Jellofart's Blog --> Relationships --> What is the relationship between fundamental frequency and string tension?
15Mar/101
What is the relationship between fundamental frequency and string tension?
Reader question: I'm trying to determine what the relationship between fundamental frequency and string tension, and am not having much luck. Any help would be appreciated!!
it's related to waves, not forces directly.
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March 15th, 2010 - 07:20
Suppose the string is fixed at both ends, and is of length L. Then
f = n*(v/(2L)),
where n is the mode number (1 for the fundamental frequency) and v is the speed of the waves on the string.
Now, because the speed is given by
v = (T/u)^(1/2),
where T is the tension in the string, and u is the mass per unit length (the lineal density), we have that
f = 1/(2L)*sqrt(T/u) for the fundamental mode.