Musical Acoustics

Does a musical tone have a single frequency?

It does not have a single frequency, but many. To understand why, consider a stringed instrument like a guitar, piano, or violin. The string can oscillate in response to it being plucked, hit, or bowed. Standing waves will be formed as they would be if you shook a rope back and forth. By shaking it at different frequencies you can make it oscillate in several different modes. The lowest frequency results in nodes only at the ends. Twice this frequency produces nodes at the ends plus one in the middle. Three times the lowest frequency give nodes at the ends plus two nodes at 1/3 and 2/3 its length.

If you pluck, hit, or bow the string of a stringed instrument you cause it to vibrate in many of those nodes at the same time, depending on the location you plucked it. The lowest frequency of oscillation is called the fundamental frequency. Plucking the string 1/4 from one end results in oscillations at 2, 3, 4, 6, and 7 times the fundamental frequency. The higher frequencies are called harmonics. For example, if the fundamental frequency were middle C, 256 hertz, then the second harmonic would have a frequency of 512 hertz, the third 728 hertz, the fourth 1,024 hertz, etc.

The sound made by the vibrating string is very weak. On acoustic stringed instruments the strings pass over the bridge that transmits the oscillations to the top plate of the body of the instrument. Low frequency sounds also excite oscillations in the air and in the bottom plate of the guitar’s body. Sounds from the oscillations of the air pass through the sound holes in the top plate into the surrounding air. The amplitude of the fundamental frequency is the largest. The relative amplitudes of the higher harmonics depend not only on the string, but the shape and size of the body of the instrument. Electric guitars will be discussed in the chapter on Magnetism.

The relative intensities of the higher harmonics depend on the instrument. The sound spectrum produced by the instrument is characterized by these relative amplitudes. The spectrum is also called the quality of sound, or the timbre. The sound quality also depends on how the sound starts and stops.


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