Sound waves are introduced into a medium by the vibration of
an object. For example, a vibrating guitar string forces surrounding air
molecules to be compressed and expanded, creating a pressure disturbanceconsisting of
an alternating pattern of compressions and rarefactions. The disturbance
then travels from particle to particle through the medium, transporting energy
as it moves. The energy that is carried by the disturbance was originally
imparted to the medium by the vibrating string. The amount of energy that is
transferred to the medium is dependent upon the amplitude of vibrations of the
guitar string. If more energy is put into the plucking of the string (that is,
more work is done to displace the string a greater amount from its rest position),
then the string vibrates with a greater amplitude. The greater amplitude of
vibration of the guitar string thus imparts more energy to the medium, causing
air particles to be displaced a greater distance from their rest position.
Subsequently, the amplitude of vibration of the particles of the medium is
increased, corresponding to an increased amount of energy being carried by the
particles. This relationship between energy and amplitude was
discussed in more detail in a previous unit.
The amount of energy that is transported past a given area of
the medium per unit of time is known as the intensity of the sound wave. The greater the amplitude of
vibrations of the particles of the medium, the greater the rate at which energy
is transported through it, and the more intense that the sound wave is.
Intensity is the energy/time/area; and since the energy/time ratio is
equivalent to the quantity power, intensity is simply the power/area.
Typical units for expressing the intensity of a sound wave
are Watts/meter2.
As a sound wave carries its energy through a two-dimensional
or three-dimensional medium, the intensity of the sound wave decreases with
increasing distance from the source. The decrease in intensity with increasing distance is explained by the
fact that the wave is spreading out over a circular (2 dimensions) or spherical
(3 dimensions) surface and thus the energy of the sound wave is being
distributed over a greater surface area. The diagram at the right shows that
the sound wave in a 2-dimensional medium is spreading out in space over a
circular pattern. Since energy is conserved and the area through which this
energy is transported is increasing, the intensity (being a quantity that is
measured on a per area basis) must decrease.
The mathematical relationship between intensity and distance is sometimes
referred to as an inverse square relationship. The intensity
varies inversely with the square of the distance from the source. So if the
distance from the source is doubled (increased by a factor of 2), then the
intensity is quartered (decreased by a factor of 4). Similarly, if the distance
from the source is quadrupled, then the intensity is decreased by a factor of
16. Applied to the diagram at the right, the intensity at point B is one-fourth
the intensity as point A and the intensity at point C is one-sixteenth the
intensity at point A. Since the intensity-distance relationship is an inverse
relationship, an increase in one quantity corresponds to a decrease in the
other quantity. And since the intensity-distance relationship is an inverse
square relationship, whatever factor by which the distance is increased, the
intensity is decreased by a factor equal to the square of the distance change factor. The
sample data in the table below illustrate the inverse square relationship
between power and distance.
Distance |
Intensity |
1 m |
160 units |
2 m |
40 units |
3 m |
17.8 units |
4 m |
10 units |
Humans are equipped with very sensitive ears capable of
detecting sound waves of extremely low intensity. The faintest sound that the
typical human ear can detect has an intensity of 1*10-12 W/m2. This intensity
corresponds to a pressure wave in which a compression of the particles of the
medium increases the air pressure in that compressional region by a mere 0.3
billionth of an atmosphere. A sound with an intensity of 1*10-12 W/m2 corresponds to a sound that will
displace particles of air by a mere one-billionth of a centimeter. The
human ear can detect such a sound. WOW! This faintest sound that a human ear
can detect is known as the threshold of hearing (TOH). The most intense
sound that the ear can safely detect without suffering any physical damage is
more than one billion times more intense than the threshold of hearing.
Since the range of intensities that the human ear can detect
is so large, the scale that is frequently used by physicists to measure
intensity is a scale based on powers of 10. This type of scale is sometimes
referred to as a logarithmic scale. The scale for measuring intensity is the decibel scale. The threshold of hearing is assigned a sound level of 0 decibels
(abbreviated 0 dB); this sound corresponds to an intensity of 1*10-12W/m2.
