There are a number of stringed instruments that are common today, including the guitar, the bass, the harp, and even the piano is considered a stringed instrument. While all of these instruments use the same principles to produce sound, the way they are constructed and the materials used changes which overtones of the frequencies played will resonate, and therefore change what the instrument sounds like, even if all of the instruments are playing the same fundamental frequency.

In all stringed instruments, the strings are fixed at both ends, and are plucked, bowed, hammered, or moved by some other means to produce a standing wave. Finding the fundamental frequency that the string vibrates at is a relatively easy task. The velocity of a wave traveling in a vibrating string, and the tension of the string is related by the equation:

v = λf, and
v = [ T / (m/L)]^½
where T is the tension in Newtons, m is the mass of the string, and L is the length of the string, therefore
[ T / (m/L)]^½ = λf
therefore

f = {[ T / (m/L)]^½} / λ


The fundamental wave has a wavelength of twice the length of the string, so the nodes in the wave are the ends of the string

This frequency is known as the fundamental frequency and has a wavelength equal to 2 times the length of the string. Because of this, the nodes or places of zero displacement on the wave are at the ends of the guitar string. Since the nodes are at the end of the strings, the strings will also vibrate at other wavelengths that would have nodes at the end of the strings. These include wavelengths that equal that length of the string, (1st harmonic). 2/3 the length of the string (2nd harmonic), 2/4 the length of the string (3rd Harmonic), and so on. The reason that many stringed instruments sound so different is because the design of the body of the instrument resonates different frequencies.

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