A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45\ \mathrm{Hz}$. The mass of the wire is $3.5 imes10^{-2}\ \mathrm{kg}$ and its linear mass density is $4 imes10^{-2}\ \mathrm{kg\,m^{-1}}$. What is the speed of transverse wave on string and…

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A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45\ \mathrm{Hz}$. The mass of the wire is $3.5	imes10^{-2}\ \mathrm{kg}$ and its linear mass density is $4	imes10^{-2}\ \mathrm{kg\,m^{-1}}$. What is the speed of transverse wave on string and tension in the wire?

Aicharya · Accepted Answer

Sol. Length of wire = $\dfrac{	ext{Mass of wire}}{	ext{Linear density}} = \dfrac{3.5	imes10^{-2}}{4	imes10^{-2}} = 0.875\ \mathrm{m}$ Now, $f = \dfrac{1}{2l}\sqrt{\dfrac{T}{\alpha}}$ $	herefore$ Tension in the wire, $T = 4f^{2}l^{2}\alpha$ $\qquad = 4(45)^{2}(0.875)^{2}(4	imes10^{-2}) = 248.1\ \mathrm{N}$ Speed of transverse wave, $v = f\lambda = f(2l)$ $\qquad = 45	imes 2	imes 0.875 = 78.75\ \mathrm{ms}^{-1}$ Answer: $78.75\ \mathrm{ms}^{-1}$

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45\…

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