1. Chapter 15 Sound: The Physics of Music PPTB
In general, tubes that produce sound have one opening or both ends open….
To understand harmonics better, we will revisit harmonics of a standing wave in a string…
Remember the 1st 6 harmonics in our wave chapter/packet?

2. Nodes and Antinodes
A node is a part of the standing wave that does not move and the anti-node is part of the standing wave that moves the most…

3. Closed-Pipe Resonators
On a closed-pipe resonator, you cannot hear a harmonic on one end, so the harmonics are only the odd # harmonics…
Frequency of wave = harmonic # * velocity/(4 * pipe length) OR fn = nv/4L
fn = nv/4L(n = 1, 3, 5,… only odd harmonics)
So, to solve for the funamental frequency in a closed tube, n=1 v=the speed of sound
and L= the length of the tube.
Then multiply by 3,5,7…for the odd harmonics, there are no even ones because the second end of the tube is closed.

4. Closed-tube Resonators

5. Open-Tube Resonators
Open-tube resonators have both ends open and have all harmonics, n=1,2,3,4…etc
For open tubes, to find the frequency of the harmonics, you plug in n=1 for the fundamental frequency, then multiply by 2 for the second harmonic, by 3 for the 3rd and so on.
Frequency of wave = harmonic # * velocity/(2 * pipe length) OR
fn = nv/2L (n = 1,2,3…)

6. Open-Tube Resonator

7. Resonance of a String
Resonance of a string uses the same formula as an open tube….

8. String Harmonics

9. Sound Quality
Combination of different frequencies or harmonics produces a sound characteristic called timbre, tone quality, or color.
The fundamental frequency is the lowest frequency at which that an instrument will vibrate.
Whole-number multiples of the fundamental frequency are called harmonics.

10. Consonance and Dissonance
Dissonance is an unpleasant combination of pitches.
Consonance is a pleasant combination of pitches.

11. Beats
When 2 frequencies are close to one another, but not the same, interference produces a phenomena known as beat.
The tones cause interference and produce the number of beats per second of the difference between the 2 tones.

12. Interference
Constructive interference is when two crests or compressions occur together.
Destructive interference is when compression and rarefaction occur together.