# How Strings Make Sound

Sound is transmitted via a pressure wave within a material. Such a pressure wave can form when an object, vibrating back and forth rapidly, pushes air forward to make way for itself, then moves away again, leaving a partial vacuum behind. A string that is under more tension will vibrate more rapidly, creating pressure waves that are closer together, and hence have a higher frequency. Thicker or longer strings, on the other hand, vibrate more slowly, creating pressure waves that are farther apart, and thus that have a lower frequency. The loudness of a sound corresponds to the amplitude of a pressure wave; the higher the pressure at the peak of the wave, the louder the sound seems to us. The only real way to get a louder sound out of a string is to put more energy into the string, probably by plucking it harder.

The wavelength of a sound wave traveling through the air is the physical length of the wave. If you could freeze a sound wave in time and space (and if you could see the wave), measuring the distance from one peak of the wave to the next peak would give you the wavelength.

An open chord, as played on a guitar, is the chord that you get by strumming a properly-tuned guitar without touching the strings. A harmonic is a frequency at which a string can vibrate; the lowest frequency at which a string can vibrate is one where the wavelength of the wave on the string is twice the length of the string itself. This lowest frequency is called the "fundamental". The nth harmonic corresponds to a string wavelength of 1/n times the wavelength of the fundamental. An overtone is much like a harmonic; the nth harmonic is the (n-1)th overtone. One of the properties of waves, when applied to this situation, states that only integer values of n can exist on a string effectively.

A standing wave is a sound wave that oscillates back and forth, often either along a string or between the ends of a pipe. A node exists at the point or points where, in a pipe containing a standing wave, the pressure is equal to the ambient pressure outside the pipe. Incidentally, in case you're following the assignment list, beat frequencies and interference are described elsewhere in this site, so I won't repeat myself here.