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

Infinity Learn · Accepted Answer

For wire $$ifM=$$ mass, ρ$$=$$ density ,$$A=$$ Area of cross section $$V=$$ volume, $$l=$$ length, Δ$$l=$$ change in length Then mass per unit length $$m=Ml=Al$$ρ$$l=A$$ρ And Young's modulus of elasticity $$Y=T/A$$Δ$$l/l$$⇒ $$T=Y$$ΔlAlHence lowest frequency of $$vibrationn=12lTm=12lY$$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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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)