Two pieces of steel wire with identical cross sections havelengths of L and 4 L

Question

Two pieces of steel wire with identical cross sections havelengths of L and 4L.Each of the wires is fixed at both ends and stretched so that thetension in the longer wire is four timesgreater than that in the shorter wire. If the fundamental frequencyin the shorter wire is 65 Hz, what is thefrequency of the second harmonic in the longer wire?
Ive tried everything, im going on vacation and this is due, notime left, please help
Two pieces of steel wire with identical cross sections havelengths of L and 4L.Each of the wires is fixed at both ends and stretched so that thetension in the longer wire is four timesgreater than that in the shorter wire. If the fundamental frequencyin the shorter wire is 65 Hz, what is thefrequency of the second harmonic in the longer wire?
Ive tried everything, im going on vacation and this is due, notime left, please help

Explanation / Answer

Let T=tension       u=Linear mass density, which is samefor both the wires f1=v/2L=1/2L x (T/u)^1/2 For longer wire, taking 4L for L and 4T for T F1=1/2(4L) x (4T/u)^1/2 = 1/8L x 2(T/u)^1/2 f1/F1= 2 F1 = 2* f1 = 2*65 = 130 Hz For second harmonic F2 = 2F1 = 2* 130 = 260Hz

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