A sound that is 10 times more intense ( 1*10-11 W/m2) is assigned a sound
level of 10 dB. A sound that is 10*10 or 100 times more intense (1*10-10 W/m2) is assigned a sound
level of 20 db. A sound that is 10*10*10 or 1000 times more intense (1*10-9 W/m2) is assigned a sound
level of 30 db. A sound that is 10*10*10*10 or 10000 times more intense (1*10-8 W/m2) is assigned a sound
level of 40 db. Observe that this scale is based on powers of 10. If one sound
is 10x times more
intense than another sound, then it has a sound level that is 10*x more
decibels than the less intense sound. The table below lists some common sounds
with an estimate of their intensity and decibel level.
Source |
Intensity |
Intensity Level |
# of Times |
Threshold of Hearing (TOH) |
1*10-12 W/m2 |
0 dB |
100 |
Rustling Leaves |
1*10-11 W/m2 |
10 dB |
101 |
Whisper |
1*10-10 W/m2 |
20 dB |
102 |
Normal Conversation |
1*10-6 W/m2 |
60 dB |
106 |
Busy Street Traffic |
1*10-5 W/m2 |
70 dB |
107 |
Vacuum Cleaner |
1*10-4 W/m2 |
80 dB |
108 |
Large Orchestra |
6.3*10-3 W/m2 |
98 dB |
109.8 |
Walkman at Maximum Level |
1*10-2 W/m2 |
100 dB |
1010 |
Front Rows of Rock Concert |
1*10-1 W/m2 |
110 dB |
1011 |
Threshold of Pain |
1*101 W/m2 |
130 dB |
1013 |
Military Jet Takeoff |
1*102 W/m2 |
140 dB |
1014 |
Instant Perforation of Eardrum |
1*104 W/m2 |
160 dB |
1016 |
While the intensity of a sound is a very objective quantity
that can be measured with sensitive instrumentation, the loudness of a sound
is more of a subjective response that will vary with a number of factors. The
same sound will not be perceived to have the same loudness to all individuals.
Age is one factor that affects the human ear's response to a sound. Quite
obviously, your grandparents do not hear like they used to. The same intensity
sound would not be perceived to have the same loudness to them as it would to
you. Furthermore, two sounds with the same intensity but different frequencies
will not be perceived to have the same loudness. Because of the human ear's
tendency to amplify sounds having frequencies in the range from 1000 Hz to 5000
Hz, sounds with these intensities seem louder to the human ear. Despite the
distinction between intensity and loudness, it is safe to state that the more
intense sounds will be perceived to be the loudest sounds.
1. A mosquito's buzz is often rated with a decibel rating
of 40 dB. Normal conversation is often rated at 60 dB. How many
times more intense is normal conversation compared to a mosquito's buzz?
a. 2 |
b. 20 |
c. 100 |
d. 200 |
e. 400 |
Answer: C. 100 times
Normal
conversation is 20 dB more intense. This 20 db difference
corresponds to a 2-Bel difference. This difference is equivalent to a sound
which is 102 more intense. Always raise 10 to a power which is
equivalent to the difference in "Bels."
close
2. The table at the right represents the decibel level for several sound
sources. Use the table to make comparisons of the intensities of the following
sounds.
How many times more intense is the front row of a Smashin' Pumpkins
concert than ...
a. ... the 15th row of the same concert?
b. ... the average factory?
c. ... normal speech?
d. ... the library after school?
e. ... the sound that most humans can just barely hear?
a. 10 X more intense - consistent with a 10 dBel (or
1 Bel) difference between the two sound levels.
b. 102 X more intense - consistent with a 20 dBel (or 2 Bel) difference between the two sound
levels.
c. 105 X more intense - consistent with a 50 dBel (or 5 Bel) difference between the two sound
levels.
d. 107 X more intense - consistent with a 70 dBel (or 7 Bel) difference between the two sound
levels.
e. 1011 X more
intense -
consistent with a 110 dBel (or 11 Bel)
difference between the two sound levels.
3. On a good night, the front row of the Twisted Sister
concert would surely result in a 120 dB sound level. An IPod produces 100 dB. How many
IPods would be needed to produce the same intensity as the front row of the
Twisted Sister concert?
Answer: 100 IPods
Since 120 db is 102 times or 100 times more
intense than 100 dB. It is necessary to
wear 100 IPods to produce the same sound level.