OBJECTIVES
After you have finished this lesson you should be able to
* describe the nature and structure of waves.
* give physical examples of waves and vibrations.
* to understand and describe the difference between transverse and longitudinal
waves
* be able to describe the processes of radio transmission and reception.
* to describe the processes of reflection and refraction of light and sound.
* to be familiar with an abstract view of waves and vibrations.
* to understand and explain the Doppler effect.
TEXT
Waves and vibrations are basic to our understanding of nature; therefore,
we must first describe what these terms refer to: A wave is a repeating structure in
space; a vibration is a repeating pattern in time. In order to discuss these basic
terms, we must first introduce terms to describe waves and vibrations, some of
which are found in the slides.
Diagrams
The first thing one thinks about when one hears the term "waves" is water,
and indeed the most common physical example one uses tends to be based on
water waves. But as we shall see, water waves are quite complicated. Therefore,
the first waves we discuss in detail are sound waves.
Sound waves can be caused by a person speaking. First, molecules of air are
set into vibrational motion by the action of the voice box; these vibrations are a
backwards and forwards motion about a central point. These vibrating molecules
collide with their neighbors, causing them to also vibrate. Various collisions
occur in the mouth, and in the end a vibration escapes into the outside air causing
air molecules near the mouth to start vibrating. These vibrations are then
transmitted, or propagated, through the air until they enter a person's ear, where
they cause the ear drum to vibrate and hence transmit nerve signals, which are
perceived as sound, to the brain. The sound wave is the propagation of the
vibration of the molecules transmitted through the air. No actual matter or
material is transported through the air; what is transported is a disturbance.
In other words, a wave is the propagation of a vibration through a material
medium. The vibrations take the form of molecules and atoms colliding with each
other and then bouncing back only to collide again with other atoms and
molecules and then bounce backÑa process that continues until the energy
involved in the bouncing motion is dissipated throughout the medium. When the
molecules and atoms collide, they form a region called a condensation, and when
they bounce back and are a maximal distance from their neighbors, they form a
region called a rarefaction. The region of condensation is a region of high
pressure, while the region of rarefaction is a region of low pressure. The pressure
varies continuously between these two extremes during a vibration. Hence one
can see that sound waves are actually pressure waves, the high point of the
pressure being the crest of the wave and the low point the trough of the wave.
High and low pressure are familiar terms in weather forecasting, referring to air
pressure; thus one could view the weather as due to complicated sound patterns!
The speed of the wave is the speed at which this propagation travels through the
medium. What property of the vibrations control the loudness or intensity of the
sound? The answer is the amplitude: the greater the amplitude, the louder the
sound. The further the sound travels from its source, the more its loudness or
intensity decreases; this is called attenuation of the wave.
Clearly, sound waves are not limited to air; molecules and atoms can be
made to vibrate in any medium. For example, in order to hear the approach of a
herd of elephants, one can place one's ear to the ground and hear them through
the ground before one hears them through the air. The reason this maneuver
gives more information than just standing and listening is that sound travels
through the ground faster and with less attenuation than through the air. What
factors affect the speed of propagation of sound? It can be shown that
Let us explain these terms: the inertial property of a medium can be its
mass, weight, or density, while the elastic property is a measure of how hard it is
to compress the medium, which in turn depends on the restoring force of the
medium. The restoring force is the force that the medium or material exerts in
order to restore displaced molecules or atoms to their original equilibrium
position. Thus the restoring force controls the rate at which displaced atoms or
molecules vibrate, which is, of course, the frequency of the vibration.
In Lesson 3 we considered the compressibility of materials in discussing the
difference between solids, liquids, and gases. We mentioned there that it is easier
to compress a gas than a liquid and easier to compress a liquid than a solid. Thus
the restoring force in a gas is weaker than that in a liquid, which is weaker than
that in a solid. So we would expect the frequency of vibrations to be greater in
solids than in liquids and least in gases. The speed of sound is a little trickier
since it depends on the ratio of two properties. One can say that if the restoring
force is the same in two materials, then the speed will be less in the material that
has the greatest density, or mass; if the mass or density are the same, the speed
will be greatest in the material that has the largest restoring force, which is the
same thing as the hardest to compress. As an example let us consider helium
and air. Helium is lighter, therefore less dense, than air (helium balloons float in
air ). They are both gases, but helium is harder to compress than air. Thus the
speed and the frequency of sound in helium is greater than that in air. How do we
perceive that the frequency of sound is higher? It is by the pitch of the sound, the
higher the pitch, the higher the frequency and vice-versa. In a given material the
speed of sound is constant, so within the same medium the frequency determines
the wavelength and the wavelength the frequency. Hence the pitch can be
associated with either property.
