1. Purdue University, Physics 220
Lecture 19
Waves
Lecture 19
Purdue University, Physics 220

2. Purdue University, Physics 220
What is a Wave
A wave is a disturbance that travels away from its source and carries energy.
A wave can transmit energy from one point to another without transporting any matter between the two points.
Examples:
Stadium waves (people move up & down)
Water waves (water moves up & down)
Sound waves (air moves back & forth)
Seismic waves (earth moving up & down)
Electromagnetic waves (what moves ??)
Lecture 19
Purdue University, Physics 220

3. Why are Waves Important?
Transport energy from one place to another
Electromagnetic waves transport energy (electromagnetic energy in the form of light) from the Sun to the Earth.
Sound waves transport energy from speakers to our ear drums.
In waves, energy is transported, but matter is not.
Lecture 19
Purdue University, Physics 220

4. Purdue University, Physics 220
Power
The power carried by a wave equals the energy emitted by the source (and carried away by the wave) per unit time. [watts]=[joules/second]
Lecture 19
Purdue University, Physics 220

5. Purdue University, Physics 220
Intensity
Average power per unit area carried by the wave past a surface which is perpendicular to the direction of propagation of the wave.
For spherical waves, the intensity decreases with distance:
Unit: W/m2
I  A2
Lecture 19
Purdue University, Physics 220

6. Purdue University, Physics 220
Plane wave
Light produced by laser good example
Intensity does not change with distance from the source.
Lecture 19
Purdue University, Physics 220

7. Purdue University, Physics 220
Types of Waves
Transverse: The medium oscillates perpendicular to the direction the wave is moving.
Water (more or less)
Slinky
Longitudinal: The medium oscillates in the same direction as the wave is moving.
Sound
Slinky
Lecture 19
Purdue University, Physics 220

8. Purdue University, Physics 220
Lecture 19
Purdue University, Physics 220

9. Purdue University, Physics 220
Waves on a String
Lecture 19
Purdue University, Physics 220

10. Purdue University, Physics 220
iClicker
A rope of mass M and length L hangs from the ceiling with nothing attached to the bottom (see picture). Suppose you start a transverse wave at the bottom end of the rope as this wave travels up the rope its speed will:
A) Stay the same
B) Decrease
C) Increase v
Lecture 19
Purdue University, Physics 220

11. Purdue University, Physics 220
Question
Suppose that a longitudinal wave moves along a Slinky at a speed of 5 m/s. Does one coil of the slinky move through a distance of five meters in one second?
A) Yes
B) No
Lecture 19
Purdue University, Physics 220

12. Purdue University, Physics 220
Harmonic Waves
y(x,t) = A sin(wt – kx)
A = Amplitude= Maximum displacement of a point on the wave
 =Wavelength: Distance between identical points on the wave
T=Period: Time for a point on the wave to undergo one complete oscillation.
f=frequency=1/T
= angular frequency= 2/T
k = wave number = 2p/l
Lecture 19
Purdue University, Physics 220

13. Purdue University, Physics 220
Period and Velocity
Period: The time T for a point on the wave to undergo one complete oscillation.
Speed: The wave moves one wavelength  in one period T so its speed is v = / T.
Lecture 19
Purdue University, Physics 220

14. Harmonic Waves Exercise
y(x,t) = A cos(wt –kx)
Label axis and tic marks if the graph shows a observation of the wave
y(x,t) = 2 cos(4t –2x) at x=0.
Recall: T = 2 p /w
What is the period of this wave?
T = 2 p / w= 2 p/ 4= 1.58 s t +2 -2
What is the velocity of this wave?
Students make plot at x=0, give them line, they mark tics
p / 2
p/4
3p/4
v = w/k= 4/2 m/s=2m/s
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Purdue University, Physics 220

15. Purdue University, Physics 220
Wave Properties
The speed of a wave is a constant that depends only on the medium, not on amplitude, wavelength or period (similar to SHM)  and T are related !
 = v T or  = 2 v / (sinceT = 2 /  or  = v / f (since T = 1/ f )  
Recall f = cycles/sec or revolutions/sec
 = 2f
Intensity I  A2
v =  / T
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Purdue University, Physics 220

16. Purdue University, Physics 220
Wave Description
– wavelength: distance between crests (meters)
T – period: the time between crests passing fixed location (seconds)
v – speed: the distance one crest moves in a second (m/s)
f – frequency: the number of crests passing fixed location in one
second (1/s or Hz)
 – angular frequency: =2f (rad/s)
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Purdue University, Physics 220

17. Purdue University, Physics 220
Direction
A wave y = A cos(t - kx) travels in +x direction
A wave y = A cos(t + kx) travels in -x direction t
After one period T – we will get the point which was at coordinate -lambda
Lecture 19
Purdue University, Physics 220

18. Purdue University, Physics 220
iClicker
Suppose a periodic wave moves through some medium. If the velocity of the wave increases, what happens to the wavelength of the wave assuming the frequency of the wave remains the same?
A) The wavelength increases
B) The wavelength remains the same
C) The wavelength decreases
 = v T
Lecture 19
Purdue University, Physics 220

19. Purdue University, Physics 220
Exercise
The wavelength of microwaves generated by a microwave oven is about 3 cm. At what frequency do these waves cause the water molecules in your burrito to vibrate?
A) 1 GHz B) 10 GHz C) 100 GHz
1 GHz = 109 cycles/sec
The speed of light is c = 3x108 m/s
Lecture 19
Purdue University, Physics 220

20. Purdue University, Physics 220
Exercise
Recall that v = lf H O
Makes water molecules wiggle
1 GHz = 109 cycles/sec
The speed of light is c = 3x108 m/s
Lecture 19
Purdue University, Physics 220

21. Superposition Principle
When two or more waves pass through the same region the actual displacement is the sum of the separate displacements.
If two waves pass through the same region they continue to move independently.
Lecture 19
Purdue University, Physics 220

22. Purdue University, Physics 220
Superposition
Lecture 19
Purdue University, Physics 220

23. Mathematical Description
y(x,t) = A cos(wt –kx)
Wavelength: The distance  between identical points on the wave.
Amplitude: The maximum displacement A of a point on the wave.
Angular Frequency w: w = 2 p f
Wave Number k: k = 2 p / l 
Wavelength
Recall: f = v / l y
Add stuff here
Amplitude A A x
Lecture 19
Purdue University, Physics 220

24. Purdue University, Physics 220
Wave Speed
Phase:
A wave y = A cos(t - kx) travels in +x direction
A wave y = A cos(t + kx) travels in -x direction
Lecture 19
Purdue University, Physics 220