Reference:
Nelson PhysicsVCE Units 3&4
Chapters 1 - 4Page 3
S.1 Sound
S.1.1 What
is sound? What causes sound?
Demo:Some
of the ones below
Perform
the following tasks and work out the common link
1.Pluck
a stretched rubber band
2.Hold
the edge of a small piece of paper to your mouth and blow
3.Blow
up a balloon.Let the air out slowly
whilst holding the neck tightly
4.Strike
a tuning fork and listen for the sound.Place
its prongs into water and observe.
5.Place
hand on vocal chord whilst talking
6.Hold
ruler on edge of desk and flick the end
In
each of the activities you saw/heard something was vibrating and this caused
the sound.There can be no sound
without vibration.Sound is a form
of energy that can travel from one point to another.
S.1.2 How
does sound travel?
You
can make a sound on Earth, but not in space.Why?Space
has no atmosphere to carry the vibrations.Sound
is carried by the particles in the atmosphere/material.The
vibrations are passed on when one particle bumps into another.
A
substance through which sound travels is called a medium.Solids,
liquids and gasses are the mediums of sound, some mediums allow sound to
travel faster than others.This
depends on how closely packed the particles are in the medium.
Demo:Electric
bell in bell jar, evacuate air and compare
Question:Do
sounds travel fastest through solids, liquids or gases?
Solids
because the particles are closer together and can pass the vibrations on
more easily.
S.1.3 Sound
waves in air
Every
vibration produces a sound wave which travels through the air in a special
way.As we said before the vibrations
pass when the particles bump into each other, this is much the same as
the chain reaction that occurs when dominos fall over.
Consider
a ruler vibrating back and forth.The
sound will travel in the following way
When
the ruler vibrates to the right, the particles get compressed.
When
the ruler moves to the left the particles are no longer pushed to the right
and return to their normal position.The
compression move s on a bit.
the
next time the ruler moves to the right, it compresses the particles again.The
earlier vibration has continued to move along.
this
process repeats itself as the ruler vibrates.These
patterns are called sound waves.This
type of wave is known as a longitudinal wave.Since
the vibration moves in the same direction as the direction of travel of
the wave.
Every
sound has its own special wave pattern.The
parts of a sound wave are named as follows.The
compressions are called crests and the parts not compressed are said to
be rarefactions and are called troughs.The
distance between two crests (compressions) is called a wavelength.
Demo:Slinky
S.1.4 The
speed of sound
Prac
#3.1:The
speed of Sound (method 1)
As
briefly mentioned before the speed of sound varies, depending on the medium
it is travelling through.The factor
that causes this variation is how closely together the molecules are packed.Thus
sound generally travels fastest in solids and slowest in gases.
S.1.4.1 The
speed of sound in Gases
The
speed of sound in air at 0°C
is 331 ms-1, in air at 18°C
is 342ms-1 and in hydrogen
at 18°C
is1300 ms-1.Why this
variation?
Hydrogen
is lighter (less dense) than air, so it is easier for the particles to
be moved, hence a faster speed.Experiments
have shown that when the temperature of a gas increases so does the speed
of sound in the gas.
The
relationship is given by:
i.e.
By
using this it is possible to calculate the speed of sound at different
temperatures.
Example:
The
speed of sound in air at 0°C
is 331 ms-1.What is
the speed of sound at 10°C?
We
havev1=
331 ms-1
T1=0°C
= 273 K
T2=10°C
= 283 K
Using
We
have
V2=337ms-1
S.2 Waves
S.2.1 Types
of Waves
Demo:Slinky,
Wave motion apparatus
Prac
#3.2:Waves
on a Spring
There
are two types of waves, transverse and longitudinal.In
a transverse wave, such as waves on water, the particles move at right
angles to the direction of travel of the wave.In
a longitudinal wave, such as sound, the direction of travel of the particles
is parallel to the direction of travel of the wave.
S.2.2 Parts
of a Wave
Longitudinal
Transverse
Often
waves are drawn showing only the wave crests.
Problem
Set #1:TextPage
18Questions 1 – 41
S.2.3 Wavelength,
Frequency
As
we have seen before the distance between two corresponding points on a
wave is called a wavelength.The
symbol for wavelength is l
(lamda).
The
number of waves produced per second (or passing a point per second) is
called the frequency.The symbol
is f.Unit sec-1 or hertz
(Hz).
Frequency
can be calculated as follows:
The
time between each wave is known as the period.The
symbol used is T and
The
speed of a wave is the distance travelled in a certain time or
Problem
Set #2:TextPage
42Questions 1 – 19
S.2.4 Pitch
and Frequency
Demo:Signal
generator, CRO
There
are many different types of sounds some are low, others are high and many
are in between.One of the properties
of sound is pitch.If we play the
notes on a piano they start off low at the left-hand end and get higher
as you move to the right.The reason
for this change is the pitch, a low sound has a low pitch and a high sound
has a high pitch.Pitch has nothing
to do with the loudness of a sound.
