Question

A steel wire of length $64cm$ weights $5g$. If it is stretched by a force of $8N$, what would be the speed of a transverse wave passing on it?

Answer 1

Step 1: Given data.

Mass, $m=5g$

Length of the wire, $l=64cm$

Tension, $T=8N=8\times {10}^{5}dyne$

Step 2: Finding the speed of a transverse wave.

We have,

Mass per unit length.

$\rho =\frac{Mass}{length}=\frac{5}{64}\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$cm$}\right.$ …..$\left(i\right)$

Where, $\rho$ is the mass per unit length.

Now,

We know that,

$v=\sqrt{\frac{T}{\rho }}$

Where $v$ is the speed

$v=\sqrt{\frac{8\times {10}^5}{{\displaystyle \raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$64$}\right.}}}$

$v=3200\raisebox{1ex}{$cm$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

$v=32\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Hence, the speed of a transverse wave is $32\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$.