A string vibrates with a particular fundamental frequency. It is possible, however, to produce pitches with different frequencies from the same string. The four properties of the string that affect its frequency are length, diameter, tension, and density.
The frequency f = 1/T = v/λ. So f = v/λ. We also saw that, for the fundamental frequency f1, the string length is λ/2, so f1 = v/2L. The wave speed is determined by the string tension F and the mass per unit lenght or linear density μ = M/L, v = (F/μ)1/2 = (FL/M)1/2.
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