Fundamental Tones and Harmonics

A tight wire or string that vibrates as a single unit produces its lowest frequency, called its fundamental. A vibrating string, having a small surface area, cuts through the air without disturbing it effectively. The string itself transfers very little of its vibrational energy to the air and therefore produces only a feeble sound. If, however, its vibrations are transferred to a larger surface, such as a sounding board, the air will be disturbed more effectively and a louder sound will be produced.

The properties of vibrating strings and the sounds they produce can be studied using an instrument called a sonometer. The sonometer may have two or more wires or strings stretched over a sounding board, which reinforces the sound produced by the wires.

By plucking a string, energy is transferred to the string and causes it to vibrate in transverse wave motion. Just as a vibrating reed transfers energy to molecules of air gases and causes them to exhibit longitudinal wave motion, so a vibrating string transfers energy to these gas molecules and causes them to vibrate and transmit a longitudinal wave.

The frequency of the longitudinal vibration of the molecules, which is the frequency of the sound wave, is the same as the frequency of the transverse vibration of the string. Since the production of sound by a vibrating string dissipates energy, energy must be continuously supplied to the string by plucking or bowing to maintain the sound.

Harmonics A string may vibrate as an entire unit and may also vibrate in two, three, four, or more segments depending on the standing wave pattern that is on the string. When a string is plucked or bowed, not only the fundamental mode but other, higher modes of vibration may be present.

The fundamental and the vibrational modes having frequencies that are whole-number multiples of the fundamental are called harmonics. The fundamental is the first harmonic because it is one times the fundamental. The vibrational mode having a frequency twice that of the fundamental is the second harmonic. The vibrational mode of three times that of the fundamental is the third and so on.

Quality of Sound The quality of a sound depends on the number of harmonics produced and their relative intensities. When stringed instruments are played, they are bowed, plucked, or struck near one end to enhance the production of harmonics that blend with the fundamental and give a richer sound.