Sound — Pressure Waves

• Sound travels in air

• Speed in air is around 1000 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 and Amplitude

• Note that we are assuming a sinusoidal wave. Good reasons for this described later

• Absolute pressure doesn't matter (within reason)

• Sound level of wave is given by either peak-to-peak amplitudes or by "root-mean-square" power (calculation)

Sound — Latency

• Latency = delay. How long between when the sound is produced and when it is heard (for example)

• Delay is not always undesirable: implies storage

• Latency matters less at lower frequencies: localization in time

Sound — Superposition

• Sounds that aren't pure sine waves are still 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 sin(w[i] t + Φ[i])


Hearing — The Ear

• Physics of hearing

• Note that the ear detects frequency directly

• The measured sound amplitude is logarithmic in the sampled sound power: big differences at low power, small differences at high power

• Thus usually use units of dB instead of linear power

P[dB] = 20 log (P[rms] / 10^-12)

• C.f. "type A" and "type B" potentiometers as "volume knobs"

Hearing — Psychoacoustics

• The brain does things with sound…

• Perceived volume of a sound is a function of

• Background volume level

• Waveshape: in particular, the brain will "fill in" "clipped" waves as though the peaks exist

• Perceived frequency of a sound is

• Relative: perfect pitch is rare, pitch is mostly judged by relation to surrounding / background pitches

• Dominated by high frequency components: dbA

• Accomodation over time, etc happens

• is an interesting audio illusion

Hearing — Safety

• Easy to damage hearing permanently

• NIOSH: More than 85 dBA (heavy city traffic) over 8 hours is hazardous

• Acute trauma over 130 dB

• Not just general hearing loss: notching, tinnitus

• How to stay safe:

• Wear ear protection around sustained loud noise: concerts, machine rooms, etc

• Avoid earbuds, as they are prone to hearing damage. If you use them, turn them down to below where they sound best: the ear / brain don't know how to deal with them

• Turn down master volume before powering up any audio equipment. Then raise the volume to a comfortable level

• Put headphones on your neck to start; you should hear silence. Then put them on and turn up the volume

• See above when working with mute buttons, plugs and jacks, etc. So easy to make a mistake

Hearing — Two Ears

• Normally hear in stereo; thus two-channel audio with separated sources (headphones, left and right speakers)

• Means two audio channels to deal with: stereo is sometimes encoded as sum and difference channels, with the difference channel at lower fidelity

• Localization in space is a function of time difference and level difference between ears

• Angle:

• Phase is used below 1KHz

• Head interference and group delay is used above 1.5KHz

• This is part of what the "ears" (pinna) do

• Distance:

• Softer, lower-frequency sounds seem farther away

• Room effects (reflection) increase perceived distance