## Sound — Foundations and Practics

## Sound — Pressure Waves

In this course, we will consider sound in

*air*- Speed in air is around 1000 feet/s
- Speed in water is around 5000 feet/s

Sound is pressure waves

Wavelength defined by speed and frequency

`s = fλ`

- s is speed of sound in feet per second
- f is frequency in cycles per second (Hertz, Hz)
- λ is wavelength in feet

Frequency vs wavelength

- 60Hz ~ 17 feet
- 1KHz ~ 1 foot
- 15KHz ~ 1 inch

## Sound — Frequency

Note that we are assuming a

*sinusoidal*wave. Good reasons for this described laterAbsolute air pressure

*doesn't matter*(within reason)

## Sound — Volume and Power

Volume is a complicated topic: we will return to it later

Amplitude of a wave is usually given one of two ways:

"Peak-to-peak" (PP) amplitude: the difference between the highest and lowest point in a cycle

"Root-mean-square" (RMS) amplitude: the "area under the curve" of the cycle. For sine waves, we can calculate that the RMS amplitude is proportional to the PP amplitude

`Arms = App / sqrt(2)`

Why RMS? Because the power delivered by a signal is proportional to the RMS amplitude. In the case of sound, the power delivered

*is*the RMS amplitude("110V" line voltage in the US is actually 110V RMS, so the peak-to-peak amplitude is about 170V)

More about sound power

## Sound — Latency

Latency = delay. For example, how long between when a sound is produced and when it is heard

Delay is not always undesirable: implies storage. A "delay line" stores a delayed copy of a signal: this is how reverb works

Latency matters less at lower frequencies due to "localization in time": hard to tell when a sound starts if it has a long wavelength

## Sound — Superposition

Sounds that aren't pure sine waves are still usually

*cyclic*Any repeating sound can be represented by a Fourier Series

Thus, the sound we hear can actually be plausibly thought of as a superposition of sine waves with different frequencies and phases

`s(t) = Σ a[i] sin(w[i] t + Φ[i])`

where

`a`

,`w`

and`Φ`

are the amplitude, frequency (in*radians*— multiply by 2π to get Hz = cycles per second) and phase of a sine wave