1. Intro to Waves

2. Intro to Waves All things wiggle/vibrate/oscillate.
A wave is a wiggle in time.
The equilibrium is the resting position of a wave.
An object is at rest when experiencing a balance of forces.
An object will remain in this position until it is disturbed.
Forced vibration: The force which sets the resting object into motion.

3. Intro to Waves Waves transfer energy without transferring matter.
Two types of waves:
Mechanical (through a medium)
Electromagnetic (through a “vacuum”, an empty space)

4. Mediums
A medium is a substance or material that carries the wave from its source to other locations.
The medium consists of particles that interact with each other.
Each particle interacts with the adjacent particle, which allows the disturbance to travel through the medium
Examples: air, metal, string, people
Waves travel at different speeds based on the medium

5. Mechanical Waves Requires a medium Ex: water, sound, slinky, stadium
2 types:
Transverse – particles of the medium move perpendicular to the direction that the wave moves
Longitudinal – particles of the medium move parallel to the direction that the wave moves

6. Wave particles move perpendicular to the direction the wave travels
Perpendicular to the direction of travel
Direction of travel
Transverse Wave:
Wave particles move perpendicular to the direction the wave travels
Ex: strings of a musical instrument

7. Particles vibrate parallel to the direction the wave travels
Longitudinal Wave:
Particles vibrate parallel to the direction the wave travels
Ex: sound wave
Direction of travel
Particles vibrate parallel to the direction of travel

8. Parts of a transverse wave
Crest
Wavelength (ג)
amplitude
Equilibrium Position
Wavelength (ג)
amplitude
Wavelength (ג)
Trough

9. Parts of a Transverse Wave – Sine Curve
Crest- highest point on a wave, maximum positive displacement from equilibrium
Trough- lowest point on a wave, maximum negative displacement from equilibrium
Equilibrium position- resting position
Amplitude- from the equilibrium position to the crest or trough
Wavelength – distance between any two identical points on a wave

10. Amplitude
Amplitude is a measure of the amount of energy carried by a wave
High energy = large amplitude
Low energy = small amplitude

11. Parts of a Longitudinal Wave
Compression- point where the particles are closest together
Rarefaction- point where the particles are furthest apart

12. Periodic Motion
A wave moves over the same path over the course of time
The object not only repeats the same motion, it does so in a regular fashion
If it takes 3.2 sec to complete the 1st cycle, it will take 3.2 sec to complete the 2nd, 3rd, 4th…
A motion that is regular and repeating is called periodic motion

13. Damping Some energy is being dissipated over the course of time.
The mechanical energy of the vibrating object is lost to other objects.
The amount of displacement from its equilibrium position changes slightly with each vibration cycle.
Eventually the vibrations will cease.

14. Pulse vs. Wave Pulse: A single disturbance of the medium particles.
The energy passes through the medium in a single cycle and then the disturbance ceases.
Wave: A repeated and periodic disturbance of the medium particles.
A wave vibrates back and forth over a period of time.

15. Wave pulse is a single wave disturbance
Wave train (continuous wave) - is a series of pulses at intervals

16. Speed of waves Speed: how fast an object is moving.
For a wave, speed is the distance traveled by a given point on the wave, such as the crest, in a given time interval
V = d/t
Ex: If a crest moves 20 m in 10 sec, what is the speed?
V = 20 m/10 s
V = 2 m/s

17. Frequency
Frequency (f) is a measure of the number of cycles per unit of time.
Measures in hertz (Hz)
F = # cycles/time

18. Wavelength
wavelength ( ג ): length of one wave (crest to crest or trough to trough)
unit: m (meter)

19. Problem:
What is the velocity of a wave that has a frequency of 3 Hz and a wavelength of 5 m?

20. Period
Period (p) is the time for a particle on a medium to make one complete vibrational cycle.
Measured in seconds
P = time/# cycles

21. Frequency and Period Frequency and Period are inversely related
P = 1/F F = 1/P
If you know one you can solve for the other.
P may also be shown as T (time)

22. Relationship between Frequency and Wavelength
Wavelength and frequency are inversely related
As frequency goes up the wavelength gets shorter (assuming no change in velocity)

23. Practice:
Example 1: The frequency of a wave is 560 Hz. What is its period?
Example 2: A girl floats in the ocean and watches 12 wave crests pass her in 46 s. Calculate the wave:
a) frequency b) period
Example 3: The period of a wave is 0.044s. How many cycles will the energy source make in 22s?

24. Wave Boundary Behavior
As a wave travels through a medium it will often reach the end of the medium and encounter an obstacle or another medium
Boundary – the interface of the 2 media
Boundary behavior – the behavior of a wave upon reaching the end of a medium

25. Wave Interactions
Reflection
Refraction
Diffraction

26. Wave interactions Reflection:
The bouncing back of a wave when it encounters a new medium or boundary
Ex: light off a mirror, or sound echo
Incident wave- incoming wave
Reflected wave – the wave that returns

27. Reflection
Law of Reflection: The angle of incidence is equal to the angle of reflection

28. Refraction The bending of a wave path as it enters a new medium
Caused by difference in speed of the new medium

29. Diffraction Spreading of waves around edges or through
an opening of a boundary

30. Superposition
Displacement of a medium by two or more waves is the sum of the displacements of the waves alone

31. Interference of Waves
Result of the superposition of two or more waves meeting while traveling along the same medium.
Constructive- when the wave displacements are in the same direction; amplitudes add
Destructive – when the waves have opposite amplitudes; amplitudes subtract
Only temporary as paths cross

32. Constructive interference

33. Destructive interference

34. Standing Wave Node Antinode A wave that appears to be standing still
Result from the interference between the incident wave and the reflected wave
The point of no displacement is the node
The point of maximum displacement is the antinode
Node
Antinode

35. Electromagnetic wave Move through empty space (no medium)
Created by moving electrons
Ex. radio waves, microwaves, light