Pitch
depends on how fast an object vibrates, as we know this is called frequency.The
faster or more frequently an object vibrates, the higher its pitch.On
an oscilloscope, one sound cycle shows up as one wavelength.
How
many cycles are shown?
A
high pitch has many/few cycles.
Questions
a)
b)
1.Which
sound above has higher frequency?
2.Which
sound vibrates slower?
3.Which
sound is higher in pitch?
S.2.5 Loudness
and Amplitude
S.2.6Intensity
The
intensity of the sound can be found by dividing the power, which depends
on the square of the amplitude (unit Watt = Joule /second) by the cross-sectional
area.Note that the cross-sectional
area must be measured at right angles to the direction of the wave.
unit
W m-2
For
a point source, the energy spreads out evenly in all directions, passing
through a spherical cross-sectional area.The
area of a sphere is A = 4pr2.For
a source of total acoustical power P, the intensity r meters away is
This
is called the inverse square law since 
Examples
1.What
is the intensity of a sound if 
W
of acoustical power passes through an open window that has an area of 0.30
m2?
2.Karen
measures the sound intensity at a distance of 5.0 m from a lawn-mower to
be 
W
m-2.Assuming that the
lawn-mower acts as a point source and ignoring the effects of reflection
and absorption, what is the total acoustical power of the mower?
3.If
the sound intensity 3.0 m from a sound source is 
W
m-2, what is the intensity at (a) 1.5m and (b) 12m from the
source?
S.2.6.1 Sound Intensity Levels
Prac
#3.3:Measuring
Sound Levels
Because
the ear responds to intensities from the threshold of hearing, I0
= 10-12 W m-2 to the threshold of pain at 1 W m-2,
and registers 10 times the intensity as a doubling in loudness, the decibel
logarithmic scale (rather than a linear scale) is used to measure sound
intensity levels L(in dB).
(unit
decibel)
where
Io = 10-12 W m-2
Example
Normal
conversation has an intensity of 10-6 W m-2.What
is the sound intensity level in decibel?
I
= 10-6 W m-2, I0 = 10-12 W
m-2
L=
10 x 6
L=
60 dB
A
rock concert can have a sound intensity level of 120 dB.What
is the intensity of this noise?
L
= 120 dB, I0 = 10-12 W/m2
1012
x 10-12 = I
I
= 1 W/m2, the threshold of pain
The table below shows the sound intensity levels for some common situations.
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Problem
Set #3:TextPage
43Questions 20 – 27
Prac: 3.4 The Inverse Square Law
S.2.6.2 Hearing
and the Ear
Demo:Signal
Generator
Our
ability to hear sounds depends on two things;
1.The
frequency
2.The
intensity or intensity level of the sound.The
lowest intensity that is able to be heard is called the threshold of hearing.
But,
constant intensity levels don't appear as constant loudness. The graph
below displays intensity levels compared with the frequencies for sounds
of equal loudness for humans.(The
three lines have constant loudness). The bottom line is the threshold of
hearing. At a 1 kHz frequency, the hearing threshold is 0 dB, but at 60
Hz the decibel level is 50. Only one percent of all human beings can hear
sounds this low, so, the lower line is mainly for those with very good
hearing. The next line up is the hearing threshold for the majority of
people. The top line is the pain threshold. Other than at one point, about
4 kHz, this line varies little. All of the other lines also dip down at
4 kHz. We can gather from this graph, then, that the human ear is most
sensitive at about 4 kHz.
Problem
Set #4:TextPage
45Questions 28 – 55
S.2.7Reflection
of Waves (in 2-D)
It
is important for us to remember that sound travels in all directions.For
simplicity we will only consider two dimensions.
Demo:Ripple
tank placed over OHP
Prac
#3.5:Properties
of Waves:Reflection and Refraction
Water
and sound waves reflect in a similar fashion to light.(In
fact anything that is formed from waves will behave in this way.E.g.
microwaves, radiowaves, etc).That
is, if waves travel straight towards a barrier then they reflect straight
back.
When
we increase the angle between the waves and the barrier we again observe
that the waves reflect in a similar fashion to light.
The
angle of incidence is the angle between the direction of propagation (travel)
of the incident waves and the normal.The
angle of reflection is the angle between the direction of propagation of
the reflected waves and the normal.
Also
|
i°=r°
|
We
also look at the reflection of circular waves from a plane barrier.
There
appears to be two sets of waves.
1.The
original waves spreading out from the real source.
2.The
reflected waves spreading out as if they came from a source behind the
barrier.The same distance behind
as the real source is in front of the barrier.
Next
lets look at reflection from a concave barrier.
