A long uniform steel wire has a diameter of $$2.0$$ mm. what should be the tension in the wire, so that the speed of the transverse wave on it equals the speed of sound at STP (320$$ $$m/s) the density of steel is $$7800$$ $$kg/m3$$.

Question

A long uniform steel wire has a diameter of $$2.0$$ mm. what should be the tension in the wire, so that the speed of the transverse wave on it equals the speed of sound at STP (320$$ $$m/s) the density of steel is  $$7800$$ $$kg/m3$$.

Infinity Learn · Accepted Answer

Volume of wire $$V=$$π$$r2l=$$π$$d2l/4$$ Mass of $$wire=(M)=Volume$$×$$density=$$π$$d2l$$ρ$$4$$ Linear Mass Density μ$$=Ml=$$π$$d2$$ρ$$4$$ Wave Speed $$v=T$$μ Tension in wire $$T=$$μ$$v2=$$π$$d2$$ρ$$v24$$⇒$$T=$$ $$3.142$$×$$(2$$×$$10$$−$$3)2$$×$$7800$$×$$(320)24Substituting$$  v, ρ, d we have $$T=2508$$ N

A long uniform steel wire has a diameter of 2.0 mm. what should be the tension in the wire, so that the speed of the transverse wave on it equals the speed of sound at STP (320 m/s) the density of steel is $7800 k g / m^{3}$ .

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A long uniform steel wire has a diameter of 2.0 mm. what should be the tension in the wire, so that the speed of the transverse wave on it equals the speed of sound at STP (320 m/s) the density of steel is 7800 kg/m3.

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Ready to Test Your Skills?

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A long uniform steel wire has a diameter of 2.0 mm. what should be the tension in the wire, so that the speed of the transverse wave on it equals the speed of sound at STP (320 m/s) the density of steel is $7800 k g / m^{3}$ .