Two pieces of steel wire with identical cross sections have lengthsof L and 2L. Each ofthe wires is fixed at both ends and stretched so that the tensionin the longer wire is five timesgreater than that in the shorter wire. If the fundamental frequencyin the shorter wire is 60 Hz, what isthe frequency of the second harmonic in the longer wire?

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broliY · Accepted Answer

For shoter wire the fundamental frequency is f1=12L⋅Tm/L  so 60Hz=12L⋅Tm/L...(1)  for longer wire the second harmonic frequency is f2=22L⋅Tm/L  so we have f2=28L⋅4Tm/4L...(2)  so (2)/(1) gives  f260Hz=28L⋅4Tm/4L12L⋅Tm/L  or f260=14L⋅16LTm12L⋅LTm  simplifying it gives  f260=2  so f2=120Hz which is the secondharmonic frequency of longer string

Two pieces of steel wire with identical cross sections have lengthsof L and 2L. Each ofthe wires is fixed at both ends and stretched so that the tensi

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