This
is similar to the reflection of light from a concave mirror.Waves
propagating parallel to the axis are reflected through a point, the focus.For
a convex barrier the waves propagating parallel to the axis are reflected
as though they have come from a point, the focus.
S.2.7.1 What
is an Echo?
Sound
that bounces off a hard surface produces an echo.Sound
reflects better off hard surfaces (just like a ball bounces better off
hard surfaces).In order to prevent
echoes a soft surface is used so that the sound is absorbed.Carpets
and curtains help to absorb sound.
The
reflection of sound is used in three ways:
1.Focussing
a Camera
auto focus cameras send outa sound
wave which bounces off the object and back to the camera.The
camera then calculates the distance and focuses the lens.
2.Sonar
for finding objects under water (fish, submarines, depth).The
ship sends down a sound wave which bounces off the object under the water
and back to the ship.The electronics
on board then calculates the depth.
3.Ultrasound sound
waves bounce off the foetus and the electronics interpret this and put
an image on a TV screen.
Example:A
ship sounds its horn and 2.0s later an echo is heard from the protruding
tip of a iceberg.If the speed of
sound in air is 330 ms-1, how far away is the iceberg?
The
distance to the iceberg is half the total distance.So
the answer is 330 m.
Problem
Set #5:TextPage
77Questions 1 - 19
S.2.8 Refraction
of Waves
We
observe that when water waves travel in water of different depths, that
the speed changes and also the wavelength changes.
I.e.
The
frequency remains the same
If
we use 
Thenif
v increases, l
increases
Orif
v decreases, l
decreases
The
waves travel faster in the deep water and have a large wavelength.
As
the angle between the waves and the boundary increases, the waves are seen
to bend.When travelling from deep
to shallow they bend towards the normal.
The
angle of incidence is greater than the angle of refraction, thus the waves
are bending towards the normal when they are slowing down.We
notice that the angle of incidence (i°)
also equals the angle between the incident wave front and the boundary,
and the angle of refraction (r°)
also equals the angle between the refracted wave front and the boundary.
S.2.9Diffraction
Prac
#3.6:Properties
of Waves: Diffraction
Demo:Ripple
Tank
Diffraction
on NELSON CD-ROM
Waves
can be seen to diffract (bend) when they pass through and aperture or near
an object.
When
wave length (l)
is kept constant, the smaller the aperture (w), the larger the amount
of diffraction.When the aperture
is kept constant, as the wavelength is increased so does the diffraction.The
region where no wave travels is called a shadow.High
frequency wave create a larger shadow than low frequency waves.
Thus
it is the relationship between the wavelength and the size of the gap that
is important.As the ratio 
increases
so does the amount of diffraction that occurs.
Problem
Set #6:TextPage
79Questions 20 – 32
Gardiner&
McKittrick Set 31 Questions 1, 2, 5
S.2.10 Superposition Principle
Demo:Nelson
CD-ROM
When
pulses approach each other, they pass through each other unaffected.When
they are at the same place on the spring, the amplitude is the sum of the
individual amplitudes.
This
is known as the principle of superposition.
S.2.11 Interference
of Waves
Demo:Ripple
tank
Two
loud speakers in phase walk across the front
Prac
#3.7:Properties
of Waves : Interference
Patterns
S.2.11.1 Constructive
and Destructive Interference
Constructive
interference occurs when the crest of one wave meets the crest of another.Thus
constructing a larger wave.Similarly
this occurs when two troughs meet.
Destructive
interference occurs when the crest of one wave meets the trough of another,
thus destroying the wave.
S.2.11.2 Interference
in Two Dimensions
Demo:Ripple
Tank
Interference
on NELSON CD-ROM
When
two sets of circular waves are produced (in water) near to each other a
pattern is produced.This pattern
is called interference.Interference
occurs when two sets of waves of the same frequency cross the same region.
The
pattern has lines where there is no displacement of the water.These
are called nodal lines and appear where there is destructive interference.I.e.
the crest of one wave meets the trough of another.For
this to happen the path difference must be half a wavelength.
Thus
or
Between
the nodal lines are areas of maximum displacement.These
areas form antinodal lines and are formed where there is constructive interference.I.e.
the crest of one wave meets the crest of another.For
this to happen the path difference must be a whole wavelength.
Thus
or
Problem
Set #7:TextPage
80Questions 33 - 54
S.2.12 Beats
Demo:Two
signal generators connected to one speaker, listen and look at on the CRO
Beats on NELSON CD-ROM
When
two waves of different frequencies interfere with each other the result
of superposition of the two waves is not uniform and beats are produced.When
heard the sound has a throbbing as the amplitudes vary.The
number of beats heard depends on the difference in the two frequencies
i.e. f2 - f1 and is called the beat frequency.