On a radio we have controls for pitch, tone, and volume, or loudness. This
property of a sound wave-loudness-corresponds to its amplitude. The smaller
the amplitude, the softer the sound. Air is a complicated medium as it is a
mixture of various components: oxygen molecules, nitrogen molecules, water
molecules, carbon dioxide, traces of some inert gases and, of course, other
pollutants! The speed, frequency, and attenuation of sound travelling through air
depends on the relative amounts of all of these in the total mixture. For instance,
let us consider water vapor. The water molecule is H2O, while the nitrogen and
oxygen molecules are respectively N2 and O2. Thus although the water molecule is
lighter than either the oxygen or nitrogen molecule, the combination found in humid
air is however heavier as the water adds to the air already there. Measurement shows
that the compressibility of nitrogen and oxygen is a little less than that of water
vapor, thus their elasticity is a little more than that of water. Hence the numerator
increases slightly and denominator increases a lot, leading to the valid prediction
that if air is more humid, sound travels slower.
How does temperature affect the speed of sound? As a material heats up, the
atoms and molecules that constitute it move faster and faster and in a sense more
randomly; thus the vibrations that make up the sound wave get lost in the general
chaos of motion and, in general, attenuate quicker. Also convection currents in
the material carrying the sound can redirect the sound wave. For instance on hot
days warm air from the ground rises, carrying a portion of sound waves produced
at ground level into the sky, while on cold nights the motion of air is downwards
towards the cold ground, keeping sound waves produced at ground level on the
ground level; thus on warm days sound attenuates quicker than on cold nights.
Sound waves also depend intimately on the medium or material through which
they travel. If there is no material, there is no sound. Thus no sound exists in a
vacuum, such as the surface of the moon; no matter how hard you talk there, no
sound will come out!
We have discussed in detail sound waves that are longitudinal waves, but
how about transverse waves, where the vibration is perpendicular to the direction
of wave propagation? Electromagnetic waves are examples of such waves. These
waves are somewhat strange since they are not material waves, but are formed by
the propagation of fluctuations in magnetic and electric fields. Such fields can
exist in a vacuum; therefore, such waves can travel through a vacuum, which is
a happy conclusion, otherwise we could not explain seeing the sun and the stars!
As we shall see later in the course, the speed of light in a vacuum is the same to
any observer no matter what their speed! This is not true for sound waves. If
observers are moving relative to the medium, they will experience a different
speed of sound than an observer stationary with respect to the medium. The speed
of light, however, does vary according to materials that it is propagating in. This
is due to the electric and magnetic fields of these materials interacting with the
fluctuating electromagnetic field that is the light. This interaction takes its toll on
the electromagnetic wave, and the wave gradually loses its intensity as its effect is
spread through the medium and its amplitude decreases. This is exactly
analogous to the attenuation of the sound waves discussed above. To what
property does the intensity of visible light waves correspond? It is the brightness,
while the frequency and wavelength correspond to the color. These terms really
only apply to electromagnetic radiation that is directly perceivable to our eyes.
Such radiation, however, occupies a very small part of the spectrum:
| Radiowave | Microwave | Infrared | Visible | Ultraviolet | X-rays | gamma-rays |
| 0 Hz | 5x10^8 Hz | 10^11Hz | 7x10^14 Hz | 10^15 Hz | 7x10^17 Hz | 10^18 Hz |
Radiowaves carry radio signals through the atmosphere to our radio sets.
The frequencies of the carrier wave of the radio station are the numbers, such as
Q102, uttered by the radio announcers. This actually refers to a radio station
transmitting at 102 Mega Hertz (MHz) (i.e., 102x10^6 Hz). It is interesting to
calculate the wavelength of this wave: the speed of light through air is 3x10^8 m/s
(meters per second); thus using the relationship speed equals wavelength times
frequency, we see that the wavelength is equal to
3x10^8/102x10^6 = 300000000/102000000 = 2.94 meters
which is about the length of two normal people. Thus as you sit or stand in your
room you fit easily into the valley between two crests of such a wave! The wave will
not notice you (remember why we can't see atoms with visible light?) and you will
not disturb the wave. However large buildings or other obstructions are bigger
than one wavelength and can interfere with the wave, causing bad reception. How
does the wave actually reach your radio? It flows past a metal antenna placed in
an unobstructed site and causes the electrons in the metal to oscillate, thus
producing an alternating electric current that is conveyed into the radio set.
