1. Interference and beats

2. 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.

3. 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.
In an auditorium you hear music directly from the stage AND a multiple echo called reverberation.

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

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

6. 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.

7. 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.

8. What do beats sound like?
Click on this simulation on page 456 to
explore beats

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

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

11. Engaging with the concepts
What do you think the formula is 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?

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

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

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

15. 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-cancelling headphones.

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

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