Waves
Chapter 25
Waves
• Waves are everywhere. Sound waves, light waves, water
waves, stadium waves, earthquake waves, waves on a string,
and slinky waves and are just a few of the examples of waves.
• Waves are an energy transport phenomenon, a way to
transport energy from one location to another.
• Waves are a disturbance that travels through a medium from
one location to another; a wiggle in space and time.
• The medium is a substance or material that carries the wave.
• Waves are caused by vibrations
• A vibration (or oscillation) is a back-and-forth or up-and-down
motion; a wiggle in time.
Types of Waves
• We will discuss two types of waves longitudinal (or
compression) and transverse
• Transverse wave - oscillations are transverse (perpendicular)
to the direction of motion
• Longitudinal (or Compression) wave - oscillations are in the
direction of motion or parallel to the direction of motion.
Anatomy of a Wave
• The parts of a wave include crest, trough,
wavelength, amplitude, frequency and period
crest
trough
The points A and F are called the
CRESTS of the wave.
This is the point where the wave
exhibits the maximum amount of
positive or upwards displacement
The points D and I are called
the TROUGHS of the wave.
These are the points where the
wave exhibits its maximum
negative or downward
displacement.
Anatomy of a Wave
• The distance between the dashed line and point A is called
the amplitude of the wave.
• The amplitude is the maximum displacement that the wave
moves away from its equilibrium.
• The distance between two consecutive similar points (in this
case two crests) is called the wavelength.
• The wavelength is also the length of the wave pulse.
Wavelength
Wavelength
Amplitude
Wavelength
Wave Frequency and Period
• Frequency measure how often something happens
over a certain amount of time (# of waves/second)
• We can measure how many times a pulse passes a
fixed point over a given amount of time, and this will
give us the frequency.
• The period (T) is the time it takes for one cycle
(wave) to complete.
• The period is also is the reciprocal of the frequency.
• T=1/f
• f=1/T
The Period of a Pendulum
• The motion of a pendulum and the motion of a mass
on a spring can be described using a wave.
• The period of a pendulum is the time is takes for one
full back and forth motion.
Wave Speed
• Wave speed is the distance the disturbance travels in a fixed
amount of time.
• Wave speed can be determined from the product of the
wavelength and the frequency
• velocity = wavelength x frequency
•
v = f
• This equation is known as the wave equation
Wave Questions
1)
2)
3)
4)
5)
Rhonda sends a pulse along a rope. How does the position of a point on
the rope, before the pulse comes, compare to the position after the
pulse has passed?
Why don't incoming ocean waves bring more water on to the shore until
the beach is completely submerged?
In order for a medium to be able to support a wave, the particles in the
wave must be
a) frictionless.
b) isolated from one another.
c) able to interact.
d) very light.
A transverse wave is transporting energy from east to west. How will the
particles of the medium will move?
A wave is transporting energy from left to right. The particles of the
medium are moving back and forth in a leftward and rightward direction.
This type of wave is known as a _______________.
More Wave Questions
6) In the diagram above, the wavelength is given by what letter?
7) In the diagram above, the amplitude is given by what letter?
8) A wave has an amplitude of 2 cm and a frequency of 12 Hz, and the
distance from a crest to the nearest trough is measured to be 5 cm.
Determine the period of such a wave.
9) A tennis coach paces back and forth along the sideline 10 times in 2
minutes. The frequency of her pacing is ________.
10) A pendulum makes 40 vibrations in 20 seconds. Calculate its period?
11) Mac and Tosh are resting on top of the water near the end of the pool
when Mac creates a surface wave. The wave travels the length of the pool
and back in 25 seconds. The pool is 25 meters long. Determine the speed
of the wave.
12) A marine weather station reports waves along the shore that are 2 meters
high, 8 meters long, and reach the station 8 seconds apart. Determine the
frequency and the speed of these waves.
Wave Behavior
• Now the we know the parts of a wave and how we
describe and analyze them, we can look at wave
behavior
• In the next section we will look at interference, the
boundary behavior of waves, standing waves and the
Doppler Effect.
The Doppler Effect
The Doppler Effect
• The Doppler Effect is the apparent change in frequency of a wave due to
relative motion between source and observer.
• As the sound move toward the observer, the apparent frequency
decreases, the waves get compressed.
• As the sound moves away from the observer, the apparent frequency
increases, the waves get “stretched out”
• A sound wave frequency change is noticed as a change in pitch.
Doppler
Shift for
Light
Doppler and Line of Sight
We are only
sensitive
to motion
between
source and
observer
ALONG
the line of
sight.
Interference and the Superposition Principle
• Suppose two waves pass through the same medium. What
happens?
• Wave interference is the phenomenon which occurs when
two or more waves meet while traveling along the same
medium.
• The superposition principle tells us how waves interact.
• The principle of superposition is sometimes stated as follows:
When two waves interfere, the resulting displacement of the
medium at any location is the algebraic sum of the
displacements of the individual waves at that same location.
Algebraic
sum of two
waves
Constructive Interference
• Constructive interference is a type of interference which
occurs at any location along the medium where the two
interfering waves have a displacement in the same direction.
The resulting displacement is greater than the displacement
of the two interfering pulses alone.
Wave Addition
Destructive Interference
• Destructive interference is a type of interference which
occurs at any location along the medium where the two
interfering waves have a displacement in the opposite
direction. The resulting displacement is less than the
displacement of the two interfering pulses alone.
Wave Subtraction
Two Opposite Waves
• When the two opposite waves arrive at the same
location, they cancel, destructively.
Interference
• Water waves from two oscillating sources
Computer Simulation
Ripple Tank
Boundary Behavior of Waves
• The behavior of a wave when it reaches the end of its medium
is called the wave’s boundary behavior.
• When one medium ends and another begins, that is called a
boundary.
• One type of boundary that a wave may encounter is that it
may be attached to a fixed end.
The reflected pulse
has the same
speed, wavelength,
and amplitude as
the incident pulse.
Standing Waves
• When a reflected wave interferes with an incident
wave, a standing wave can form.
Nodes are points of no motion
Anti-nodes are points of
maximum motion
Harmonics
• There are a variety of patterns by which the guitar
string could naturally vibrate; each pattern is
associated with one of the natural frequencies of the
guitar strings.
Sources
• Conceptual Physics by Paul Hewitt
• www.physicsclassroom.com
• pls.atu.edu/physci/physics/people/robertson/
courses/phsc1013/PHSC1013-Waves.ppt –
• Waves and Vibrations -Physics: Mr. Maloney