1. Purdue University, Physics 220
Mean: 65.7 (or 55%) Std. Dev.: 21.1
Lecture 20
Purdue University, Physics 220

2. Purdue University, Physics 220
Lecture 20
Waves
Lecture 20
Purdue University, Physics 220

3. Constructive Interference
The net disturbance is the sum of the individual disturbances.
When waves cross in a point and have the same sign amplitude, they add
constructively.
Since intensity is proportional to amplitude squared, the resulted intensity is more than the sum of the intensities of individual waves.
Lecture 20
Purdue University, Physics 220

4. Destructive Interference
The net disturbance is the sum of the individual disturbances.
When waves cross in a point and have the opposite sign amplitude, they add destructively.
Since intensity is proportional to amplitude squared, the resulted intensity is less than the sum of the intensities of individual waves.
Lecture 20
Purdue University, Physics 220

5. Purdue University, Physics 220
Interference
Out of phase by =
Out of phase by =(2/3)
In phase =0
Fully Destructive
Destructive
Constructive
Destructive
Lecture 20
Purdue University, Physics 220

6. Coherence and Interference
Two waves are coherent when their frequencies are same and they maintain a constant phase difference.
A path difference L of  corresponds to a
phase difference  of 2
Lecture 20
Purdue University, Physics 220

7. Purdue University, Physics 220
Interference
Coherent waves may interfere constructively or distructively.
For constructive interference:
Amplitudes add: A=A1+A2
For destructive interference:
Amplitudes subtract: A=|A1-A2|
Lecture 20
Purdue University, Physics 220

8. Purdue University, Physics 220
Interference
Lecture 20
Purdue University, Physics 220

9. Purdue University, Physics 220
Interference
The total amplitude (thus intensity) at each location depends on phase shift between two waves.
Constructive:
Destructive:
Maxima with twice the amplitude occur when phase shift between two waves is 0, 2, 4, 6 …
(or path difference is 0, , 2…)
Minima with zero amplitude occur when phase shift between two waves is , 3, 5 …
(or path difference is 0, /2, 3/2…)
Lecture 20
Purdue University, Physics 220

10. Purdue University, Physics 220
Intensity
Constructive interference:
I > I1 + I2
Destructive interference:
I < I1 + I2
Incoherent superposition:
I = I1 + I2
Lecture 20
Purdue University, Physics 220

11. Purdue University, Physics 220
Diffraction
Diffraction is the spreading of a wave around an obstacle
in its path.
Lecture 20
Purdue University, Physics 220

12. Purdue University, Physics 220
Reflection
When a wave strikes an obstacle or comes at the end of the medium it is travelling in, it is reflected (at least in part).
If the end of the rope is fixed the reflected pulse is inverted
If the end of the rope is free the reflected pulse is not inverted
Lecture 20
Purdue University, Physics 220

13. Purdue University, Physics 220
Reflection
When a wave travels from one boundary to another, reflection occurs. Some of the wave travels backwards from the boundary
Traveling from fast to slow inverted
Traveling slow to fast upright
Lecture 20
Purdue University, Physics 220

14. Purdue University, Physics 220
Reflection
When the end of the rope is fixed to a support the pulse reaching the fixed end exerts a force (upward) on the support. The support exerts a force equal and opposite (downward) on the rope.
This downward force generates the inversion that can be thought as a change of phase of 180.
If the end of the rope is free it can overshoot. The overshoot exerts an upward pull on the rope and the reflected pulse is not inverted.
Lecture 20
Purdue University, Physics 220

15. Speed of Waves Depends on Medium
When a wave reaches a boundary between two different media the speed and the wavelength change, but the frequency remains the same.
Lecture 20
Purdue University, Physics 220

16. Purdue University, Physics 220
Law of Refraction 1 2
Lecture 20
Purdue University, Physics 220

17. Purdue University, Physics 220
Standing Waves
Shake the end of a string
If the other end is fixed, a wave travels down and it is reflected back  interference
The two waves interfere => standing wave
Nodes when sin (kx)=0:
Anti-nodes sin (kx)=+/- 1, half way between nodes
Anti-nodes
nodes
Lecture 20
Purdue University, Physics 220

18. Purdue University, Physics 220
iClicker
A standing wave on a string is given by:
Is there a node or antinode at x=0?
A) Node B) antinode C) neither node nor antinode
Lecture 20
Purdue University, Physics 220

19. Purdue University, Physics 220
iClicker
What is the distance between nodes?
A wavelength/4
B wavelength/3
C wavelength/2
D wavelength/1
Lecture 20
Purdue University, Physics 220

20. Purdue University, Physics 220
Standing Waves
The natural frequencies are related to the length of the string L. The lowest frequency (first harmonic) has one antinode
The second harmonic has two antinodes
The n-th harmonic
Lecture 20
Purdue University, Physics 220

21. Purdue University, Physics 220
Standing Waves
Fixed endpoints
f = v/l
Fundamental n=1
ln = 2L/n
fn = n v / (2L)
fn = n f1
No energy is transmitted by a standing wave
Lecture 20
Purdue University, Physics 220