The speed of the wave is given by:
v = √(T/μ)
where T is the tension in the string and μ is the linear density (mass per unit length).
Tension of segments with amplitude 0.5cm can be estimated as:
T'=F*0.005
where F is the force required to stretch a segment with amplitude 0.5cm.
For a string fixed at both ends and vibrating in its fundamental mode (i.e. with one antinode in the middle), the wavelength λ is twice the length of the string, so λ = 2l.
Therefore, the frequency f of the wave is given by:
f = v/λ = v/(2l)
Substituting the expressions for v and λ, we get:
f = √(T'/μ)/(2l) = √(F/μ*0.005)/(2l)
We need some additional information about the force required to stretch a segment with amplitude 0.5cm, or about the linear density of the string, in order to calculate the frequency.
A string of mass 0.2kg/m has length l = 0.6m. It is fixed at both ends and stretched such that it has a tension of segments with amplitude =0.5cm.Find frequency of the wave?
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