1. Waves 1
The Transfer of Energy

2. The Basics: A λ d(m) (#λ or m) d = displacement
Amplitude = max displacement from origin
λ = wavelength (in m)
f = frequency = oscillations per second = Hz = s-1 = 1/s
T = period = time per oscillation (in seconds)
V = velocity = λ /T or λf (in m/s)
f (units = 1/s) so f = 1/T

3. Wave types
Longitudinal wave = motion of particle in same direction as motion of energy ( )
Sound waves –
Transverse wave = motion of particle is perpendicular to motion of the energy ( )
Slinky, light -

4. Waves investigation A
Discuss your observations as a class when finished….

5. Waves on a string calculations
L in m Ft in N Mass in kg velocity in m/s
Strings: v = Ft
m/l
(length density)

6. Waves on a string question 1
1) A guitar string has a length of 70cm, a mass of 1.5g, and is strung to a tension of 100N. (a) At what speed do waves travel in the string when it is plucked?
This type of question will be on the quiz!

8. Waves on a string question 2
If the density of a violin string is 7.8 x 10-4 kg/m, then if a wave on the string has a frequency of 440 Hz, and a wavelength of 65 cm, then what is the tension in the string?

9. Key

10. Follow up questions: 1) Violin string L = .9m, mass = 2g., Ft = 80N
What is the velocity of the wave on the string?
2) String density = 4.6 x 10-3 kg/m,
f of wave = 300 1/s, wavelength = 80cm
What is the force of tension on the string?

11. Key
1) m/s = v
2) 265 N = Ft

12. Mode (n) = basic unit of oscillation: L of the wave =( n/2)(λ)
node anti-node
1st Fundamental 1st mode
Lowest f of periodic waveform:
L =n/2 λ = ½ λ
2nd mode (3 nodes):
L = n/2 λ = 2/2 λ = 1λ
3rd mode (4 nodes) L = 3/2λ
4th mode (5 nodes)
L = 4/2λ = 2λ
n = 1
n = 2
n = 3
n = 4
n = 5

13. Superposition
Waves in a medium pass each other without being disturbed

14. Constructive and destructive interference

15. Standing waves
2 waves moving in opposite directions have interference that results in a stationary wave pattern – no net propagation of energy! (demo)
Note: wave can appear and disappear in same spot – no forward propagation!
Also happens when medium is moving in opposite direction as wave (standing wave in river)
Show Waimea river standing wave
Making standing waves 30s – 1:30s

16. Conduct investigation B here

17. Follow up questions
Orville and Wilber are standing 3 meters apart with a spring that has a total of 5 nodes (including the ends) when it has a frequency of 3 cycles/second.
A. What is the wavelength of the wave on the spring?
What is the velocity of the wave on the spring?

18. λ = 1.5m
V = 4.5 m/s

19. Quiz
Waves on a string here

20. Sound waves
Longitudinal waves = particle motion in same direction as energy motion
Hearing ~ 20 to 20,000 Hz
Loudness = amplitude
Pitch = frequency

21. Diffraction
Apparent bending of waves around obstacles and spreading out of waves past an opening.

22. Refraction (into higher density)

23. Refraction (into/out of water)

24. Refraction – consider angles

25. Sinθi Vi λi nr Sinθr = vr = λr = ni

26. Wave interference

27. Graphic at: http://www.youtube.com/watch?v=CAe3lkYNKt8

28. Destructive interference =
peak1 + trough2 = cancel out =
0 amplitude = no sound
Constructive interference =
peak1 + peak2 = double amplitude =
double the sound (also with trough and trough)

29. Multiple frequency interference (music when a mathematical relationship is present)

31. BEATS
Periodic and repeating fluctuations heard in the intensity of a sound when two sound waves of similar frequencies interfere with each other.

33. The beat frequency = the difference in the frequency of the two notes.
Ex: 2 sound waves with 256 and 254 Hz are played at the same time, a beat frequency of 2 Hz will be detected.

34. Standing Waves in Pipe

35. Last part of lab
Tuning fork
you
¼ λ 1λ

36. Reflection For all waves θi θr θi = θr Why????
Conservation of momentum
In coming ray has x and y components
Y component changes direction

37. Electromagnetic wavesY E X
Z B
Transverse wave: Both E and B are to the direction of travel of the wave.
= particle motion perpendicular to energy flow

38. The speed of light c = 3.0 x 108 m/s In a vacuum
Slower through dense materials