## Physics & analysis of sound

__The Nature of Sound__

There are two important variables in a sound wave:

1. It's

**frequency**, which is the number of waves that pass any point in a second, measured in cycles per second or Hertz (Hz), this has the subjective correlate of

**pitch**, sounds of high frequency having a high pitch.

2. It's

**amplitude or intensity**, which is related to the magnitude of the movements produced. This has the subjective correlate of

**loudness**.

1. A sound wave produces compression and rarefaction of the air, the molecules of which vibrate around their mean positions. The extent of the pressure variation has a subjective correlate in loudness. The frequency, or number of waves passing a point in a second has a subjective correlate in pitch. Frequency is measured in cycles per second, known as herts (Hz).

2. The particle velocities produced by a pressure variation depend on the impedance (the effective resistance of an electric circuit or component to alternating current, arising from the combined effects of ohmic resistance and reactance (acoustic impedance - the ratio of the pressure over an imaginary surface in a sound wave to the rate of particle flow across the surface.) of the medium. If the impedance is high, high pressures are needed to produce a certain velocity. Impedance is usually expressed as a complex quantity Z = R + jX, where R is resistance, X is reactance, and j is the imaginary square root of −1.

3. When a sound pressure wave meets a boundary between two media of different impedance, some of the sound energy is reflected.

4. Complex sounds can be analyzed by Fourier analysis, that is by splitting the waveforms into component sine waves of different frequencies. The cochlea seems to do this too, to a certain extent.

5. In a linear system, the output to two inputs together is the sum of the outputs that would have been obtained if the two inputs had been presented separately. Moreover, in a linear system, the only Fourier frequency components that are present in the output are those that were present in the input Neither is true for a non-linear system.

2. The particle velocities produced by a pressure variation depend on the impedance (the effective resistance of an electric circuit or component to alternating current, arising from the combined effects of ohmic resistance and reactance (acoustic impedance - the ratio of the pressure over an imaginary surface in a sound wave to the rate of particle flow across the surface.) of the medium. If the impedance is high, high pressures are needed to produce a certain velocity. Impedance is usually expressed as a complex quantity Z = R + jX, where R is resistance, X is reactance, and j is the imaginary square root of −1.

3. When a sound pressure wave meets a boundary between two media of different impedance, some of the sound energy is reflected.

4. Complex sounds can be analyzed by Fourier analysis, that is by splitting the waveforms into component sine waves of different frequencies. The cochlea seems to do this too, to a certain extent.

5. In a linear system, the output to two inputs together is the sum of the outputs that would have been obtained if the two inputs had been presented separately. Moreover, in a linear system, the only Fourier frequency components that are present in the output are those that were present in the input Neither is true for a non-linear system.

- Vibration-induced particle oscillation is represented by sinusoidal motion
- mass-elasticity

- Waveform has 4 dimensions of interest
- Amplitude, frequency (period), phase, wavelength

- Vibrations don't last infinitely
- due to opposition from motion and friction
- total opposition to motion is impedance
- two components resistance/reactance