Unit 1 Lesson 1
Basics of Waves
Waves – a series of disturbances that travels through a medium, transporting energy from
one location (its source) to another location without transporting matter. Each individual
particle of the medium is temporarily displaced, and then returns to its original
equilibrium position. Ex. water, sound, light, radio waves etc.
Study of a single wave pulse shows that it begins with a vibration and is transmitted
through internal forces in the medium.
Continuous waves start with vibrations too. If the vibration is SHM, then the wave will
be sinusoidal.
Pulse –A pulse is a single disturbance moving through a medium from one location to
another location.
Medium – A medium is a substance or material that carries the wave. The wave medium
is not the wave and it doesn't make the wave; it merely carries or transports the wave
from its source to other locations.
Particle-to-Particle Interaction
To fully understand the nature of a wave, it is important to consider the medium as a
collection of interacting particles. In other words, the medium is composed of parts that
are capable of interacting with each other. The interactions of one particle of the medium
with the next adjacent particle allow the disturbance to travel through the medium.
Wave
Medium
Particles
Slinky
slinky coils
individual coils
Sound
air
air molecules
Stadium wave
fans
fans
Ocean
water
water molecules
Earthquake
Earth
ground
Check Your Understanding
1. TRUE or FALSE: In order for John to hear Jill, air molecules must move from
the lips of Jill to the ears of John.
Answer: False. A sound wave involves the movement of energy from one location to
another, not the movement of material. The air molecules are the particles of the medium,
and they are only temporarily displaced, always returning to their original position.
2. Mac and Tosh are experimenting with pulses on a rope. They vibrate an end up
and down to create the pulse and observe it moving from end to end. How does
1
the position of a point on the rope, before the pulse arrives, compare to the
position after the pulse has passed?
Answer: The point returns to its original position. Waves (and pulses) do not
permanently displace particles from their rest position.
Types of waves: Waves can be categorized on the basis of their ability or inability to
transmit energy through a vacuum - electromagnetic waves and mechanical waves.
Electromagnetic Waves
All light waves, radio waves, microwaves, Xrays etc.
Mechanical
Sound waves, slinky waves, water waves, stadium
waves, and jump rope waves
Do not require a medium for transfer; can
be transferred through a vacuum
Mechanical waves require a medium in order to
transport their energy from one location to another.
Speed (in vacuum) is 3.0 x 108 m/s
Speed depends on the mechanical properties of the
medium
Some mechanical waves undergo back and forth
displacement - longitudinal (ex. Sound wave)
All EM waves are sinusoidal transverse
(EMF field, electric and magnetic fields
perpendicular to motion)
Some waves are transverse -particles undergo up and
down displacement (ex. Waves on a string)
2
Types of mechanical waves: Waves can be categorized on the basis of the direction of
movement of the individual particles of the medium relative to the direction that the
waves travel - transverse waves, longitudinal waves.
Transverse (sinusoidal): A transverse wave is a wave in which particles of the medium
move in a direction perpendicular to the direction that the wave moves.
As a wave passes through a point, the particles vibrate at right angles to the direction in
which the wave is moving.
As the wave moves through point A, the particle does not return to its original position
until point E.
Crest - High points of each wave—maximum upward displacement.
Trough - Low points of each wave—maximum downward displacement
Mean Position - Equilibrium line, at rest position, average position
Amplitude - Maximum displacement (distance) of wave from mean position
3
Longitudinal: As a wave passes through a point, the particles vibrate parallel to the
direction in which the wave is moving.
4
Wave characteristics:
Wavelength: The distance between corresponding points on consecutive waves; the
symbol is λ and the SI unit is meters.
Amplitude: maximum displacement of wave from mean position; measure of wave’s
energy.
Frequency: the number of vibrations per second; symbol is f and SI unit is Hertz (Hz)
Period: time to complete one vibration; symbol is T, and SI unit is second
Speed: speed with which the wave moves through the medium is the product of the
wavelength and the frequency; SI unit is m/s
speed = v = distance/time = wavelength/period
5
Variables Affecting Wave Speed: Wave speed depends only upon the mechanical
properties of the medium - density, temperature, elasticity. Wave speed does not depend
on wave properties such as amplitude, wavelength, frequency, period etc. Even though
the wave speed is calculated by multiplying wavelength by frequency, an alteration in
wavelength does not affect wave speed. A doubling of the wavelength results in a halving
of the frequency; yet the wave speed is not changed.
