Lesson 2: Sound Properties
and Their Perception
The Speed of Sound
A sound wave is a pressure
disturbance which travels through a medium by means
of particle interaction. As one particle becomes
disturbed, it exerts a force on the next adjacent
particle, thus disturbing that particle from rest and
transporting the energy through the medium. Like any
wave, the speed of a sound  wave refers to how fast the disturbance is passed from
particle to particle. While frequency refers to the number of vibrations which an individual
particle makes per unit of time, speed refers to the
distance which the disturbance travels per unit of time.
Always be cautious to distinguish between the two often
confused quantities of speed (how fast...) and
frequency (how often...).
Since the speed of a
wave is defined as the distance which a point on a wave
(such as a compression or a rarefaction) travels per unit
of time, it is often expressed in units of meters/second
(abbreviated m/s). In equation form, this is
speed =
distance/time
The faster which a sound wave travels, the more
distance it will cover in the same period of time. If a
sound wave is observed to travel a distance of 700 meters
in 2 seconds, then the speed of the wave would be 350
m/s. A slower wave would cover less distance - perhaps
600 meters - in the same time period of 2 seconds and
thus have a speed of 300 m/s. Faster waves cover more
distance in the same period of time.
The speed of any wave depends upon the
properties of the medium through which the wave is
traveling. Typically there are two essential types of
properties which effect wave speed - inertial properties
and elastic properties. The density of a medium is an
example of an inertial
property. The greater the inertia (i.e., mass
density) of individual particles of the medium, the less
responsive they will be to the interactions between
neighboring particles and the slower the wave. If all
other factors are equal (and seldom is it that simple), a
sound wave will travel faster in a less dense material
than a more dense material. Thus, a sound wave will
travel nearly three times faster in Helium as it will in
air; this is mostly due to the lower mass of Helium
particles as compared to air particles.
Elastic properties
are those properties related to the tendency of a
material to either maintain its shape and not deform
whenever a force or stress is applied to it. A material
such as steel will experience a very small deformation of
shape (and dimension) when a stress is applied to it.
Steel is a rigid material with a high elasticity. On the
other hand, a material such as a rubber band is highly
flexible; when a force is applied to stretch the rubber
band, it deforms or changes its shape readily. A small
stress on the rubber band causes a large deformation.
Steel is considered to be a stiff or rigid material,
whereas a rubber band is considered a flexible material.
At the particle level, a stiff or rigid material is
characterized by atoms and/or molecules with strong
attractions for each other. When a force is applied in an
attempt to stretch or deform the material, its strong
particle interactions prevent this deformation and help
the material maintain its shape. Rigid materials such as
steel are considered to have a high elasticity (elastic
modulus is the technical term). The phase of matter has a
tremendous impact upon the elastic properties of the
medium. In general, solids have the strongest
interactions between particles, followed by liquids and
then gases. For this reason, longitudinal sound waves
travel faster in solids than they do in liquids than they
do in gases. Even though the inertial factor may favor
gases, the elastic factor has a greater influence on the
speed (v) of a wave,
thus yielding this general pattern:
vsolids
> vliquids >
vgases
The speed of a sound
wave in air depends upon the properties of the air,
namely the temperature and the pressure. The pressure of
air (like any gas) will effect the mass density of the
air (an inertial property) and the temperature will
effect the strength of the particle interactions (an
elastic property). At normal atmospheric pressure, the
temperature dependence of the speed of a sound wave
through air is approximated by the following
equation:
v = 331 m/s + (0.6
m/s/C)*T
where T is the temperature of the air in degrees
Celsius. Using this equation is used to determine the
speed of a sound wave in air at a temperature of 20
degrees Celsius yields the following solution.
v = 331 m/s + (0.6 m/s/C)*T
v = 331 m/s + (0.6 m/s/C)*20 C
v = 331 m/s + 12 m/s
v = 343
m/s
(The above equation relating the speed of a sound wave
in air to the temperature provides reasonably good speed
values for temperatures between 0 and 100 Celsius. The
equation itself does not have any theoretical basis; it
is simply the result of inspecting temperature-speed data
for this temperature range. Other equations do exist
which are based upon theoretical reasoning and provide
accurate data for all temperatures. Nonetheless, the
equation above will be sufficient for our use as
introductory Physics students.)