Problem
Set #8:TextPage
85Questions 55 – 61
S.2.13 Standing
Waves
Demo:Spring,
Ripple Tank
Standing
waves on NELSON CD-ROM
In
travelling waves the wavefronts advance at the wavespeed transporting energy
from one point to the another.All
the particles vibrate in exactly the same way although adjacent particles
have different phases.Another type
of wave is the stationary wave
Standing waves are created in a closed system when two waves identical in all respects except that they travel in opposite directions interfere.This can happen when the incident wave is reflected.A standing wave has nodes separated by l/2 and anti-nodes also separated by l/2.The particles at the nodes do not vibrate, while those at the anti-nodes have the largest amplitude.
Standing
waves can occur in stretched strings fixed at both ends such as for stringed
instruments. In pipes open at both ends such as tubular bells and xylophone.
In pipes open at one end and closed at the other such as flutes, trumpets
etc.Inpipes
closed at both ends such as oboes, some organ pipes and french horns with
a fist up the bell.The length of
the pipe or string determines the allowed wavelengths and hence the allowed
frequencies.
Problem
Set #9:TextPage
117Questions 1 – 17
S.2.14 Resonance
Demo:Tuning
Fork, resonance tubes, bottle
All
objects have a natural frequency of vibration.If
a sound of the same frequency is made near an object then it will start
to vibrate, this is called resonance.This
phenomenon is used in musical instruments to make the sound louder.
S.2.14 Harmonics
·Multiples
of the lowest allowed frequency are called harmonics.
·All
harmonics are possible for strings fixed at both ends and pipes open at
both ends or closed at both ends.
·For
pipes closed at one end and open at the other, only the odd harmonics are
possible.
·The
lowest allowed frequency is called the fundamental frequency or first harmonic.
·The
second allowed frequency is the second harmonic and is called the first
overtone.
·The
third allowed frequency is the third harmonic and is called the second
overtone, etc.
·Overtones
are frequencies above the fundamental frequency that are produced by a
musical instrument.fn
= n f1 where n = 1, 2, 3, ………………
S.2.15 End
Conditions for Strings and Air Columns
·The
frequencies allowed for standing waves on strings and pipes depend on both
the length and end conditions
·The
end condition determines the shape of the reflected wave
·The
fixed end of a string must be a node
·The
free end of a string must be an anti-node
·The
closed end of a pipe must be a displacement node and pressure anti-node
·The
open end of a pipe must be a displacement anti-node and pressure node
S.2.16 Sound
from Strings: Standing Waves in a String Fixed at Both Ends
·A
string fixed at both ends can only vibrate when the length of the string
l is a multiple of half the wavelength,
·So
the only allowed frequencies are:
Example
What
are the allowed wavelengths for the G string on a violin if the wavespeed
for the string is 125.4 m/s and its length is 0.32 m?What
is the frequency of the second harmonic?
Solution
v
= 125.4 m/s, l = 0.32 m
The
second harmonic corresponds to a wave length of 0.32 m.
S.2.17 Sound
from Pipes
A
wind instrument uses the principle of vibrating air to produce a sound.By
blowing into the instrument the musician sets up a standing wave, by changing
the length of the air column the musician can change the pitch easily.Short
thin air columns produce high pitched sounds and long fat columns produce
low pitched sounds.In addition to
this the resonance of the instrument increases the loudness of the sound.
S.2.17.1 Standing
Waves in a Pipe Open at Both Ends or Closed at Both Ends
·A
pipe open at both ends or closed at both ends can only vibrate when the
pipe length l is a multiple of half the wavelength
·So
the only allowed frequencies:
S.2.17.2Standing
Waves in a Pipe Open at One End and Close at the Other
·A
pipe open at one end and closed at the other can only vibrate when the
pipe length l is an odd multiple of quarter of the wavelength
·So
the only allowed frequencies are the odd harmonics - the resonant frequencies
are:
Example
Anorgan
pipe, open at both ends, is to be tuned so that its fundamental frequency
is an E at 330 Hz in a room at 18o C.
a.What
length must the pipe be
b.What
frequencies have the first two overtones?
c.If
the pipe is now closed at one end, what will be the frequencies of the
first three allowedharmonics?
Solution
a.f1
= 330 Hz for n = 1, v = 342 m/s at 18o C,
b. fn=
n f1n = 1, 2, 3, ...
The
first two overtones have frequencies of 660 Hz and 990 Hz
c.
.f1 = 330 Hz for m =
1, v = 342 m/s at 18o C
fm
= m f1m = 1, 3, 5,...
Only
the odd harmonics are possible.The
first harmonic is 165 Hz, the third is 495 Hz, the fifth is 825 Hz
Prac
#3.8:Speed
of Sound - The Resonance Method
Problem
Set #10:TextPage
120Questions 17 – 73