## 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)

## 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