Sound — Foundations and Practics

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)

  • More about sound power

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

Last modified: Thursday, 4 April 2019, 12:56 AM