At normal atmospheric pressure and a
temperature of 20 degrees Celsius, a sound wave will
travel at approximately 343 m/s; this is approximately
equal to 750 miles/hour. While this speed may seem fast
by human standards (the fastest humans can sprint at
approximately 11 m/s and highway speeds are approximately
30 m/s), the speed of a sound wave is slow in comparison
to the speed of a light wave. Light travels through air
at a speed of approximately 300 000 000 m/s; this is
nearly 900 000 times the speed of sound. For this reason,
humans can observe a detectable time delay between the
thunder and lightning during a storm. The arrival of the
light wave from the location of the lightning strike
occurs in so little time that it is essentially
negligible. Yet the arrival of the sound wave from the
location of the lightning strike occurs much later. The
time delay between the arrival of the light wave
(lightning) and the arrival of the sound wave (thunder)
allows a person to approximate his/her distance from the
storm location. For instance if the thunder is heard 3
seconds after the lightning is seen, then sound (whose
speed is approximated as 345 m/s) has traveled a distance
of
distance = v * t = 345 m/s
* 3 s = 1035
m
If this value is converted to miles (divide by 1600
m/1 mi), then the storm is a distance of 0.65 miles
away.
Another phenomenon related to the
perception of time delays between two events is the
phenomenon of echolocation.
A person can often perceive a time delay between the
production of a sound and the arrival of a reflection of
that sound off a distant barrier. If you have ever made a holler within a canyon, perhaps you have heard an
echo of your holler off a distant canyon wall. The
time delay between the holler and the echo
corresponds to the time for the holler to travel
the round-trip distance to the canyon wall and back. A
measurement of this time would allow a person to estimate
the one-way distance to the canyon wall. For instance if
an echo is heard 2.2 seconds after making the
holler, then the distance to the canyon wall can
be found as follows:
distance = v * t = 345 m/s
* 1.1 s = 380
m
The canyon wall is 380 meters away. You might have
noticed that the time of 1.1 seconds is used in the
equation. Since the time delay corresponds to the time
for the holler to travel the round-trip distance
to the canyon wall and back, the one-way distance to the
canyon wall corresponds to one-half the time delay.
While the phenomenon of echolocation is
of relatively minimal importance to humans, it is an
essential trick of the trade for bats. Being
merely blind, bats must use sound waves to navigate and
hunt. They produce short bursts of ultrasonic sound waves
which reflect off their surroundings and return. Their
detection of the time delay between the sending and
receiving of the pulses allows a bat to approximate the
distance to surrounding objects. Some bats, known as
Doppler bats, are capable of detecting the speed and
direction of any moving objects by monitoring the changes
in frequency of the reflected pulses. These bats are
utilizing the physics of the Doppler effect discussed in an earlier unit (and
also to be discussed later in
Lesson 3). This method of echolocation enables a bat
to navigate and to hunt.
Like any wave, a
sound wave has a speed which is mathematically related to
the frequency and the wavelength of the wave. As
discussed in a previous
unit, the mathematical relationship between speed,
frequency and wavelength is given be the following
equation.
Speed = Wavelength *
Frequency
Using the symbols v,
 ,
and f, the equation can be rewritten as
v = f * 
The above equations are useful for
solving mathematical problems related to the speed,
frequency and wavelength relationship. However, one
important misconception  could
be conveyed by the equation. Even though wave speed is
calculated using the frequency and the wavelength, the
wave speed is not dependent upon these quantities.
An alteration in wavelength does not effect (i.e.,
change) wave speed. Rather, an alteration in wavelength
effects the frequency in an inverse manner. A doubling of
the wavelength results in a halving of the frequency; yet
the wave speed is not changed. The speed of a sound wave
depends on the properties of the medium through which it
moves and the only way to change the speed is to change
the properties of the medium. |