1. Superposition and Wave Interference
IB Physics
Superposition
and
Wave Interference

2. What happens when two waves are present at the same place at the same time?
Web Link: Wave Interference

3. The Principle of Superposition
The net effect = The sum of the individual effects
For waves:
The resulting wave = the sum of the individual waves
This applies to all waves: water, light, sound, etc.

4. Interference of Sound Waves
Imagine two speakers, each playing a pure tone of wavelength 1 meter:
3 m
3 m

5. This is called Constructive Interference
We also say that these two waves are In Phase

6. Now suppose the listener moves:
What does he hear now??

7. He moves again:
3.5 m
6 m
Path length difference = 2.5 m = 2.5 
off by ½ wavelength

8. This is called Destructive Interference
We also say that these two waves are Exactly Out of Phase

9. Ex: Noise canceling headphones

10. If you’re standing in a place where destructive interference is occurring, where did the energy of the sound waves go?
Is energy still conserved in this case??
Web Link: Interference patterns

11. Interference Summary
path 1
path 2
If the difference in path lengths is………
0, 1, 2, 3, etc…… Constructive
½ , 1½ , 2½ , etc…… Destructive

12. Ex:
If these two speakers are each playing a 412 Hz tone, and the listener is standing 3.75 m away from one and 5.00 m away from the other, what does he hear?

13. Diffraction –
The bending of a wave around an obstacle
with diffraction
without diffraction
Web Link: Diffraction
Why does a wave bend??
Huygen’s Principle – Every point on a wavefront acts as a new spherical source
Web Link: Huygen’s Principle

14. All waves exhibit diffraction, including light
So why can’t you see around corners?
The extent of diffraction is determined by this ratio:
tiny for light
larger for sound (better dispersion)
wavelength
size of obstacle

15. Huygen’s principle + math = …………
For a single slit (or doorway) of width D : D 
Angle of 1st diffraction minimum
Web Links: Diffraction of light
Sun diffraction
For a circular opening of diameter D : D 
Angle of 1st diffraction minimum

16. Remember Constructive and Destructive Interference?
So far, we’ve only looked at interference between waves of the same frequency What if the frequencies are slightly different?
We can still use Superposition to add them

19. fbeat = f1 – f2 The beat frequency of an additional loudness wave
Web Links: Sound Beats, Beats
Ex: Piano Tuning

20. Transverse Standing Waves
Hits the wall and bounces back
If the frequency is just right, an integral number of these fit on the string, and we have Resonance
Web Link: Transverse Standing Wave
There are actually a number of different frequencies that will result in a standing wave

21. nodes (no vibration)
antinodes (max. vibration)

22. In the previous example, the string was fastened to the wall:
Hard Reflection: inverts the wave
Soft Reflection: the wave returns upright
If it had been loose instead:
This creates an antinode at the end
This creates a node at the end
Web Link: Hard & soft reflections

23. back to…… Harmonics-
Natural frequencies of the system
(f1, f2, f3, etc.)
fundamental frequency

24. Ex: The Cello
The C-string on a cello plays a fundamental frequency of 65.4 Hz. If the tension in the string is 171 N, and the linear density of the string is 1.56 x 10-2 kg/m, find the length of the string.

25. We can derive a formula to calculate all of the harmonic frequencies for any string:
Web Link: String Harmonics

26. Longitudinal Standing Waves
nodes (no vibration)
antinodes (max. vibration)
Web Link: Longitudinal standing wave

27. When air is blown over a bottle, it creates a standing longitudinal (sound) wave
Remember, this is a longitudinal wave even though we draw it like this to visualize the shape.
open end: antinode
vibrating air molecules
closed end: node

28. You can also ring a tuning fork over a bottle or tube, and if it creates wavelengths of just the right length, you’ll get a standing wave (loud sound).

29. Just like we did for strings, we can also derive a formula to calculate……
The Harmonic Frequencies for a tube open at one end
speed of sound
odd harmonics only

30. Standing waves can also occur in a tube that is open at both ends

31. Harmonic Frequencies for a tube open at both ends
Web Link: Flute

32. Ex:
Find the range in length of organ pipes that play all frequencies humans can hear. Assume that the organ pipes are open at both ends, and they each play their fundamental frequency.

33. Complex Sound Waves
Musical instruments play different harmonics at the same time
Web Links: String Harmonics, Flute f1 f2 f3 =
Shape identifies the instrument

34. The shape of a vocal sound wave tells us who’s singing
(or who’s on the other end of the phone)

35. Now imagine starting with the complex sound wave, and trying to separate it into sine waves:f1 f2 f3 =
Fourier Analysis
Any periodic wave form can be represented as the sum of sine waves.
Web Link: Fourier series