Quicknotes Chapter 12
Wind Instruments
1. Wind instruments work due to a vibrating standing waves within a column of air
inside a tube.
2. The lowest frequency standing wave is called the fundamental
3. Higher frequency standing waves are called overtones or harmonics
4. The air itself is now moving!
5. Can discuss either the displacement of air or the pressure in the air
6. If the tube is open (open tube) on both ends will have antinodes at the ends
7. A closed tube (closed on one end) will have antinode on the open end and nodes on
the closed end.
8. A single node in an open tube if the fundamental frequency (f1) =v/ =v/2l
a. Where v is the velocity of sound of air in the tube
b. The l is the length of the tube and is 1/2
c. Look at figure 12-11 on 338 for 2nd and third harmonics
9. Pressure in the open tube, in an open end the pressure is the same as the
atmosphere
10. In a closed tube, the fundamental is equal to ¼  within the length of the tube. The
fundamental frequency is f1 =v/4l
11. Only odd harmonics are present in a closed tube, with frequencies equal to 3,5,7
times the fundamental frequency --see figure 12-12
12. Pressure is a closed tube, the open end will be the same as the atmosphere but the
closed end can alternate above and below atmospheric pressure
Quality of Sound and noise and Superposition
1. Quality of sound is a third aspect of musical sound, which is also called timbre
and tone color
2. Quality of sound is why a flute and a piano don’t sound the same even when they
play the same note
3. Instruments play fundamentals and overtones at the same time creating
waveforms (a composite wave)
4. The relative amplitudes of the overtones are different for different instruments
which gives the different quality to different instruments
5. How an instrument is played effects the one quality
Interference of Sound Waves--Beats
1. In sound waves, a crest is a compression and troughs are rarefaction
2. Two speakers with a single frequency and in phase, will send out wanes that will be
constructive at some points and destructive at others
3. Destructive interference occurs when distance of one wave is ½ the wavelength of
the other. This is why certain places in the theater are better than others for
hearing. This is also why if someone is in a place where there is destructive
interference, if you turn one speaker off they can suddenly hear clearly---cool!!!
4. Beats are regularly spaced intensity changes caused by two waves sometimes in
phase and sometimes out of phase.
5. Beats are the result of the superposition of two sound waves of slightly different
frequencies. Beat frequency is the difference in frequency between the two waves.
6. When beats disappear then we know an instrument is in tune with a tuner.
Doppler Effect
1. Pitch sounds higher as objects move toward you and lower as they move away
2. As an objects moves forward it is catching up with previously emitted waves, so to
an observer the frequency of the wave is faster and the pitch would be higher
3. As it moves away from an observer, the wave crests would be further apart and the
frequency would be less and the pitch would sound lower.
4. T (period)=1/f = /v (velocity of sound)
5. Doppler effect can also occur when the object is at rest and the observer is moving
toward or away from the object. So f=vsound +/- v0bserver/
6. When a sound wave is reflected from a moving obstacle, the reflected wave will be
different from the incident wave.
7. There is a single equation for both observer and source:
f’=f(voound + v0bserver/ voound + vsource
8. Doppler effect works for electromagnetic radiation, such as the redshift for galaxies
Shockwaves and the Sonic Boom
1. An airplane going faster than the speed of light is called supersonic speed
2. A Mach number is defined as the ratio of the speed of the object to the speed of
sound (in a particular medium)
3. Shock waves occur due to wave crests overlapping one another forming one large
crest
4. There is a large trough behind this crest
5. When a listener hears a shock wave it is a sonic boom
6. To exceed the speed of sound an object must break the sound barrier