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what is the frequency of the tuning fork?
A 0.0145 kg, 2.17 m long wire is fixed at both ends and vibrates in its simplest mode under a tension of 213 N. When a tuning fork is placed near the wire, a beat frequency of 4.85 Hz is heard. The beat frequency increase as the the tension of the wire decreases; what is the frequency of the tuning fork?
L = 1/2lambda
lambda = 2L = 2(2.17m) = 4.34 m
mu (mass/unit length) = 0.0145 kg/2.17m = 6.68E-3 kg/m
v = sqrt(T/mu) = sqrt(215N / 6.68E-3kg/m) = 179.4 m/s
f(frequency) of string = v/lambda = 179.4 m/s / 4.34m = 41.3 Hz
beat frequency = (f of fork) - (f of string)
f of fork = 4.85Hz + 41.3Hz = 46.2 Hz
That should be the right answer, unless I made a calculator error. Good luck with it!
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