another distance that we will need in our discussion of waves is the wavelength,
lambda). The wavelength is defined as the distance from one point on the wave pattern to the
next point in a similar position. The distance from the top of a crest to the top of the next crest is
a wavelength. Also the distance from the bot
is also the same distance, one wavelength. The distance
Let us next consider sinusoidal wave motion im
oscillating body. Assume that the oscillating body is a sphere attached to a vertical spring.
After the spring has been oscillating for some time, the physical situation is as shown in figure
5.3.
The frequency (f) of the oscillating body is defined as the number of complete osc
second. Frequency is expressed in cycles/sec. or Hertz. The period (T) is defined as the time
for one complete oscillation. It is expressed in seconds.
Let us suppose that the oscillating body completes 6 oscillations in one second. It fol
the time for one oscillation is one
aves
rt a wave in the slinky, either transverse or longitudinal. we can watch it travel from
However, if the far end of the slinky is fixed, waves are reflected back. These can combine with
the waves traveling in opposite directions can produce a stationary or standing
There are many types of waves: light waves, sound waves, radio waves, cosmic rays, x
that type which is called just “wave”, that is, a water wave.
Let us assume that a stone is thrown into
the middle of a large, calm pond on a day
when there is no wind. If there is a
perpendicular plane surface cutting the
water surface through a point where the
n observer would
see the water surface disturbed in such a
way that a curve would be visible. This curve
would have a shape as shown in figure 5.2.
it is important to note that the
pattern of crests and troughs is moving. If the stone hits the water surface at the point (P), the
g with a definite speed, called the wave speed (v).
Another distance that we will need in our discussion of waves is the wavelength,
a wavelength. Also the distance from the bottom of one trough to the bottom of the next trough
is also the same distance, one wavelength. The distance λ is also shown in the diagram.
Let us next consider sinusoidal wave motion impressed on a very long flexible cord by an
hat the oscillating body is a sphere attached to a vertical spring.
The frequency (f) of the oscillating body is defined as the number of complete osc
for one complete oscillation. It is expressed in seconds.
Let us suppose that the oscillating body completes 6 oscillations in one second. It fol
the time for one oscillation is one-sixth of a second.
Figure 5.2: Waveform dimensions
we can watch it travel from
These can combine with
stationary or standing wave. Here
There are many types of waves: light waves, sound waves, radio waves, cosmic rays, x-rays.
e water surface at the point (P), the
Another distance that we will need in our discussion of waves is the wavelength, λ (Greek letter
tom of one trough to the bottom of the next trough
is also shown in the diagram.
pressed on a very long flexible cord by an
hat the oscillating body is a sphere attached to a vertical spring.
The frequency (f) of the oscillating body is defined as the number of complete oscillations in one
Let us suppose that the oscillating body completes 6 oscillations in one second. It follows that
Figure 5.2: Waveform dimensions

5-11
© Copyright 2012
In this case:
F = 6Hz and T=
6
1
sec.
From this example we see that f and T are reciprocals of each other.
f
1
T = and
T
1
f =
We next seek a relationship between wave speed (v), frequency (f), and wavelength (λ).
We note that the wave moves forward a distance of one wavelength in a time of one period. Of
course, the wave moves with speed (v).
Since the distance equals the speed times the time, we can write the equation:
λ = vT
From this equation, we have:
v
T
=
λ
And finally:
f λ = v
v = f λ
λ
λ
λ
EXAMPLE:
(a) A body oscillates with a frequency of 8 Hz, and sends out a wave having a
wavelength of 0.2 ft. What is the speed of the wave?
V = (8 cycles/sec.) (0.2 ft.) = 1.6 ft./sec.
(b) What is the wavelength of a wave moving with a speed of 5 ft./sec. If the
frequency of the oscillating body which is the source of the wave is 12 Hz?
Figure 5.3: A waveform produced on a piece of string by a mass
oscillating on the end of a spring

ST Aerospace Ltd
© Copyright 2012
.
ft
417
.
0
.
sec
/
cycles
12
.
sec
/
ft
5
f
v
=
=
=
λ
(c) An observer times the speed of a water wave to be 2 ft./sec. and notes that the
wavelength is 0.5 ft. What is the frequency of the disturbance that gives rise to this
wave?
Hz
4
.
sec
/
cycles
4
.
ft
5
.
0
.
sec
/
ft
2
v
f =
=
=
λ
=