Examples:
1. A sound wave produced by a clock chime is heard 515 m away 1.50 s later.
a. What is the speed of sound of the clock’s chime in air?
b. The sound wave has a frequency of 436 Hz. What is its period?
c. What is its wavelength?
2. A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 m/s. How
far apart are the wave crests (compressions)?
3. (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz) and
travel with a speed of 3.00 × 108 m/s. What are the wavelengths of these signals?
(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the
same speed; what are their wavelengths?
6
Boundary Behavior of Waves
As a wave travels through a medium, it may reach the end of the medium and
encounter an obstacle, or perhaps another medium through which it could travel. The
behavior of a wave (or pulse) upon reaching the boundary between media is referred
to as boundary behavior.
Waves at boundaries between different media:






Speed of wave doesn’t depend upon the frequency or amplitude of the wave;
speed depends upon the properties of the medium
At a boundary, part of the incident wave is reflected back upon itself in the
original medium and part is transmitted through the second medium
The more dense the second medium is, the less wave energy is transmitted
The reflected wave, the incident wave, and the transmitted wave all have the
same frequency; the velocity and the wavelength of the waves change
When a wave passes from a less dense to a more dense medium, the
reflected wave is inverted
When a wave passes from a denser medium to a less dense medium, the
reflected wave is unchanged.
From high speed to low speed (low density to high density)
From low speed to high speed (high density to low density)
7
If medium is constant
If medium changes
http://phet.colorado.edu/sims/wave-on-a-string/wave-on-a-string_en.html
Interference: Interference is the interaction of two or more waves passing the same
point. It is the result of the superposition of two or more waves. As a result, the medium
takes on a shape that combines the effect of the two individual waves upon the particles
of the medium.
Constructive Interference- Constructive interference is a type of interference that
occurs at any location along the medium where the two interfering waves have a
displacement in the same direction.
Destructive Interference - Destructive interference is a type of interference that occurs
at any location along the medium where the two interfering waves have a displacement in
the opposite direction.
8
Superposition Principle – when two waves are in the same place at the same time, the
displacement caused by the waves is the algebraic sum of the two waves.
Traveling waves are observed when a wave is not confined to a given space along the
medium. The most commonly observed traveling wave is an ocean wave.
Standing wave – two identical waves (ie. with the same wavelength, frequency, and
amplitude) traveling through a medium in opposite directions, and confined to a given
space, interfere producing a standing wave.
Node – Point of no displacement on a standing wave—point of maximum destructive
interference on a standing wave
Antinode – point of maximum displacement on a standing wave—point of maximum
constructive interference on a standing wave.
Identify the nodes and antinodes in the diagram.
9
Doppler Effect
The Doppler effect is observed whenever the source of waves is moving with respect to
an observer. The Doppler effect can be described as the effect produced by a moving
source of waves in which there is an apparent upward shift in frequency for observers
towards whom the source is approaching and an apparent downward shift in
frequency for observers from whom the source is receding. It is important to note that
the effect does not result because of an actual change in the frequency of the source.
The Doppler effect can be observed for any type of wave - water wave, sound wave, light
wave, etc. We are most familiar with the Doppler effect because of our experiences with
sound waves. Perhaps you recall an instance in which a police car or emergency vehicle
was traveling towards you on the highway. As the car approached with its siren blasting,
the pitch of the siren sound (a measure of the siren's frequency) was high; and then
suddenly after the car passed by, the pitch of the siren sound was low. That was the
Doppler effect - an apparent shift in frequency for a sound wave produced by a moving
source.
The Doppler Effect is of intense interest to astronomers who use the information about
the shift in frequency of electromagnetic waves produced by moving stars in our galaxy
and beyond in order to derive information about those stars and galaxies. The belief that
the universe is expanding is based in part upon observations of electromagnetic waves
emitted by stars in distant galaxies. Furthermore, specific information about stars within
galaxies can be determined by application of the Doppler Effect. Galaxies are clusters of
stars that typically rotate about some center of mass point. Electromagnetic radiation
emitted by such stars in a distant galaxy would appear to be shifted downward in
frequency (a red shift) if the star is rotating in its cluster in a direction that is away from
the Earth. On the other hand, there is an upward shift in frequency (a blue shift) of such
observed radiation if the star is rotating in a direction that is towards the Earth.
http://www.astro.ubc.ca/~scharein/a311/Sim/doppler/Doppler.html
10