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An oscillation is a movement back and forth.
An oscillation that travels is a wave.
What is a wave?What is a wave?
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 and energyWaves and energy
Waves in time and spaceWaves in time and spaceA wave oscillates up and down over time at a given point in 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.
Waves in time and spaceWaves in time and space
A
The amplitude A of a wave is the maximum amount the water rises or falls compared to its average resting level.
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.
Amplitude Amplitude
The wavelength λ is the distance a wave travels before it begins to repeat itself.
The wavelength can be measured from peak to peak, or trough to trough.
How many wavelengths appear in this figure?
Wavelength Wavelength
λ
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 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 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 Frequency
The frequency of a wave conveys information.
Frequency remains the same even if the wave amplitude decreases as it spreads out.
• the frequency of a light wave determines its color.
• the frequency of a sound wave determines its pitch.
Frequency Frequency
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 Wave speed
As a wave moves forward, it advances one wavelength with each complete cycle.
distance:
Wave speed Wave speed
As a wave moves forward, it advances one wavelength with each complete cycle.
distance:
speed:
Wave speed Wave speed
As a wave moves forward, it advances one wavelength with each complete cycle.
distance:
speed:
frequency:
Wave speed Wave speed
As a wave moves forward, it advances one wavelength with each complete cycle.
distance:
speed:
frequency:
wave speed:
Wave speed Wave speed
A water wave has a speed of 5.0 m/s and a wavelength of 2.0 m. What is its frequency?
Engaging with the conceptsEngaging with the concepts
5.0 2.0
Frequency
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
Engaging with the conceptsEngaging with the concepts
Frequency
5.0 2.02.5
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?
Engaging with the conceptsEngaging with the concepts
Wavelength
343 686
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
What happens if frequency is doubled?
Engaging with the conceptsEngaging with the concepts
Wavelength
343 0.50686
Increase the volume. What wave characteristic is affected?
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
What happens if frequency is doubled? Pitch increases and wavelength is halved.
Engaging with the conceptsEngaging with the concepts
Wavelength
343 0.251372
Increase the volume. What wave characteristic is affected? the amplitude
Test your knowledgeTest your knowledge
This wave’s motion is graphed as a function of time and distance.
a. What is the wave frequency?
b. What is the wavelength?
c. What is the amplitude?
d. Calculate the speed of the wave.
This wave’s motion is graphed as a function of time and distance.
a. What is the wave frequency? 1 Hz
b. What is the wavelength? 5 cm
c. What is the amplitude? 10 cm
d. Calculate the speed of the wave. 5 cm/s (0.05 m/s)
Test your knowledgeTest your knowledge
Test your knowledgeTest your knowledgeTwo 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:
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 knowledgeTest your knowledge
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.
Wave energyWave energy
lower energy
low frequency(slower oscillations)long wavelength
The energy of a wave increases with frequency:
Energy and frequencyEnergy and frequency
lower energy higher energy
low frequency high frequency(slower oscillations) (faster oscillations)long wavelength short wavelength
The energy of a wave increases with frequency:
Energy and frequencyEnergy and frequency
The energy of a wave also increases with amplitude:
lower energy
small amplitude
Energy and amplitudeEnergy and amplitude
lower energy higher energy
small amplitude large amplitude
Energy and amplitudeEnergy and amplitudeThe energy of a wave also increases with amplitude:
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.
Waves in 3-D spaceWaves in 3-D space
A transverse wave causes oscillations that are perpendicular to the forward motion of the wave.
Examples:•waves in a string•light waves
Transverse wavesTransverse 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.
Transverse wavesTransverse waves
Move a Slinky® rapidly forward and back to create a longitudinal compression wave.
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
Longitudinal wavesLongitudinal waves
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 y-direction—not in the x-direction.
PolarizationPolarization
What kind of waves can be polarized? Transverse waves? longitudinal waves? or both types?
PolarizationPolarization
What kind of waves can be polarized? Transverse waves? longitudinal waves? or both types?
PolarizationPolarization
•Transverse waves, such as light waves, can be polarized.
•Longitudinal waves, such as sound waves, cannot be polarized.
AssessmentAssessment1. 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.
AssessmentAssessment1. 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.
2. Provide an example of a transverse wave and a longitudinal wave. Describe how they are similar and how they are different.
AssessmentAssessment
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.
AssessmentAssessment