Waves
Objectives
•
Investigate and analyze the characteristics of waves
including: velocity, frequency, amplitude, and
wavelength.
•
Compare the characteristics and behaviors of transverse
waves and longitudinal waves.
Physics terms
•
oscillation
•
transverse wave
•
wave
•
longitudinal wave
•
wavelength
•
polarization
•
frequency
•
amplitude
Equations
Wave velocity equals the frequency
multiplied by the wavelength.
What is a wave?
Drop a pebble on a pond on a calm day.
As the pebble breaks the surface, the
water oscillates up and down—in
harmonic motion.
Ripples form and spread out.
An oscillation that travels is a wave.
Waves and energy
Waves are an essential way in
which energy travels from one
place to another.
Waves propagate through space,
spreading energy out to other
regions which may be quite far
away.
Waves in time and space
A wave oscillates up and down
over time at a given point in space.
Waves in time and space
A wave oscillates up and down
over time at a given point in space.
The wave’s oscillations extend
in space at any instant in time.
Amplitude
The amplitude A of a wave is the
maximum amount the water rises
or falls compared to its average
resting level.
A
The amplitude of different types of
waves may have different units:
• Water wave amplitude is a distance, in meters.
• Sound wave amplitude is a pressure, in pascals.
Wavelength
The wavelength λ is the
distance a wave travels before
it begins to repeat itself.
λ
The wavelength can be
measured from peak to peak,
or trough to trough.
How many wavelengths
appear in this figure?
Frequency
The frequency f of a wave is a measure
of how quickly it oscillates.
The unit for frequency is the hertz, or Hz.
One hertz equals one cycle per second.
Frequency
When a wave has a frequency of 10 Hz = 10 cycles/second,
then 10 waves travel past a given point each second.
What is the frequency of the wave shown below?
Frequency
When a wave has a frequency of 10 Hz = 10 cycles/second,
then 10 waves travel past a given point each second.
What is the frequency of the wave shown below? 2 Hz
Frequency
The frequency of a wave conveys information.
• the frequency of a light wave determines its color.
• the frequency of a sound wave determines its pitch.
Frequency remains the same even if the wave amplitude
decreases as it spreads out.
Wave speed
The speed of a wave depends on the
type of wave and on its medium.
Examples:
• speed of typical water waves: 5 m/s
• speed of sound in air: 343 m/s
• speed of light: 300,000,000 m/s
(in a vacuum)
Wave speed
As a wave moves forward, it
advances one wavelength with
each complete cycle.
distance:
Wave speed
As a wave moves forward, it
advances one wavelength with
each complete cycle.
distance:
speed:
Wave speed
As a wave moves forward, it
advances one wavelength with
each complete cycle.
distance:
speed:
frequency:
Wave speed
As a wave moves forward, it
advances one wavelength with
each complete cycle.
distance:
speed:
frequency:
wave speed:
Engaging with the concepts
A water wave has a speed
of 5.0 m/s and a wavelength
of 2.0 m. What is its
frequency?
Frequency
5.0
2.0
Engaging with the concepts
A water wave has a speed
of 5.0 m/s and a wavelength
of 2.0 m. What is its
frequency? 2.5 hertz
Frequency
5.0
Find two different ways to
get a speed of 100 m/s.
2.5
2.0
Engaging with the concepts
A water wave has a speed
of 5.0 m/s and a wavelength
of 2.0 m. What is its
frequency? 2.5 hertz
Speed of wave
100
Find two different ways to
get a speed of 100 m/s.
There are many
correct answers!
25
4.0
Engaging with the concepts
A sound wave has a speed
of 343 m/s in air. What is the
wavelength of a sound wave
with frequency of 686 Hz?
Wavelength
343
686
Engaging with the concepts
A sound wave has a speed
of 343 m/s in air. What is the
wavelength of a sound wave
with frequency of 686 Hz?
λ = 50 cm
Wavelength
What happens if frequency
is doubled?
Increase the volume. What
wave characteristic is
affected?
343
686
0.50
Engaging with the concepts
A sound wave has a speed
of 343 m/s in air. What is the
wavelength of a sound wave
with frequency of 686 Hz?
λ = 50 cm
Wavelength
What happens if frequency
is doubled? Pitch increases
and wavelength is halved.
Increase the volume. What
wave characteristic is
affected? the amplitude
343
137
2
0.25
Test your knowledge
This wave’s motion is graphed as a function of time and distance.
a.
b.
c.
d.
What is the wave frequency?
What is the wavelength?
What is the amplitude?
Calculate the speed of the wave.
Test your knowledge
This wave’s motion is graphed as a function of time and distance.
a.
b.
c.
d.
What is the wave frequency? 1 Hz
What is the wavelength? 5 cm
What is the amplitude?
