A wire of density $$9$$×$$103$$ kg $$/m3$$ is stretched between two clamps $$1$$ m apart and is subjected to an extension of $$4.9$$ × $$10-4$$ m. The lowest frequency of transverse vibration in the wire is (Y$$ $$=$$ $$9$$ × $$1010$$ N $$/$$ $$m2)

Question

A wire of density $$9$$×$$103$$ kg $$/m3$$ is stretched between two clamps $$1$$ m apart and is subjected to an extension of $$4.9$$ × $$10-4$$  m. The lowest frequency of transverse vibration in the wire is (Y$$ $$=$$ $$9$$ × $$1010$$ N $$/$$ $$m2)

Infinity Learn · Accepted Answer

For wire if M $$=$$ mass, ρ $$=$$ density, A $$=$$ Area of cross section V $$=$$ volume, l $$=$$ length, Δl $$=$$ change in length Then mass per unit length $$m=Ml=Al$$ρ$$l=A$$ρAnd Young’s modules of elasticity $$y=T/A$$Δ$$l/l$$⇒$$T=Y$$ΔlAl. Hence lowest frequency of vibration   $$n=12lTm=12ly$$ΔllAAρ$$=12ly$$Δllρ⇒$$n=12$$×$$19$$×$$1010$$×$$4.9$$×$$10$$−$$41$$×$$9$$×$$103=35Hz$$

A wire of density 9 $\times$ 10³ kg /m³ is stretched between two clamps 1 m apart and is subjected to an extension of 4.9 $\times$ 10^-4 m. The lowest frequency of transverse vibration in the wire is (Y = 9 $\times$ 10¹⁰ N / m²)

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A wire of density 9×103 kg /m3 is stretched between two clamps 1 m apart and is subjected to an extension of 4.9 × 10-4 m. The lowest frequency of transverse vibration in the wire is (Y = 9 × 1010 N / m2)

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Ready to Test Your Skills?

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A wire of density 9 $\times$ 10³ kg /m³ is stretched between two clamps 1 m apart and is subjected to an extension of 4.9 $\times$ 10^-4 m. The lowest frequency of transverse vibration in the wire is (Y = 9 $\times$ 10¹⁰ N / m²)