A steel wire has a length of 12.0 ;m and a ma | vedclass

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(B) Length of the steel wire,$l = 12.0 \;m$.Mass of the steel wire,$m = 2.10 \;kg$.Velocity of the transverse wave,$v = 343 \;m s^{-1}$.Mass per unit

Vedclass · Accepted Answer

$2.06 	imes 10^{4} \;N$

Vedclass · Answer

(B) Length of the steel wire,$l = 12.0 \;m$.Mass of the steel wire,$m = 2.10 \;kg$.Velocity of the transverse wave,$v = 343 \;m s^{-1}$.Mass per unit length,$\mu = \frac{m}{l} = \frac{2.10}{12.0} = 0.175 \;kg \;m^{-1}$.For tension $T$,the velocity of the transverse wave is given by the relation: $v = \sqrt{\frac{T}{\mu}}$.Rearranging for $T$,we get $T = v^2 \mu$.Substituting the values: $T = (343)^2 	imes 0.175 = 117649 	imes 0.175 = 20588.575 \;N$.Rounding to three significant figures,$T \approx 2.06 	imes 10^{4} \;N$.

$A$ steel wire has a length of $12.0 \;m$ and a mass of $2.10 \;kg$. What should be the tension in the wire so that the speed of a transverse wave on the wire equals the speed of sound in dry air at $20\,^{\circ}C = 343 \;m s^{-1}$?

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