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SOUND
1.
The characteristic properties
of sound waves - longitudinal waves - calculations using speed and wave
formula
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1.
The characteristic properties
of sound waves
Longitudinal waves
and calculations using the wave equation
Sound waves are caused by some object or material vibrating e.g. your
vocal chords vibrating, plucked guitar strings, something grating on a
surface, the diaphragm (cone) moving back and forth in a loudspeaker etc.
The vibrations from a sound source are carried along by
any available medium - gas (e.g. air), liquid (e.g. water) or solid (e.g.
wall). Sound cannot travel in a vacuum of empty
space - there is no material to vibrate.
You can do a simple experiment with an electric
ringing bell paced in a large bell jar attached to a pump.
As you pump out the air, the sound of the bell gets
fainter and fainter until you can't hear it as the medium is removed
from around it. However, you can still see the striker of the bell
vibrating.
BUT, what exactly happens to the medium and enables it
to convey the energy of a sound wave?
The above diagram gives an idea of
a longitudinal wave of sound where the oscillations are in the direction the
wave moves.
The oscillations in the same direction as the
wave progression, can be considered as vibrations or disturbances
in the medium through which the sound wave is travelling.
Reminder: Contrast this oscillation with transverse waves like water
waves or electromagnetic radiation where the oscillations are at 90o
to the direction of wave movement.
These oscillations in longitudinal sound waves show areas
of compression and rarefaction.
A compression is where the particles of the
medium are compressed to a maximum pressure and a rarefaction is where the particles of
the medium are spaced out the most to the minimum pressure.
When the particles get squeezed closer
together or spaced apart more than 'normal' they will want to return to
their rest position.
This they do, driving the wave in a forward direction.
So the wave is a continuous series of compressions and decompressions
(rarefactions) in which the particles pushed together and then spaced apart
again.
In the diagram above, where the lines are
close together, imagine the particles e.g. air molecules or atoms in a metal
crystal, are also packed together - the opposite is true where the vertical
lines are far apart.
In the diagram above for longitudinal
sound waves, wave B has twice the frequency and half the wavelength of wave
A.
Reminder of the general wave equation
applied to sound:
speed of sound wave (m/s)
= frequency of sound (Hz) x wavelength of sound wave
(m)
in symbolic 'shorthand'
v = f x λ,
rearrangements: f = v ÷ λ
and
λ = v ÷ f
Sound waves that we hear travel at the
same speed whatever the frequency, so, with reference to the diagram, if the
speed stays constant and you halve the wavelength, you must then double
frequency for the equation to be valid.
Where the vertical lines are close together
you can imagine the particles in a material being compressed closer to one
another (compression) and where the lines are spaced well apart, so are the
particles of the medium (the rarefaction).
 The frequency of a sound wave (or any wave) equals the number
of compressions passing a point per second, and is perceived as the pitch eg
of a musical note.
The frequency of sound is the
number of vibrations per second (unit hertz, Hz).
The amplitude is the maximum
compression with respect to the 'rest line' and is perceived as loudness.
The 'rest line' is effectively
the point of no disturbance, zero amplitude - neither compression or
rarefaction.
You can think of a sound wave as a pressure wave - a continuous variation of
high and low pressure regions of the wave.
The diagram above illustrate the simulation
of sound waves by push and pulling
on a slinky spring to create pulses of energy being transmitted along the slinky
spring (the 'medium'). Its a good simulation of the compression and rarefaction
behaviour of a longitudinal wave.
NOTE: Not all frequencies of sound can
be transmitted through an object or material.
The nature of the material can affect
which frequencies can be transmitted.
The shape, size as well as the structure
of an object affects the frequencies that can pass through.
When you hit a solid object that is
'sonorous' e.g. a metal block that rings when structure, it will
vibrate-resonate most strongly with certain 'natural' frequencies - you will
hear one particular note most loudly e.g. as with a tuning fork in music.
The frequency of sound doesn't change as it passes from
one medium to another.
However, the speed does change and therefore the
wavelength must change too.
v = f x λ,
rearrangements: f = v ÷ λ
and λ = v ÷ f
If the frequency
f stays constant, then
increase in speed v
must be matched by an increase in the wavelength
λ to keep the ratio speed / wavelength constant.
Unlike electromagnetic light waves, sound cannot travel through empty space (vacuum) because
you need a
material substance (gas, liquid or solid) which can be compressed and
decompressed to transmit the wave vibration.
The more dense a material, the
faster the sound wave travels (its the opposite for light in transparent
materials).
