1. Interference

2. Objectives Investigate wave interference.
Describe constructive and destructive interference.

3. Assessment
Which of the following is not an example of wave interference and the superposition principle?
A car muffler produces sound to counteract noise from the engine.
Ocean waves hit the shore and are absorbed by the beach.
Noise-canceling headphones eliminate background noise by producing sound that is out of phase with the background noise.
Light shown through two thin slits creates a diffraction pattern.

4. Assessment Describe how two wave pulses can combine destructively.
In your own words, describe the difference in appearance between a wave with a single frequency and a wave composed of more than one frequency.

5. Physics terms superposition principle interference
constructive interference
destructive interference
phase

6. Multiple waves Examine this picture of the ocean.
Notice that there are ripples on top of the waves. These ripples are actually smaller waves that are combining with larger waves.

7. Multiple waves Examine this picture of the ocean.
Notice that there are ripples on top of the waves. These ripples are actually smaller waves that are combining with larger waves.
Waves of different amplitudes, wavelengths, and frequencies are often present at the same time.
The sounds in a classroom are another example of waves of many different amplitudes, wavelengths, and frequencies are all present at the same time.

8. Rogue waves
How are small ripples and the huge walls of water called “rogue waves” related?
The answer lies in an understanding of interference.

9. Sine waves
The simplest wave can be described by a single amplitude, wavelength, and frequency.
These are referred to as sine waves.

10. Sine waves
The simplest wave can be described by a single amplitude, wavelength, and frequency.
These are referred to as sine waves.
Graphs of amplitude vs. position and amplitude vs. time can be modeled using the sine function.

11. Sine waves
The sine function repeats every cycle, or every 2π radians.

12. Sine waves The sine function repeats every cycle, or every 2π radians.
What happens when two or more of these simple waves combine with each other?

13. Investigation
In Investigation 15C you will experiment with multi-frequency waves composed of multiple sine waves.
The investigation is found on page 427.

14. Investigation Open the Physics of Sound application.
Select the Analyze Waveform tab.
Turn on the green sine wave.
Adjust the amplitude frequency, and phase of the wave.
Adjust the green wave.

15. Investigation Part 1: Constructive and destructive interference
Create a wave that has a frequency of 50 Hz; adjust the axes so you can see about 5 cycles.
Add a second red wave of the same frequency and set the display to show the sum of the two waves.
Adjust the green wave.
Adjust the red wave.

16. Investigation Part 1: Constructive and destructive interference
Adjust the phase and amplitude of the individual waves to make the largest possible or the smallest possible sum.

17. Investigation Questions for Part 1
Describe what the phase and amplitude variables do.
Describe how you can create constructive interference.
Describe how you can create destructive interference.

18. Turn Show Sum ON and Show Sines OFF.
Investigation
Part 2: Superposition principle
Create a wave that has a frequency of 50 Hz; adjust the axes so you can see about 5 cycles.
Add a second wave of a different frequency and set the display to show only the sum of the two waves.
Turn Show Sum ON and Show Sines OFF.

19. Investigation Part 2: Superposition principle
Vary the frequency difference between the waves and observe the waveform on both a short time scale (3-5 periods) and a long time scale (1 second or more).
What do you notice?

20. Investigation Questions for Part 2
Describe the difference in appearance of a single frequency and multi- frequency wave.
Describe how amplitude changes over time when waves interfere that differ in frequency by a small amount (such as 2 Hz out of 100 Hz).
In your own words, what does the superposition principle mean?
Students may discover for themselves the visual appearance of the phenomena of “beats”, and the beat envelope, as shown in this illustration. Beats is treated in the sound chapter (ch 16).

21. Superposition principle
The superposition principle says that the total amplitude at any point equals the sum of the amplitudes of all of the waves that occur at that same place and time.

22. Superposition principle
When more than one wave is present, they can sum to make a larger or smaller amplitude wave.

23. Constructive interference
When more than one wave is present, they can sum to make a larger or smaller amplitude wave.
If the result is a larger amplitude wave, constructive interference has occurred.

24. Destructive interference
Two waves can also add up to
make a smaller wave.

25. Destructive interference
Two waves can also add up to
make a smaller wave.
When two or more waves add
up to make a smaller amplitude wave, destructive interference has occurred.
If the amplitudes are exactly matched, there can be total destructive interference.

26. Interference and superposition
In most real situations,
many waves will be present.
Some will interfere constructively; others
will interfere destructively.

27. Interference and superposition
In most real situations,
many waves will be present.
Some will interfere constructively; others
will interfere destructively.
The interference is often temporary, lasting only until the waves pass by each other.

28. Two opposite pulses start at opposite ends of this spring.
Temporary interference
Two opposite pulses start at opposite ends of this spring.
Students can “mouse over” this illustration on page 426 to view the temporary interference depicted on these next three slides.

29. Two opposite pulses start at opposite ends of this spring.
Temporary interference
Two opposite pulses start at opposite ends of this spring.
When they meet in the
middle, they cancel.

30. Temporary interference
Two opposite pulses start at opposite ends of this spring.
When they meet in the
middle, they cancel.
They re-appear after
passing through each other.

31. Assessment
Which of the following is not an example of wave interference and the superposition principle?
A car muffler produces sound to counteract noise from the engine.
Ocean waves hit the shore and are absorbed by the beach.
Noise-canceling headphones eliminate background noise by producing sound that is out of phase with the background noise.
Light shown through two thin slits creates a diffraction pattern.

32. Assessment
Which of the following is not an example of wave interference and the superposition principle?
A car muffler produces sound to counteract noise from the engine.
Ocean waves hit the shore and are absorbed by the beach.
Noise-canceling headphones eliminate background noise by producing sound that is out of phase with the background noise.
Light shown through two thin slits creates a diffraction pattern.

33. Assessment
Describe how two wave pulses can combine destructively.

34. Assessment Describe how two wave pulses can combine destructively.
If a “up” pulse traveling to the left and a “down” pulse traveling the right reach each other, they will interfere destructively. If they have equal amplitudes, they will cancel each other out.
The cancellation is temporary. In the next instant they will reappear and continue on as before.

35. Assessment
In your own words, describe the difference in appearance between a wave with a single frequency and a wave composed of more than one frequency.

36. Assessment
In your own words, describe the difference in appearance between a wave with a single frequency and a wave composed of more than one frequency.
Single frequency waves can be represented as simple sine waves.
Multi-frequency waves are more complex in appearance;
a multi-frequency wave typically has peaks within peaks, giving the repeating waveform a more serrated shape.