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Q. A metallic wire of $1\,m$ length has a mass of $10 \times10^{-3}$ kg. If a tension of $100\, N$ is applied to a wire, what is the speed of transverse wave ?

KCETKCET 2014Waves

Solution:

We know that
Linear mass density is defined as measure of mass per unit of length
$\therefore $ Linear mass density $\mu =\frac{\text { Mass }}{\text { Length }}$
$=\frac{10 \times 10^{-3}}{1}$
$=10 \times 10^{-3} kg / m$
$\therefore $ The speed of transverse wave
$v=\sqrt{\frac{T}{\mu}} =\sqrt{\frac{100}{10 \times 10^{-3}}}$
$=\sqrt{10 \times 10^{3}}$
(where $\mu=$ volume per unit $\times$ density)
$=1 \times 10^{2}=100\, ms ^{-1}$