Chapter 14
Section 1: Types of Waves
There are several ways to understand what waves and wave motion are:
1) Waves and wave motion are a way to transfer energy from one place to another WITHOUT any
overall transfer of matter. While this definition is correct, it does NOT really explain how waves behaves
or why/how the transfer of energy occurs.
2) Waves and wave motion are characterized by some characteristic that repeats itself for ever on a
periodic basis IF frictional “losses” are neglected. Once again, this definition is NOT very clear because
there is no indication of what is “waving” AND how/why the “waving” occurs.
Mechanical Waves:
To make things a little easier to understand, only mechanical waves will be considered (at this time). A
mechanical wave is some kind of disturbance in a medium/substance where the distance
moves/propagates at a certain speed but retains its shape as it moves. In mechanical waves, particles
of the medium move short distances and return to their original position as the wave disturbance passes
by. There is NOT any overall motion of the particles in the medium BUT there is overall motion of the
disturbance. The overall motion of the disturbance is what we identify as the wave. The small
motions of the particles in the medium are NOT what we call “wave motion” but it is possible to analyze
this motion in a way that displays wave motion characteristics.
Examples of Mechanical Waves:
1) Water waves
2) Sound waves
3) Seismic waves (caused by an earthquake)
4) Waves on a “whipped” string
Electromagnetic Waves:
There is one kind of wave that does NOT require a material medium. This type of wave is an
electromagnetic wave (or electromagnetic radiation). Scientists were VERY surprised to discover this
fact. ALL forms of EM radiation travel through empty space at the speed of light. Some forms of EM
radiation travel through material objects (light travels through glass and water). In EM radiation, the
things that are “waving” are electric and magnetic fields rather than particles of a medium.
Energy Transfer in Wave Motion:
The further you are from a source of wave motion, the less you are affected by the energy transmitted by
the wave. HOWEVER, never look directly at the Sun. Even though the Earth is 93 million miles from the
Sun, the energy in the EM radiation given off by the Sun WILL damage your eyes. EVEN DURING A
SOLAR ECLIPSE, do NOT look directly at the Sun.
If a wave disturbance propagates/moves in 3 dimensions, the energy that reaches you decreases
inversely with the square of the distance from where the wave starts. For example, at a rock concert, a
person who is 30 meters from the stage gets 1/9 of the sound’s energy compared to a person who is only
10 meters from the stage (30 is 3 times 10; 32 is 9 but the energy is inversely proportional to the square
of the distance from the source of the wave).
The Human Voice:
Sound is alternating high and low pressure regions in the air that strike our ear drum and cause it to
vibrate. Eventually, the vibrations of the ear drum are transmitted to our brain where they are interpreted
as sound. Air passing through the vocal folds (sometimes called vocal cords) becomes sound waves as
the vocal folds vibrate based on precise muscular control. The tongue, mouth, and lips modify the
sound waves so that precise words are spoken.
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Weight on a Frictionless Spring:
A weight on a frictionless spring will continue to “bounce” up and down forever, repeatedly showing the
same displacement from its original position. The regularly repeating displacement is considered wave
motion because it repeats on a regular basis the wave motion does. Another interesting effect is shown
below. The motion of the spring on the left is transferred to the other springs.
If there were no friction, the motion would continue forever called simple harmonic motion. However,
there IS friction and the motion fades out, technically called damped simple harmonic motion.
Waves on a String:
Shaking a string is a good illustration of wave motion. The wave is the deformation of the string that
travels horizontally (or vertically). The particles in the string move back and forth as the wave passes but
do NOT undergo any net motion from their original positions.
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Transverse and Longitudinal Waves:
There are two possible relationships between the direction of motion of a wave and the direction of
motion of the particles in a mechanical wave or the electromagnetic fields in EM radiation.
In a transverse wave, the direction of motion of the particles in the wave medium (or the direction of
change of an electromagnetic wave) is perpendicular to the direction of motion of the wave. Waves on a
string are transversel waves as are electromagnetic waves (EM radiation). Doing “the wave” at a sporting
event is also an example of a transverse wave.
In a longitudinal wave, the direction of motion of the particles in the wave medium is parallel to the
direction of motion of the wave. Sound waves are longitudinal waves as are waves in a spring.
Surface Waves:
Surface waves occur at the boundary between two different material media. The particles in a surface
wave move in a circular motion (a combination of both transverse and longitudinal motion).
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Section 2: Characteristics of Waves
Recall that one characteristic of wave motion is the repetition of something dealing with the wave. This
aspect of wave motion is so important that there are various characteristics of wave motion that describe
the repetition.
The Amplitude of a wave is a measure of the “size” or “strength” of a wave. When a wave is described
mathematically, its amplitude is the length of the largest displacement. For a transverse mechanical
wave, amplitude is relatively easy to visualize. For a longitudinal mechanical wave, the alternating
compressions and expansions produce changes in the density of the medium which vary in a regular way
when plotted vs. the distance from the wave source.
The Wave Length of a wave is the shortest distance between two points on a wave that have the same
displacement or amplitude.
The Frequency of a wave is the number of repetitions of the wave in 1 second.
The Period of a wave is the time it takes for the wave motion to make 1 repetition.
The Speed of a wave is the distance the wave disturbance travels in 1 second
Relationships Between Wave Characteristics
v = wave speed
 = wavelength
v = f
f = frequency
T = period
1
f = --T
The SI System unit for frequency is the Hertz (Hz). 1 Hz = 1 vibration per second. The SI System unit for
period is the second.
