1. Wave Interference Principle of Superposition
Works for both longitudinal waves and for transverse waves

2. Wave Interference
Simply align the waves in time and add the amplitudes
Amplitudes can be either positive or negative
If the amplitudes are of the same sign, the wave is reinforced and grows bigger
If the amplitudes are of opposite sign, the wave is diminished and grows smaller

3. Wave Interference

4. Wave Interference

5. Wave Interference
So far, we have only looked at waves that have the same wavelength or frequency
What happens if the frequencies are different?
According to the Superposition Principle, we simply add the two waves together to see what results

6. Wave Interference Produces “Beats”
This is how musicians “tune” their instruments to match in the orchestra

7. Wave Interference
10% Frequency Difference
20% Frequency Difference

8. Standing Waves

9. Standing Waves

10. Doppler Effect

11. Doppler Effect
Doppler effect occurs for all types of waves, water, sound and even light. This is how we know the universe is expanding.

12. Wave Barriers
The object is moving at the speed of waves in the medium.
See how the waves pile up at the source.

13. Shock Waves
The source is moving faster than the wave speed in the medium.
A shock wave is formed and it is very difficult to break through the previous wave barrier.
These waves produce sonic booms.

14. Waves and Music

15. Guitar Strings

16. Guitar Strings
A combination wave composed of the 1st harmonic and the third harmonic.

17. Music
What makes instruments unique is the combination of harmonics produced by the different instruments.
Flutes produce primarily the 1st harmonic
They have a very pure tone
Oboes produce a broad range of harmonics and sound very different

18. Combining Waves Revisited

19. Combining Waves

20. Musical Instruments Three ways to make sound Vibrate a string
Vibrate an air column
Vibrate a membrane

21. Vibrating Strings Violin, viola, cello, string bass Guitars Ukuleles
Mandolins
Banjos
All vibrate a structure to amplify the sound

22. Vibrating Air Columns
Pipe Organs
Brass Instruments
Woodwinds
Whistles

23. Vibrating Membranes Percussion Instruments Snare Drum Bass Drum Bongos
Timpani are unique in that they are tuned to produce particular 1st harmonics
You see the timpanist tunes each drum during a performance