Strings (music) - String Vibration

String Vibration

A string vibrates in a complex harmonic pattern. Every time the player sets a string in motion, a specific set of frequencies resonate based on the harmonic series. The fundamental frequency is the lowest (and loudest), and it is determined by the density, length and tension of the string. This is the frequency we identify as the pitch of the string. Above that frequency, overtones (or harmonics) are heard, each one getting quieter the higher it is. For example, if the fundamental pitch is 440 Hz (A above middle C), the overtones for an ideal string tuned to that pitch are 880 Hz, 1320 Hz, 1760 Hz, 2200 Hz, etc. The note names for those pitches would be A, A, E, A, C♯, etc. Due to the physical nature of the strings, however, the higher up the overtones go, the more out of tune (or "false") they are to the fundamental. This is an important consideration for piano tuners, who try to stretch the tuning across the piano to keep overtones more in tune as they go up the keyboard.

In a phenomenon called sympathetic vibration, a string seems to vibrate by itself. This happens when sound waves strike the string at a frequency close to the string's fundamental pitch or one of its overtones. The string is connected to this similar sound wave through the air, which picks up the vibrations of the sound waves at the same frequency, and in turn causes the string to vibrate on its own. When an outside source applies forced vibration that matches a string’s natural frequency, the string vibrates.

Resonance can cause audio feedback. For example, in a setup with an acoustic guitar and a PA system, the speaker vibrates at the same natural frequency of a string on the guitar and can force it into vibrational motion.

For a typical high-E nylon string, the maximum transverse force is roughly 40 times greater than the maximum longitudinal force amplitude. However the longitudinal force increases with the square of the pulse amplitude, so the differences diminish with increasing amplitude. The elastic (Young’s) modulus for steel is about 40 times greater than for nylon, and string tensions are about 50% greater, so the longitude and transverse force amplitudes are nearly equal. For a typical high-E nylon string, the maximum transverse force is roughly 40 times greater than the maximum longitudinal force amplitude. However the longitudinal force increases with the square of the pulse amplitude, so the differences diminish with increasing amplitude. The elastic (Young’s) modulus for steel is about 40 times greater than for nylon, and string tensions are about 50% greater, so the longitude; and transverse force amplitudes are nearly equal.