Examples:
If the wavelength of a wave is 2 meters and the frequency is 3,000 Hz, the wave speed is 2(3,000) m/s =
6,000 m/s.
If the frequency of a wave is 20 Hz, then the period of the wave is 1/20 seconds = 0.05 seconds.
The speed of ALL electromagnetic waves is the speed of light, approximately 3 × 108 m/s. This means
that for electromagnetic waves, f is a constant. Therefore, for electromagnetic waves, as the
frequency increases the wavelength decreases and vice versa.
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The Electromagnetic Spectrum
Wave Speed in Relation to Medium:
The speed of a wave, even electromagnetic waves, depends on the medium that the wave is passing
through. The speed of EM radiation is 3.00 × 108 m/s IN A VACUUM. When light passes through air,
glass, or water, the speed is less. BUT all EM radiation travels at the same speed through a given
medium.
Likewise, sound waves and seismic waves also change their speed when moving through different
media. But like EM radiation, the speed of sound and seismic waves is a constant in a given medium –
the speed does NOT depend on the frequency or wavelength individually.
For a mechanical wave, wave speed increases as the density of the medium increases. The speed of
sound in air is slower than it is in water and the speed of sound in water is slower than it is in a solid. The
opposite is true for EM waves: EM waves move slower in a denser medium than in a vacuum.
The Doppler Effect:
When a source of a wave disturbance is moving toward you the frequency (as recorded by you)
increases. The opposite occurs as the source moves away from you. This occurs because (as far as you
are concerned) the waves are arriving at a higher rate (higher frequency) as the source moves towards
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you and a lower rate (lower frequency) as the source moves away from you. The Doppler effect is real;
it is NOT an illusion. And it occurs for ALL wave phenomena, even EM waves.
The Doppler effect is often described in terms of pitch for sound waves – pitch is simply a way to describe
frequency when sound is involved.
Section 3: Wave Interactions
One of the “strangest” things about waves is what happens when two waves meet/collide. When two
particles collide they either stick together or bounce off each other or a combination of these interactions
occur. Waves behave differently.
Reflection:
When a wave meets an impenetrable boundary, it is reflected (its velocity is reversed in direction but
NOT magnitude). For mechanical waves, exactly how the reversed wave behaves depends on how the
impenetrable boundary is “connected” to the vibrating medium.
Electromagnetic waves,
reflection.
mechanical waves,
and macroscopic particles exhibit
Refraction:
When a wave is incident on a boundary such that the direction of the wave is NOT perpendicular to the
boundary (the wave strikes the boundary “at an angle”), the direction of motion of the wave will change.
When the wave is light, the light is said to “bend”, giving the appearance that things are bent or that
things are located in different positions from their actual location. When a wave is refracted, its velocity
changes in both direction and magnitude and the wave is said to “bend.”
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BOTH Electromagnetic waves and mechanical waves exhibit refraction BUT macroscopic
particles do NOT exhibit refraction.
Diffraction:
When a wave is incident on the edge of a boundary, the wave can “go/bend around the corner” of the
boundary by “spreading out” as if the source of the wave were at the edge of the boundary. This
“bending” of a wave “around a corner” or edge of a boundary is different from the apparent bending of an
object in a glass of water.
BOTH Electromagnetic waves and mechanical
macroscopic particles do NOT exhibit diffraction.
waves
exhibit
diffraction
BUT
Interference:
When two or more waves meet at the same place, the waves “interfere” with each other by combining
their effects. Moreover, the individual waves retain their individual velocities which are not changed;
when each wave continues in its original direction, the wave emerges unchanged from the “meeting.”
Depending on the wave in which the waves meet, a new combined wave may result or the individual
waves may emerge unchanged.
There are two kinds of interference: (1) constructive interference refers to the situation where waves of
the same frequency and wavelength meet and the amplitude of the combined wave is the sum of the
individual amplitudes of the waves. (2) destructive interference refers to the situation where waves of
the same frequency and wavelength meet and the amplitude of the combined wave is the difference of
the individual amplitudes of the waves.
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BOTH Electromagnetic waves and mechanical waves exhibit interference BUT
macroscopic particles do NOT exhibit interference.
Wave Interference
BOTH Electromagnetic waves and mechanical waves exhibit interference BUT
macroscopic particles do NOT exhibit interference.
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Beats:
When two sound waves of almost the same frequencies (f1 and f2) are “played” simultaneously, a sound
wave with frequency (f1 + f2)/2 results whose amplitude varies with the frequency |(f1 - f2)/2|. The
pulsating amplitude is sensed by our ears. This pulsation is called beats. Musicians use beats to tune
instruments to the same notes. When the beats disappear, the two instruments are playing the same
note (same frequency).
Standing Mechanical Waves:
Standing mechanical waves occur when wave motion occurs between boundaries where no motion of the
medium occurs at the boundaries. Standing waves result from reflection and interference where the
positions at which no motion of the medium occurs remain the same. Even though waves are traveling in
opposite directions and interfering (both constructively and destructively), it appears as if the vibrating
medium is “standing still.” The points at which no motion of the medium occurs are called nodes.
The longest wavelength for a standing wave in a rope of length L is 2L.
Chapter Review Questions
page 480: #1, #2, #3 (does NOT depend on …), #4, #6 - #15
page 481: #16 - #19 (assume spring is frictionless), #20 (use the term density), #23 - #27, #29 - #34
page 482: #36 - #41, #43
page 483: #48, #52
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