-A Sample Problem-

Using these properties of harmonics and frequencies, there is a formula that is helpful when dealing with certain numerical problems. The formula is

v = 2L/n * fn

where v is the speed of the wave on the string, L is the length of the string, n is a positive integer representing the nth normal mode of oscillation, and f is the fundamental frequency.

Problem: A guitar's high E string is 64 cm long, and has a fundamental frequency of 330 hz. If the first fret is pressed down, the string is now shorter, and the new frequency is now 350 hz, and it is now an F note. How far is the fret from the neck end of the string?

Using this useful formula, this is a simple problem to solve. We use n = 1, because it is the fundamental frequency initially, which gives us, with L = 0.64m, and f = 330 hz,

2(0.64m)(330Hz) = 422m/s

The speed of the wave on the string is 422 m/s. We do not adjust the tension in the string, so this wave speed remains constant. We again use the same equation, but fill in the values after the first fret is held down. And now we are solving for L. Turn the page for more excitement...

Next Page