1. Waves

2. What is a wave? An oscillation is a movement back and forth.
An oscillation that travels is a wave.

3. 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.

4. Waves in time and space
A wave oscillates up and down over time at a given point in space.

5. 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.

6. Amplitude
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: A
Water wave amplitude is a distance, in meters.
Sound wave amplitude is a pressure, in pascals.

7. Wavelength λ
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?

8. 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.

9. 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?

10. 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

11. 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.

12. 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)

13. Wave speed
As a wave moves forward, it advances one wavelength with each complete cycle.
distance:

14. Wave speed
As a wave moves forward, it advances one wavelength with each complete cycle.
distance:
speed:

15. Wave speed
As a wave moves forward, it advances one wavelength with each complete cycle.
distance:
speed:
frequency:

16. Wave speed
As a wave moves forward, it advances one wavelength with each complete cycle.
distance:
speed:
frequency:
wave speed:

17. 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

18. 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? hertz
Frequency
5.0
2.5
2.0

19. 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

20. 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
What happens if frequency is doubled?
Wavelength
343
686
0.50
Increase the volume. What wave characteristic is affected?

21. 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
What happens if frequency is doubled? Pitch increases and wavelength is halved.
Wavelength
343
1372
0.25
Increase the volume. What wave characteristic is affected? the amplitude

22. Test your knowledge
This wave’s motion is graphed as a function of time and distance.
What is the wave frequency?
What is the wavelength?
What is the amplitude?
Calculate the speed of the wave.

23. Test your knowledge
This wave’s motion is graphed as a function of time and distance.
What is the wave frequency? 1 Hz
What is the wavelength? 5 cm
What is the amplitude? cm
Calculate the speed of the wave. 5 cm/s (0.05 m/s)

24. 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:

25. 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:

26. 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.

27. Energy and frequency The energy of a wave increases with frequency:
lower energy
low frequency
(slower oscillations)
long wavelength

28. Energy and frequency The energy of a wave increases with frequency:
lower energy higher energy
low frequency high frequency
(slower oscillations) (faster oscillations)
long wavelength short wavelength

29. Energy and amplitude
The energy of a wave also increases with amplitude:
lower energy
small amplitude

30. Energy and amplitude
The energy of a wave also increases with amplitude:
lower energy higher energy
small amplitude large amplitude

31. 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.

32. Transverse waves
A transverse wave causes oscillations that are perpendicular to the forward motion of the wave.
Examples:
waves in a string
light waves

33. 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.

34. 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.

35. Longitudinal waves
Point out that amplitude for this wave is not a distance. it is the coil density. Show the students that the wave crests and troughs on the graph correspond to points of most and least coils per centimeter in the Slinky® illustration.

36. 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 y-direction—not in the x-direction.

37. Polarization
What kind of waves can be polarized? Transverse waves? longitudinal waves? or both types?

38. 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.

39. Assessment
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.
What is the frequency?
What is the wavelength?
What is the amplitude?
Calculate the wave speed.

40. Assessment
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.
What is the frequency? 0.5 Hz
What is the wavelength? 20 cm
What is the amplitude? 0.5 cm
Calculate the wave speed.

41. Assessment
Provide an example of a transverse wave and a longitudinal wave. Describe how they are similar and how they are different.

42. Assessment
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.

43. Homework
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