10 cm
Calculate the speed of the wave. 5 cm/s (0.05 m/s)
Test your knowledge
Two students use a 10-meter-long spring to create a standing
wave. The wavelength is 2.0 m and the frequency is 2.0 Hz.
How fast is the wave traveling along the spring?
Asked: speed v
Given:
Relationship:
Solution:
Test your knowledge
Two students use a 10-meter-long spring to create a standing
wave. The wavelength is 2.0 m and the frequency is 2.0 Hz.
How fast is the wave traveling along the spring?
Asked: speed v
Given:
Relationship:
Solution:
Wave energy
A wave is an organized mechanism
for transferring energy.
• As a wave moves through matter,
its energy causes the matter to
respond.
• After the wave passes, the matter
returns to equilibrium.
Energy and frequency
The energy of a wave increases with frequency:
lower energy
low frequency
(slower oscillations)
long wavelength
Energy and frequency
The energy of a wave increases with frequency:
lower energy
higher energy
low frequency
(slower oscillations)
long wavelength
high frequency
(faster oscillations)
short wavelength
Energy and amplitude
The energy of a wave also increases with amplitude:
lower energy
small amplitude
Energy and amplitude
The energy of a wave also increases with amplitude:
lower energy
higher energy
small amplitude
large amplitude
Energy and amplitude
As a wave spreads out, its amplitude decreases.
• One reason is damping; friction
reduces the wave’s energy over time.
Energy and amplitude
As a wave spreads out, its amplitude decreases.
• One reason is damping; friction
reduces the wave’s energy over time.
• Another reason is that as the wave
propagates outward, its energy is
spread over a larger area.
Test your knowledge
Although speech gets quieter farther
from its source, the words and tone
stay the same. Why?
Test your knowledge
Although speech gets quieter farther
from its source, the words and tone
stay the same. Why?
As the wave spreads out the amplitude
of the sound waves is reduced, but the
frequency remains constant.
The waves still transfer the same
information, even though they have
less energy.
Waves in 3-D space
Waves can cause oscillations
in three dimensions.
The direction of motion of the
wave is defined as the
forward dimension.
The other two dimensions
(left-right and up-down) are
perpendicular to the direction
of motion.
Transverse waves
A transverse wave causes
oscillations that are
perpendicular to the forward
motion of the wave.
Examples:
• waves in a string
• light waves
Transverse waves
Transverse waves can oscillate in
any direction that is perpendicular
to the direction the wave is
traveling!
Try creating both vertically and
horizontally oscillating transverse
waves using a wave motion rope.
Longitudinal waves
A longitudinal wave causes
oscillations that move back and
forth in the same direction as
the traveling wave.
Examples:
• sound waves
• the waves in a spring as
shown in this figure
Move a Slinky® rapidly forward
and back to create a longitudinal
compression wave.
Longitudinal waves
Polarization
Polarization describes the direction of
the oscillation in a plane perpendicular
to the wave velocity.
The wave in this figure is polarized. It
is traveling in the z-direction and its
oscillations occur only in the ydirection—not in the x-direction.
Polarization
What kind of waves can be polarized?
Transverse waves? longitudinal waves?
or both types?
Polarization
What kind of waves can be polarized?
Transverse waves? longitudinal waves?
or both types?
• Transverse waves, such as light
waves, can be polarized.
• Longitudinal waves, such as
sound waves, cannot be polarized.
Assessment
1. These graphs show the oscillation
of a point on a wave as a function
of time, and the oscillation of the
extended wave in space at a
moment in time.
a. What is the frequency?
b. What is the wavelength?
c. What is the amplitude?
d. Calculate the wave speed.
Assessment
1. These graphs show the oscillation
of a point on a wave as a function
of time, and the oscillation of the
extended wave in space at a
moment in time.
a. What is the frequency? 0.5 Hz
b. What is the wavelength? 20 cm
c. What is the amplitude? 0.5 cm
d. Calculate the wave speed.
Assessment
2. Provide an example of a transverse wave and a longitudinal wave.
Describe how they are similar and how they are different.
Assessment
2. Provide an example of a transverse wave and a longitudinal wave.
Describe how they are similar and how they are different.
Each wave is an oscillation that transfers energy.
Waves in a string are transverse waves. Each segment of the string
oscillates perpendicular to the forward motion of the wave.
Sound is a longitudinal wave. The air molecules oscillate back and
forth, parallel to the direction of the wave’s forward motion.
Assessment
3. Describe, in your own words, how a sound
speaker moves to create sound waves.
Assessment
3. Describe, in your own words, how a sound
speaker moves to create sound waves.
A sound speaker oscillates back and forth to
create sound waves, which are longitudinal
compression waves.