1. Waves

2. Waves Wave: an oscillation that moves from one place to another.
Movement of energy
Sound, light, water waves, radio waves

3. Medium: the material the wave moves through
Sound waves move through air
Water waves move through water
X-rays move through your body
Waves always move outward

4. Types of Waves
Transverse Wave: oscillate perpendicular to the direction the wave moves.
Longitudinal Wave: vibrate in the same direction the wave moves.

5. Describing a Wave
Frequency: the rate that the every point on the wave moves back and forth
Higher frequency, faster it moves back and forth
# cycles / # seconds
Amplitude: the maximum amount a wave moves from the equilibrium position
Half the distance from top to bottom

6. Parts of a Transverse Wave
Crest: the high point of a wave
Trough: the low point of a wave
Wavelength (λ): the length of one cycle of a wave
Crest to crest
Trough to trough
Point to point

7. How many waves are in the diagram?
What is the λ?

8. Parts of a Longitudinal Wave
Compression: compressed portion, high point
Rarefaction: stretched portion, low point
Wavelength: compression to compression

9. Wave Interactions
Boundary: where the conditions or the medium changes.
When a wave meets a boundary, it does one of four things, which are:
Reflection: the wave bounces and goes in a new direction
Refraction: the wave bends as it passes into and through an object
Diffraction: the wave bend around or through holes in an object
Absorption: the wave is absorbed and disappears

10. Interference
Interference (superposition): when two or more oscillations/waves combine (add together)
They are in the same space at the same time
Constructive Interference: when parts of two waves add together
Destructive Interference: when parts of two waves cancel each other

16. Standing Waves
Standing Wave: a wave that resonates in a confined space
Nodes: points where the medium does not move
Antinodes: points in a standing wave that have the greatest amplitude (bumps)

17. Standing Waves Wavelength: length of 1 cycle (2 bumps).
Harmonics: natural frequencies a medium oscillates at
Numbered by how many antinodes the wave has
Fundamental: lowest natural frequency; 1st harmonic; 1 bump; 1/2 λ

18. Standing Waves
The frequency of each harmonic is a multiple of the fundamental frequency.
The wavelength needs to be determined
1 wave = 2 antinodes
Harmonic
Frequency 1
12 Hz 2
24 Hz 3
36 Hz 4
48 Hz

19. Resonance and Energy Transfer
If a driving force is in resonance with another system, there can be a large energy transfer. (shattering wine glass, pushing a kid on a swing, etc)
If the driving force is out of phase with the other system, there can be an energy loss. (noise canceling headphones, etc)

20. Superposition Practice

21. Superposition Practice

22. Standing Waves Speed of a wave is the same, no matter the frequency
Only if the medium does not change

23. Speed of a Wave Energy moves in a wave
The medium stays in the same average place

24. A wave has a wavelength of 0. 25 meters and has a frequency of 20 Hz
A wave has a wavelength of 0.25 meters and has a frequency of 20 Hz. Determine the speed of the wave.

25. Sound moves at a speed of 340 m/s
Sound moves at a speed of 340 m/s. If a particular sound wave has a frequency of 800 Hz, what is the wavelength of the sound wave?

26. Beats
These two different frequencies, when in superposition with each other, created a third wave with it’s own frequency.

27. Beats
2 Hz
1 Hz
3 Hz
F1 – F2 = Fb
The difference between the two starting frequencies was the frequency of the resulting signal, which had moments of high amplitude once every second (1 Hz) . Those moments of constructive interference are called “beats”.

28. More Beats

29. Basic Problems
A 8 Hz sound wave interferes with a 5 Hz sound wave. What is the frequency of the beats you would hear?
How many beats could you count in a minute?

30. Basic Problems
You have two sets of tuning forks: Small/Large for set A and Medium/Large for set B.
Which set will produce beats at higher frequency? Why?
Which set will produce beats at a longer interval? Why?

31. Standing Waves and Music
Almost all brass instruments work on the same principle, which is that you vibrate your lips to create a disturbance in the instrument. If the frequency of your lips matches the resonant frequency of the instrument, sound (a musical note) will be produced at that frequency. (demo)

32. However, in the confined space of the metal tubing, only whole number wavelengths will resonate, so, once you hit the lowest note possible (without changing the valves), it’s possible to hit twice that frequency, three times that frequency etc. as long as you can produce that frequency vibration with your lips. (demo)

33. Each successive frequency is a whole number multiple of the fundamental frequency.
In music, each whole number multiple of the fundamental frequency is called an “octave.” (demo)
So, the three boxes above show the 1st, 2nd, and 3rd octaves.

34. By pressing down valves you open or close parts of the metal tubing, thereby reducing or extending the length of the tubes. Longer tubes will produce lower frequency notes.