A metallic wire of 1 m length has a mass of $10 \times 10^{-3}\text{ kg}$. If a tension of 100 N is applied…
A metallic wire of 1 m length has a mass of $10 \times 10^{-3}\text{ kg}$. If a tension of 100 N is applied to a wire, what is the speed of transverse wave?
100 $\text{ms}^{-1}$
10 $\text{ms}^{-1}$
200 $\text{ms}^{-1}$
0.1 $\text{ms}^{-1}$
Solution
The linear mass density is defined as a measure of mass per unit of length.
$\therefore$ Linear mass density, $\alpha = \frac{\text{Mass}}{\text{Length}} = \frac{10 \times 10^{-3}}{1}$
$= 10 \times 10^{-3}\text{ kg m}^{-1}$
$\therefore$ The speed of transverse wave,
$v = \sqrt{\frac{T}{\alpha}}$ (where, $\alpha = \text{volume per unit} \times \text{density}$)
$= \sqrt{\frac{100}{10 \times 10^{-3}}} = \sqrt{10 \times 10^3} = 1 \times 10^2 = 100\text{ ms}^{-1}$