Inside the set the tuning control can be varied to make the radio especially
sensitive to oscillations of a certain frequency, the frequency at which the radio
station of choice transmits. The alternating current in the radio set then passes to
the loudspeaker causing it to vibrate and produce vibrations of air molecules (i.e.,
sound waves) that then travel to your ears. The term FM refers to Frequency
Modulation, which means that the frequency of the carrier wave is altered a little
around the carrier frequency in order to convey the variation of musical sound
and speaking. The term AM refers to Amplitude Modulation, which means that
the amplitude of the carrier wave is varied to convey music and so on. The
amplitude of a wave is more easily distorted by the atmosphere and obstructions
than the frequency; thus FM is more interference free than AM.
What happens when waves hit obstructions? Some of the incident wave is
reflected, while some of it enters the obstructing material, which causes the wave
to bend from its original path due to the fact that the speed of the wave changes.
This is called refraction of the wave. If the material is thin enough, a portion of
the wave will emerge from the other side and one says that it has been
transmitted. But usually some of the wave is absorbed by the material and the
wave attenuates as it continues on its passage through the material. All of the
preceding is valid for both light and sound waves. In the case of light most of these
effects are necessary for us in order to observe objects and people around us,
including ourselves, which we see mostly by reflected light. For sound they
determine the acoustic properties of concert halls or living rooms or the echo
across the valley.
Up to now we have barely mentioned water waves. Are they transverse waves
or are they longitudinal waves? They turn out to be neither; they are a mixture of
both types resulting in circular waves. The medium (water) vibrates in a circular
fashion: 
We noted above that the observed speed of a wave only depends on the nature
of the medium and the motion of the observer with respect to the medium and not
at all on the motion of the wave's source. But what if the source is moving with
respect to the medium? What effect does this have? If the source is moving toward
the observer, it catches up to the waves it has already set in motion (remember the
wave's speed does not depend on the source, but on the medium ) so there is less
distance between the crest of waves; hence the wavelength is decreased and the
frequency increased. (Again remember the speed is constant; thus using the
formula wavelength times frequency equals speed, we get an increased
frequency.)
If the source is moving away from the observer, the distance between
the waveÕs crest increases and the frequency decreases. This change of
wavelength and frequency due to a moving source is called the Doppler Effect. An
often observed example of this effect with sound waves is when a train coming
toward you is blowing its whistle; the pitch of the whistle increases until the train
passes and then the pitch decreases. The Doppler Effect is also observed with light
waves.
If a source is coming towards you, the frequency increases, while if the
source is going away from you, the frequency decreases. Thus if a star is emitting
yellow light, like our sun, but is travelling away from the earth, the light seen on
the earth from the star will be red, as the observed frequency is less than the
emitted one. This is called a Red Shift. If the star is moving towards the earth, the
observed color will be blue as the observed frequency is more than the emitted one.
This is called a Blue Shift. There is a very famous law in astrophysics, called
HubbleÕs Law, that relates the speed of recession, which is proportional to the
amount of red shift, to the distance the star is away from the earth. The validity of
this law is crucial for many astronomical theories. Astronomical distances can be
immense, thus light takes time in travelling from distant sources to the earth.
For instance, it takes eight minutes for light to reach us from the sun. Thus we
see the sun as it was eight minutes ago, not as it is now! This is even more
pronounced for distant stars from which it can takes millions of years for the light
to reach us, which means we see these stars as they were millions of years ago,
not as they are now-if indeed they still exist! By Hubble's Law the older the light
reaching us, the greater the red shift.
Why would stars and galaxies be moving away from us faster the further they
are from us? One explanation is that the structure of the universe is due to a huge
explosion of one concentrated point of matter about sixteen billion years ago and
the ensuing expansion is gradually slowing down. Thus we observe distant stars and
galaxies, which we see as they were in the past, as moving away from each other
and from us at a greater speed than we observe closer ones doing.
To conclude this unit, let us view waves and vibrations in a more abstract
setting. It can be shown that the frequency of a wave is proportional to its energy.
(We will discuss this further when we describe quantum mechanics in later
lessons.) The amplitude of a wave is related to the probability that the wave will
transfer its energy and the number of vibrators of that frequency present. If a
wave has a very small amplitude, it will disturb its surroundings minimally, no
matter what its frequency. If it has a larger amplitude, it will disturb its
environment more (i.e., it will interact with its surroundings, forcing its
surroundings to vibrate). We can look at this as a transfer of energy. The bigger
the amplitude, the more likely it is that energy will be transferred-that the wave
will have a disturbing effect on its environment.It is the probability of energy
transfer, in other words the degree of interaction, not energy itself, that we and
nature in general experience.