pure tone sine wave

1
pure tone sine wave

• Definite period single, constant
  frequency
• Described by only two numbers f, A

What creates a sine wave?
How can we describe more complicated sounds?
2
The sine function
Angle in radians

• What about the numbers that describe
• amplitude?
• frequency?

3
superposition
pressure or displacement
time (ms)
The resultant frequency is the Greatest Common
Factor of the component frequencies fnew
GCF(f1,f2)
4
Beating
f1 5 f2 5.5 Fnew .5
f1 20 f2 21 Fnew 1
f1 500 f2 501
f1 500 f2 505
f1 500 f2 510
5
Superposition of many sine wavessawtooth wave
f 2f (A2 1/2)
f 500 Hz (A 1)
f 2f 3f (A3 1/3)
f 2f 3f4f5f (A5 1/5)
10 harmonics
6
Superposition of many sine wavessquare wave
f 500 Hz (A 1)
f 3f (A3 1/3)
f 3f5f (A5 1/5)
f 3f5f7f9f (A9 1/9)
10 harmonics
7
A sound is the sum of its parts
Piano
Fundamental only Harmonics 1 2 Harmonics 1,
2, 3 Harmonics 1-4 Harmonics 1-5 Harmonics
1-6 Full sound