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"The Physics of Music"	Page 5	copyright: David F. Bills 1997

For a stretched string of a given mass per unit length ( ) and under a given tension (F ), the speed (v ) of a wave in the string is given by the following equation: When a string of a given length (L ) is plucked gently in the middle, a vibration is produced with a wavelength () that is twice the length of the string: The frequency (f ) of this vibration can then be obtained by the following reformulation of the previous equation: As the vibration that is the lowest frequency for that particular type and length of string under a specific tension, this frequency is known as the fundamental, or first harmonic.

The principle of tuning is based on matching pitches. The size of the vibrational source is the determinant of pitch. When these pitches are tuned, a musician utilizes the concept of beating.

The apparent rise and fall in loudness occurring when two notes of slightly different frequency are played in in unison is called "beating." The beating for an "out of tune" note is equivalent in periodicity to the difference in frequency between the two notes. (see figure 2) For humans this is just a few hertz. The further away the frequencies, the faster the beating. With a certain degree of frequency separation, the beating becomes coarse. If the two notes are far enough away from each other, the tones will sound like two separate notes.

A violin is tuned by adjusting the tension of the strings. A string is tightened if the instrument is flat and relaxed if sharp. There are two methods for tuning. If the tuning is far away from the desired pitch, a tuning peg is adjusted on the head of the violin. (see figure 5) If the instrument is only slightly out of tune, a small nob is turned which minutely adjusts string tension from on the tailpiece of the violin (see figure 6) as described in the equation above. In both cases, the tension of the string is adjusted to change the frequency of the sound wave.

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"The Physics of Music"	Page 5	copyright: David F. Bills 1997