Chapter 1. Physical Sound
1.1. Sound Waves
Sound waves are air molecules vibrating under the influence of an initial shock: a string being plucked; a drum head being hit. Any movie with loud explosions in outer space should have their technical staff flogged in public: there are no air molecules in space; no air means no sound.
The movement of the string displaces the air molecules around it; these air molecules form alternating zones of higher and lower pressure. When we say that sound is propagating, we mean that those zones are propagating; the air molecules themselves do not move. If a sensitive membrane (e.g. a microphone) is put in front of the sound source, it will feel those alternating zones of higher and lower pressure as alternating moments of higher and lower pressure.
The best way to represent this type of behavior is with an oscillating function, going from some lower boundary measuring troughs in pressure to some higher boundary measuring peaks in pressure, with at some point in the middle values which represent the average pressure felt by the measuring device (see below).
Figure 1 Sound Waves: A string S vibrates, creating mobile high (H) and low (L) air pressure areas; this can be represented by a sine wave like function of pressure (P) versus time (t); the device T feels the varying pressure; why T? Read on.
Equation 1 Sine Wave
where A is the wave’s amplitude, describing how large or small it can be, ν (Greek letter “nu”) is the frequency, λ (Greek letter “lambda”) is the wave’s wavelength (see Equation 2 below); 2*Π*x/λ is sometimes represented by the symbol Φ (Greek letter “phi”) and is called the wave’s phase. P represents the pressure recorded at a certain time t by the microphone which is located at the x position.
The wavelength represents the distance between two points of the function which have the same characteristics, for example two peaks or two troughs. The frequency ν can be obtained with the following formula which is valid in air (linear medium) but not in water (dispersive medium):
Equation 2 Wavelength and Frequency
where is the speed of sound; sound travels at roughly 113 feet per second / 343 meters per second at 20° Celsius / 68° Fahrenheit. A linear medium (like air) is a medium in which the waves with different frequencies all travel at the same speed; in a dispersive medium (like water), the waves with different frequencies travel at different speeds; the sound gets progressively deformed as it moves.
Frequencies are measured in Hertz (Hz) and wavelengths in meters (m). Examples of typical wavelengths and corresponding frequencies can be found in the next table.
|1 m||343 Hz|
|1 ft.||1.12 kHz|
|17 m = 56 ft.||20 Hz|
|17 mm = 0.67 in.||20 kHz|
|0.78 m = 31 in.||A (440 Hz)|
|1.31 m = 4 ft. 4 in.||C4 (261 Hz)|
The lowest frequency a human ear can hear is called the human hearing threshold (more on that in Section 4.4); its value is 20 Hz and is represented by a wave of length 17 m, while the highest frequency a human ear can hear is 20 kHz (17 mm length). Standard tuning with the A note at 440 Hz is 0.78 m long while the middle C on a piano is 1.31 meters long.
Again, note that air molecules do not travel with sound; they literally oscillate in place in the direction of the sound, which is why sound waves are longitudinal waves and why there is wind coming with them. What does move in the direction of the sound are pressure changes caused by those vibrating air molecules.
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