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 later

  • Absolute 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

Last modified: Sunday, 29 March 2020, 8:46 PM