5-13
© Copyright 2012
Resonance
In the case of water waves and in the case of waves
on a very long cord, we were able to neglect waves
that were reflected back along the medium. We now
must consider reflected waves.
The most common example is the case of waves
originating in a disturbance impressed on a cord or
string of a definite length. Many musical instruments
depend on such vibrations.
If a sinusoidal disturbance is impressed on a very
long cord a sinusoidal wave travels continuously
along the cord. However, if the sinusoidal wave
meets a fixed end, a reflected wave moves back
along the cord.
The wave patterns which are observed are called
the normal modes of vibration of the cord. In figure
5.4. the length of the cord is L. The wavelength in
the various modes of vibration are X. The n is the
index of the mode. In the equations which follow, n
has an integral value, that is n = 1, 2, 3, 4.
We can write a general relation as follows:
L
n
2
n =
λ
The vibration where n = 1 is called the fundamental
mode of vibration of the body. The other vibrations
are called overtone vibrations. Every body which
can vibrate has a certain fundamental mode of
vibration of a definite frequency. If this frequency is
impressed on the body, it will vibrate with a relatively
large amplitude. We say that the body is vibrating in
resonance with the impressed frequency.
Figure 5.4: Normal modes of vibration

ST Aerospace Ltd
© Copyright 2012
Intentionally Blank

5-15
© Copyright 2012
Problems
1. A water wave has a wavelength of 0.9 ft. and the wave speed is 4.5ft/sec. What is the
frequency of the disturbance setting up this wave?
2. A wave on a cord is set up by a body oscillating at 12 Hz. The wavelength is 0.25ft. What
is the wave speed?
3. A water wave is set up by a source oscillating at 12 Hz. The speed of the wave is
24ft/sec. What is the wavelength?

ST Aerospace Ltd
© Copyright 2012
Intentionally Blank

5-17
© Copyright 2012
Answers
1. 5 Hz
2. 3ft/sec.
3. 2 ft.

ST Aerospace Ltd
© Copyright 2012
Intentionally Blank

5-19
© Copyright 2012
Sound
Sound waves are usually defined as pressure waves in air or in some other material medium.
Sound waves originate in some vibrating body such as the oscillation of a person’s vocal cords
or the periodic rotation of a plane’s propeller.
As the source of sound vibrates, the air surrounding the source is periodically compressed and
rarefied (made less dense). This periodic change in the atmospheric pressure moves forward
with a definite speed of propagation called the “speed of sound”.
The speed of sound in air is dependent on the temperature of the air. This is not surprising
since the molecules of air move faster in their random motion if the temperature is higher. Thus
we should expect these pressure waves to move somewhat more rapidly in warmer air.
The speed of sound in air is approximately 331.5 m/s at 0°
C
At an air temperature of 20°
C, the speed of sound i ncreases to 344 m/s
If an ear and its eardrum are in the vicinity of a sound wave, the air which strikes that eardrum
has a periodically changing atmospheric pressure. If the frequency of the sound is middle C
(256 Hz), and the atmospheric pressure that day is 14.7 lbs/in2
, 256 times each second the air
pressure is slightly above 14.7 lbs/in2
and 256 times each second the pressure is slightly below
14.7 lbs/in2
it should be emphasized that “slightly” means very small. The human ear is a
remarkably sensitive instrument. It can detect air pressure variations as small as about
0,000000005 lbs./in.2
Sound travels faster in liquids, and even faster still, in solids.
Intensity of Sound
For those working in the aviation industry it is important to understand something regarding the
intensity of a sound wave.
The intensity level (IL) of sound waves is measured in a unit called the decibel (after Alexander
Graham Bell).
The equation is:
IL = 10 log
o
I
I
In this equation IL is in decibels. The intensity, (lo), is the intensity of the “threshold of hearing”,
the softest sound that the average human ear can detect. Also in the equation, I is the intensity
of the sound we are measuring.
We note that:
Io = 10-12
Watts/m2
We also review that the log 10n
= n.

ST Aerospace Ltd
© Copyright 2012
EXAMPLE:
The intensity of a given sound is 10~ Watts/rn2
.
What is the intensity level (IL) in decibels?
)
10
)(
10
(
log
10
10
10
Log
10
IL 12
5
12
5
−
−
−
=
=
= 10 log 107
IL = 10 (7) = 70db
It should be noted that 120 db is the
“threshold of pain”. Sound of this
intensity is painful to the normal ear. If
the ear is continuously subjected to
sound of this intensity, ear damage
and hearing loss can result.
Those who work in the aviation
industry should take precautionary
measures and wear ear protectors.
The intensity of sound decreases
inversely with the square of the
distance from the source of sound.
Therefore, doubling the distance from
a source of sound decreases the
intensity to one-fourth of the previous
value. A worker who is suddenly
subjected to a very intense sound with
unprotected ears should move as
quickly as possible away from the
sound of the source.
Sound Waves and Resonant Vibrations
Intense sound waves can cause resonant vibrations in pieces of equipment. There is a
fundamental mode of vibration and a set of overtone vibrations (multiples of the fundamental)
for any body that can vibrate. The frequencies of these vibrations are all natural frequencies for
the given body. Vibrations of moving parts of equipment are often caused by “sympathetic
vibrations” to some impressed sound wave.
Table 5.1: Intensity levels of some common sounds