Therefore in general for sound: speed in
solids > speed in liquids > speed in gases
This is borne out by the data of sound
speeds quoted below:
Typically at room temperature, the speed of
sound waves in various materials at ~20-25oC
air 343 m/s (0.34 km/s),
that's why if a thunderstorm is 1 km
away, you hear the thunderclap about 3 seconds after the flash of
lightning - the speed of light is so much greater than the speed of
sound that the flash is virtually instantaneous,
the speed of sound increases in air
with temperature, an empirical formula (from experiment, no theoretical
basis) I found on the internet is: speed of sound in air in m/s = 331
+ 0.6T (where T = 0 to 100oC).
water 1493 m/s (1.49 km/s),
sea water 1533 (1.53 km/s), high velocity useful in sonar scanning of sea
bed
kerosene 1324 m/s (1.32 km/s)
(liquid hydrocarbon)
ordinary glass 4540 m/s, pyrex
glass 5640 m/s (5.64 m/s), much more dense than water
iron 5130 m/s (5.1 km/s), steel
5790 m/s (5.8 km/s)
rocks 2000 to 7000 m/s (2-7 km/s),
the speed tends to be greater in the more dense igneous rocks compared to
less dense sedimentary rocks.
for comparison:
longitudinal earthquake P-waves
typically travel at 2 to 7 km/s depending on whether the wave is in
the Earth's crust, mantle or core and the speed will also depend on
density and temperature
Some sound wave calculations
speed of sound wave (m/s)
= frequency of sound (Hz) x wavelength of sound wave
(m)
v = λ x f,
rearrangements: f = v ÷ λ
and λ = v ÷ f
Q1 A typical audible
high frequency sound might be
2 kHz.
Speed of sound = 340 m/s
(a) Calculate the wavelength of this
sound wave.
(b) The musical note 'middle C' has a
frequency of ~262 Hz
(c) How is it that you can hear sounds
from room to other rooms in the house?
Worked out ANSWERS to wave calculation questions
Q2
A musical note has a wavelength of 1.13 m.
If the speed of sound in air is 340 m/s
calculate the frequency of the note.
Worked out ANSWERS to wave calculation questions
Q3
Two people, 20 m apart, conduct an experiment using iron railings.
One taps the railings and the other
places their ear on the iron railings.
(a) Why does the listener hear two
sounds?
(b) Which sound arrives first and why?
Worked out ANSWERS to wave calculation questions
INDEX of physics notes
on SOUND
Keywords, phrases and learning objectives for
sound waves
Be able to draw and interpret diagrams to explain
the characteristic properties of
longitudinal sound waves.
Be able to do calculations using speed and wave formulae
with the correct matching units.
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Summary of knowledge for this section on sound for Parts 1 to 8
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Know and understand that electronic systems can be
used to produce ultrasound waves, which have a frequency higher than the
upper limit of hearing for humans.
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Know and ultrasound waves are
partially reflected when they meet a boundary between two different media.
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Be able to calculate the distance
between interfaces in various media.
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Be able to use the equation
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s = v x t
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s is distance in metres,
m
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v is speed in metres per
second, m/s
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t is time in seconds,
s
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Know how ultrasound waves can be
used in medicine.
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Know and understand that sound waves are longitudinal
waves and cause vibrations in a medium, which are detected as sound.
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The oscillations
(rarefactions<=>compressions) of longitudinal waves are in the same
direction as the wave motion.
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Longitudinal waves eg sound, show areas
of compression and rarefaction (diagram above illustrates longitudinal
sound waves, wave B has twice the frequency and half the wavelength of wave
A).
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Sound waves are produced by
mechanical vibrations and travel through any medium, gas, liquid or solid,
but not vacuum, where there is nothing to vibrate!
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In music, if a middle C tuning
fork is struck, the two prongs vibrate from side to side 262 times every
second ie middle C has a frequency or pitch of 262 Hz.
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The more dense a material, the
faster the sound wave travels. Typically at room temperature, the speed of
sound is 340 m/s but in steel its 6000 m/s.
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Sound is limited to human
hearing and no details of the structure of the ear are required.
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Ultrasound is a very high
frequency sound wave used in scanning pregnant women to monitor the progress
of unborn baby.
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The ultrasound waves enter the
woman's body and the echoes-reflections are picked up by a microphone and
converted into electronic signals from a which an internal picture can be
constructed.
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Tissues or fluids of different
density give different intensities of reflection and so differentiation of
the structure of the womb, foetus or baby can be seen.
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Check out your
practical work you did or teacher demonstrations you observed
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all of this is part of good revision for your
module examination context questions and helps with 'how science works'.
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demonstrating transverse and longitudinal waves with a slinky
spring
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demonstrating the Doppler effect for sound.
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