Why is the speed of sound different in different materials and more importantly through the differen

1
The speed of sound
Sound is a longitudinal wave.  It travels as a
series of compressions and rarefactions.  We know
that in air the speed 336 m/s.  If you are not
sure about the nature of longitudinal waves
revise waves in Module 4.  Sound also travels in
other materials.  In steel the speed is 6000
m/s.  In water sound travels at 1500 m/s. There
is formula that can be used to relate the speed
of sound to the density and the bulk modulus of a
solid.  You are not expected to know it for the
exam.

• Why is the speed of sound different in different
  materials and more importantly through the
  different states of matter

2
Acoustic Impedance

• Some materials conduct sound better than others.
• Acoustic impedance Z is the ability of a
  material to resist the transmission of sound
  through it. It is the product of the density
  and the speed of sound in the material. A
  material with low acoustic impedance conducts
  sound well.  One with a high acoustic impedance
  conducts sound badly. 
• At the boundary of two materials with widely
  differing acoustic impedances most of the sound
  is reflected and little is transmitted.  This has
  important implications in ultrasound scanning.

Give an analagy for this from the physics you
already know.
Write a mathematical expression for acoustic
impedance. What is its unit
3
Intensity

• The intensity I of a sound is the power per unit
  area.
• The further you are away from any source the
  lower the intensity.  Like all progressive waves
  the intensity decreases with an inverse square
  law.  Double the distance and the intensity
  drops to a quarter. 

Write a mathematical expression for the intensity
of a sound. What is its unit
If the power output of a loud speaker at source
is 100W what will its intensity be at a distance
of 100m away What about 400m away
4
Attenuation

• When sound travels through a medium its
  intensity diminishes with distance. All materials
  produce an effect which further weakens the
  sound. This further weakening results from two
  basic causes which are scattering and
  absorption. The combined effect of scattering and
  absorption is called attenuation.

On axes of intensity vs distance sketch two
lines one for a material with low acoustic
impedance and one for a material with high
acoustic impedance. Which shows the greater
attenuation
5
http//www.gohear.org/anims/EAR_X.qt
http//www.infj.ulst.ac.uk/pnic/HumanEar/Andys2
0Stuff/MScProject/workingcode_Local/RunTest.html
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Frequency response
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• Notice that
• At low frequencies the ear is very insensitive. 
  The intensity of sound needed at 20 Hz is about 1
  watt per square metre (Very loud).
• As the frequency goes up the threshold of
  hearing gets rapidly less.  At 100 Hz the
  intensity needed to hear a sound is 10-10 W/m2.
• The ear has a very low threshold of hearing for
  3000 Hz.  A sound of this frequency is very
  penetrating.
• The graph itself has logarithmic scales.  A
  logarithm is a number expressed as a power of
  10.  For example 100 is 102 and 200 is 102.3010. 
  It is a useful way of compressing long graphical
  axes. 

8
Equal loudness curves
Intensity Response (Loudness) The loudness of a
sound depends not just on the intensity but also
of the energy transfer characteristics of the
ear.  Loudness is measured in units called phon. 
The graph below shows how the ear responds to
sounds of equal loudness but of different
frequencies.
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A sound of intensity of 10-12 Wm-2 at a
frequency 3000Hz will sound just as loud as a
sound of intensity 10-6 Wm-2 at 10 000Hz. The
perception of changes in loudness does not
correspond directly to the change in intensity. 
There is a strong frequency element in this. 
Small changes in intensity can be detected at
3000 Hz but not at 100 Hz.
10
The Decibel Scale
The range of intensities we have seen is huge
and we use logarithmic scales to compress the
graph into something more manageable.  In the
decibel scale we use the minimum threshold of
hearing I0 1.0 10-12 W m-2 as a point of
reference. 1 Bel is the intensity change from
10-12 to 10-11 W m-2. 2 Bels is the intensity
change from 10-12 to 10-10 W m-2 etc. The Bel
(B) is rather a big unit and we use the decibel
(dB) instead.  
11
The dBA Scale
The dBA scale is used to take into account the
frequency dependence.  Remember that the ear is
most sensitive at  frequencies between 100 to 10
000 Hz .
12
Questions
The maximum limit that is acceptable in a noisy
environment is 1.0 x 10-3 Wm-2. What is this in
dB The intensity of noise from a jet engine is
0.4Wm-2 at a distance of 10m away. When the
plane is directly overhead at an altitude of
200m estimate (a) The intensity of the noise
heard (b) The noise level in dB 10m away and
200m away. Calculate the loudest intensity sound
that a human ear can stand given that the
intensity level relative to the threshold for
human hearing is 120dB.
13
Exam Question
5 (a) State two reasons why the logarithmic dB
scale is used to compare sounds of different
intensities. (2 marks) (b) Another scale used
to compare sounds of different intensities is the
dBA scale. What are the main differences between
the dBA and the dB scales (3 marks) (c) A
reading of 94 dB is obtained on a sound meter
placed near a drill. Calculate the intensity of
the sound incident on the meter reference
threshold intensity I0 1.0 x 10-12Wm-2 (3
marks) (d) An identical drill is now placed next
to the first drill and both are switched on.
Calculate the new reading on the sound meter. (2
marks)