5-21
© Copyright 2012
The Italian tenor, Enrico Caruso, had a powerful voice. Wine glasses have a natural frequency
of vibration. As an attention getter at parties. Caruso used to sing the resonant note of a wine
glass and cause the glass to vibrate with such amplitude that it would shatter! Try it sometime!
Constructive and Destructive Interference
When two sinusoidal waves superimpose, the resulting waveform depends on the frequency (or
wavelength) amplitude and relative phase of the two waves. If the two waves have the same
amplitude A and wavelength the resultant waveform will have an amplitude between 0 and 2A
depending on whether the two waves are in phase or out of phase.
Noise Cancelling Headphones
Noise-cancelling headphones reduce unwanted
ambient sounds (i.e., acoustic noise) by means of
active noise control. Essentially, this involves using
a microphone, placed near the ear, and electronic
circuitry which generates an "anti-noise" sound
wave with the opposite polarity of the sound wave
arriving at the microphone. This results in
destructive interference, which cancels out the
noise within the enclosed volume of the headphone.
Keeping noise low at the ear makes it possible to
enjoy music without raising the volume
unnecessarily. It can also help a passenger sleep in
a noisy vehicle such as an airliner.
Resultant
(combined)
waveform
Wave 1
Wave 2
Waves in-phase
Figure 5.5: Constructive and destructive interference
Figure 5.6: Noise cancelling headphones

ST Aerospace Ltd
© Copyright 2012
Another effect of constructive and destructive
interference is the “dead zones” produced when
two identical waves emanate from separate
locations, as shown in figure 5.7.
Here, water waves are progressing from two
points, causing destructive interference where a
peak from one source coincides with a trough
from the other source, the effect being to cancel
each other at those points.
Striations (or “rays”) of undisturbed water result.
Figure 5.7: Destructive interference
causing “dead zones”

5-23
© Copyright 2012
Reflected Waves
Let us look in more detail at how to set up standing waves. We set off a short wave on a slinky
which has been firmly fixed at its far end. Assume that the wave consists of one and a half
wavelengths. The wave travels along the slinky until it reaches the far end.
At this point, the wave can travel no further forwards and is reflected back. This means that the
velocity has changed sign. In addition, the phase of the wave has changed. If the displacement
of the forward wave is upwards at the instant of time when it reaches the far end, then its
displacement is downwards on reflection. This makes sense. At the fixed end, the displacement
of the incoming and outgoing waves sum to zero. This must be so because there can be no
displacement of the string at the fixed point. The reflected wave is out of phase by it. It passes
back 'through' the forward wave (think how ripples can pass through each other on the surface
of a pond). Where the two waves overlap, the displacement of the slinky is the sum of the two
waves. But, eventually, we see the reflected wave emerge complete and pass back along the
slinky.
The frequency, velocity and wavelength of the wave all remain the same in reflection. If no
energy is lost at the far end, the amplitude of the reflected wave equals that of the incoming
one. The phase difference of π which we have identified and is crucial to the setting up of
standing waves.
When waves pass through each other, the displacement at any point is the sum of the individual
displacements of the two waves passing in opposite directions.

ST Aerospace Ltd
© Copyright 2012
Producing Stationary Waves
Stationary waves are set up in stringed instruments such as a guitar. What we see is the string
vibrating from side to side. At the moment that the string is plucked, a progressive transverse
wave is set up traveling out from that point. It meets the fixed end of the string and is reflected
back. The amplitudes of the two waves add together as they meet.
The string vibrates naturally at certain frequencies because it is fixed at both ends. When the
outgoing and reflected waves are added together subject to this condition, a stationary wave is
set up in the string. If the string is plucked centrally we get the fundamental mode (shape of
wave). In this case, the string vibrates with maximum displacement at the central position
(called the antinode) and the displacement falls away to zero at the two ends (called nodes).
When a string on an instrument is plucked, vibrations, that is, waves, travel back and forth
through the medium being reflected at each fixed end. Certain sized waves can survive on the
medium. These certain sized waves will not cancel each other out as they reflect back upon
themselves. These certain sized waves are called the harmonics of the vibration. They are
standing waves. That is, they produce patterns which do not move.
On a medium such as a violin string several harmonically related standing wave patterns are
possible. The first four of them are illustrated above. It is important to understand that for any
Fundamental Frequency or 1st Harmonic
2nd
Harmonic
or
1st
Overtone
3rd
Harmonic
or
2nd
Overtone
4th
Harmonic
or
3rd
Overtone
Figure 5.8: Stationary waves and harmonics
node
anti-node

