A wire having a linear density of $$0.05$$ $$g/cm$$ is stretched between two rigid supports with a tension of $$4.5$$×$$102N$$ it is observed that the wire resonance at a frequency of $$420$$ Hz. The next higher frequency at which the wire resonates is $$490$$ Hz. Determine the length of the wire.

Question

A wire having a linear density of  $$0.05$$ $$g/cm$$ is stretched between two rigid supports with a tension of $$4.5$$×$$102N$$ it is observed that the wire resonance at a frequency of $$420$$ Hz. The next higher frequency at which the wire resonates is $$490$$ Hz. Determine the length of the wire.

Infinity Learn · Accepted Answer

Expression for Frequency when both ends are tied f $$=$$ $$n2LT$$μ  Now,  $$420=n2LT$$μ→(i) $$490=n+12LT$$μ→(ii) Divide equation    i÷$$iin=6Putting$$ in equation $$(i)420=62L4.5$$×$$1020.05$$×$$10$$−$$310$$−$$2$$⇒ $$L=2.14$$ m

A wire having a linear density of $0.05 g / c m$ is stretched between two rigid supports with a tension of $4.5 \times 10^{2} N$ it is observed that the wire resonance at a frequency of 420 Hz. The next higher frequency at which the wire resonates is 490 Hz. Determine the length of the wire.

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A wire having a linear density of 0.05 g/cm is stretched between two rigid supports with a tension of 4.5×102N it is observed that the wire resonance at a frequency of 420 Hz. The next higher frequency at which the wire resonates is 490 Hz. Determine the length of the wire.

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Ready to Test Your Skills?

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A wire having a linear density of $0.05 g / c m$ is stretched between two rigid supports with a tension of $4.5 \times 10^{2} N$ it is observed that the wire resonance at a frequency of 420 Hz. The next higher frequency at which the wire resonates is 490 Hz. Determine the length of the wire.