1. Interference and beats

2. Objectives
Investigate and analyze characteristics of waves, including frequency and amplitude.
Investigate and analyze behaviors of waves, including constructive and destructive interference.
Describe the role of wave interference in industrial applications such as noise cancellation technology.

3. Assessment
What happens when two sound waves of the same frequency interfere with each other if they are 180° out of phase?
Noise-canceling headphones use destructive interference. Which of the following explains destructive interference?
harmonic motion
refraction
Fourier's theorem
superposition principle

4. Physics terms
echo
reverberation
phase
beats
active noise cancellation

5. Echoes and reverberation
An echo is a reflected sound wave.
If you clap your hands 170 meters away from a large wall . . .

6. Echoes and reverberation
An echo is a reflected sound wave.
If you clap your hands 170 meters away from a large wall . . .
the sound will echo back to you one second later.
What happens if you clap or sing in a shower stall, where the wall is much closer? What do you hear?

7. Echoes and reverberation
In an auditorium you hear music directly from the stage AND a multiple echo called reverberation.
Sound from this performer travels to the listener via three paths.
Which path is the direct path?
Which paths are the echoes?
Do they all arrive at the same time? A B C

8. Echoes and reverberation
In an auditorium you hear music directly from the stage AND a multiple echo called reverberation.
Sound from this performer travels to the listener via three paths.
Which path is the direct path? B
Which paths are the echoes? A, C
Do they all arrive at the same time? A B C
A and C are almost simultaneous with B.

9. Echoes and reverberation
Reverberation is the addition of multiple reflections of a sound to the original sound. This adds liveliness, depth, and richness to sound.
Reverberation is why it’s so fun to sing in the shower.

10. Echoes and reverberation
Acoustical engineers design concert halls to create the right amount of “reverb”.
There should be no “dead” spots where sound waves interfere destructively.

11. Echoes and reverberation
Absorbent wall panels dampen side reflections
Acoustical engineers design concert halls to create the right amount of “reverb”.
There should be no “dead” spots where sound waves interfere destructively.
Some auditoriums have panels that can be rearranged to balance the reverberation for different performances.
Angled back walls help project sound forward
if time allows, a class might take a mini field trip to their school auditorium to examine at the acoustic features.

12. Phase
A full wave has a phase of 360 degrees. Interference between two or more sound waves depends on their phase difference.

13. Constructive interference
Two waves are in phase when both begin at the same point in their cycle.
Waves that are in phase interfere constructively.

14. Destructive interference
Two waves are out of phase if one wave begins half a cycle ahead or behind the other. Waves that are out of phase interfere destructively.

15. Two frequencies
What happens when two simultaneous sound waves are very close in frequency?
To find out, click the simulation on page 458.

16. Engaging with the concepts
Create a set of two sound waves at 440 Hz and 441 Hz.
Set time to 5 s.
Can you see the beats?
Can you hear the beats?
What is the beat frequency?

17. Engaging with the concepts
Change the frequencies to 440 Hz and 442 Hz.
How does the beat frequency change?
Does it increase or decrease?

18. Engaging with the concepts
What is the formula for the beat frequency?
Test your hypothesis with a new set of frequencies. You may need to adjust the time scale to see the beats.
What wave behavior causes beats?

19. Beats
When two frequencies are close but not the same, the sound waves drift in and out of phase, making beats.
When the waves are in phase, they add to create a louder wave.
When the waves are out of phase they cancel, reducing the sound.
The result is a “beat envelope” with its own beat frequency.

20. Test your knowledge
What is the beat frequency between a 120 Hz wave and a 140 Hz wave?

21. Test your knowledge
What is the beat frequency between a 120 Hz wave and a 140 Hz wave?
20 Hz (20 beats per second).

22. Beats and tuning
Musicians listen for beats when tuning their instruments.
When the beats disappear, the instruments are in tune with each other.
This last set of slides provides examples of useful applications of sound wave interference.

23. Applications of interference
Tuning an instrument by using beats is one application of interference.
Can you think of any other applications?
Why might you want to use destructive interference?

24. Noise reduction
There are sounds you WANT to hear and sounds you DON’T want to hear.
Sound wave interference can be used to help get rid of unwanted sound.

25. Noise reduction Typical background noise has:
Sound you WANT to hear generally has:
amplitude that is relatively constant
typically low frequency
amplitude that changes quickly
frequency above a few hundred hertz.

26. Active noise cancellation
A microphone in these noise-canceling headphones samples the external noise.
The microphone is connected to a computer chip that controls a miniature amplifier.
The amplifier drives a speaker inside the head phones that sends canceling sound waves directly into your ear.

27. Noise + anti-noise = quiet

28. Assessment
What happens when two sound waves of the same frequency interfere with each other if they are 180° out of phase?

29. Assessment
What happens when two sound waves of the same frequency interfere with each other if they are 180° out of phase?
Two waves that are 180° apart in their cycles will be out of phase, because they will be one half wavelength apart.
These waves will interfere destructively. If the waves have the same amplitude, they will cancel each other out completely. This is the idea behind noise-canceling headphones.

30. Assessment
Noise-canceling headphones use destructive interference. Which of the following explains destructive interference?
harmonic motion
refraction
Fourier's theorem
superposition principle

31. Assessment
Noise-canceling headphones use destructive interference. Which of the following explains destructive interference?
harmonic motion
refraction
Fourier's theorem
superposition principle