5-25
© Copyright 2012
one given medium fixed at each end only certain sized waves can stand. We say, therefore, that
the medium is tuned.
The first pattern has the longest wavelength and is called the first harmonic. It is also called the
fundamental.
The second pattern, or second harmonic, has half the wavelength and twice the frequency of
the first harmonic. This second harmonic is also called the first overtone. This can get confusing
with the second member of the harmonic group being called the first member of the overtone
group.
The third harmonic, or pattern, has one third the wavelength and three times the frequency
when compared to the first harmonic. This third harmonic is called the second overtone.
The other harmonics follow the obvious pattern regarding wavelengths, frequencies, and
overtone naming conventions described in the above paragraph.
Depending upon how the string is plucked or bowed, different harmonics can be emphasized. In
the above animation all harmonics have the same maximum amplitude.
This is for purposes of illustration. Actually, the higher harmonics almost always have maximum
amplitudes much less than the fundamental, or first harmonic.
It is the fundamental frequency that determines the note that we hear. It is the upper harmonic
structure that determines the timber of the instrument.
Beats
Suppose we tune two strings of a guitar to vibrate at almost, but not quite, the same frequency.
Plucked simultaneously, the volume of the sound produced by them appears to rise and fall
continuously. This rise and fall has a fixed frequency called the beat frequency. What is
happening is that the sound waves produced by the two guitar strings interfere and our ears
detect the variation of the resultant intensity. Maximum intensity is heard when the waves add
together (interfere constructively) and minimum intensity is heard when the waves cancel each
other out (interfere destructively).
We can see what is happening by adding together the two separate waves as shown in the
diagram below. The resultant, obtained by the principle of superposition, is shown.

5-27
© Copyright 2012
Supersonic Speed and Mach Number
Jet planes can travel at speeds greater than the speed of sound. In this case, we have a source
of sound, the plane, moving at a greater speed than the sound itself. The pressure waves of the
sound all “pile up” and a very strong V-shaped pressure “bow-wave” is produced. A sonic boom
results as this strong pressure ridge reaches the earth.
The Mach number is the ratio of the speed of the plane (v0) to the speed of sound (v). If a plane
is travelling at 1.000 MPH and the local speed of sound is 750 MPH. the Mach number is
calculated in the following way:
Mach Number = 25
.
1
MPH
750
MPH
000
,
1
V
V
sound
of
speed
Local
speed
Aircraft o
=
=
=
We say that the plane is travelling at Mach 1.25.
The Doppler Effect
The “Doppler effect” is named after Christian Doppler (1803-1853), the American physicist who
first named the effect.
The effect is present for all wave motion. However, we will describe it for sound waves since it is
most easily understood for a case where it can be observed (heard might be a better word).
Whenever you have stood on a railway platform and a train blows its whistle as it approaches,
passes, and recedes, you have heard the Doppler effect. In this case, the sound suddenly
changes from a higher pitch (frequency) as the source of sound approaches to a lower pitch as
the source of sound recedes from your ear at rest on the station platform. The change in pitch
occurs at the instant the train passes. Before this instant the source of sound was approaching
your ear and after this instant, the source of sound is receding from your ear.
Figure 5.10: Effect on frequency of a stationary and moving sound source

ST Aerospace Ltd
© Copyright 2012
There is another problem to be considered. Suppose that the source is at rest and the ear is
moving. Consider the figure 5.11.
As the ear moves to the left, it picks up more waves than it normally would if it were at rest.
If the observer moves away from the source, the ear picks up less waves than it would if it were
at rest.
As a conclusion, note that the ear hears a higher frequency if source and observer approach
each other. Also, the ear hears a lower frequency if the source and observer recede from each
other.
Figure 5.11: Doppler effect caused by a
stationary sound source and moving ear

2.5.pdf

Recommended

Recommended

More Related Content

Similar to 2.5.pdf

Similar to 2.5.pdf (20)

More from premnarain4

More from premnarain4 (6)

Recently uploaded

Recently uploaded (20)

2.5.pdf