Linear mass density, $\mu=\frac{\text{m}}{\text{l}}=4.0\times10^2\text{kg m}^{-1}$
Frequency of vibration, v = 45Hz
$\therefore$ length of the wire, $\text{l}=\frac{\text{m}}{\mu}=\frac{3.5\times10^{-2}}{4. 0\times10^{-2}}=0.875\text{m}$
The wavelength of the stationary wave $(\lambda)$ is related to the length of the wire by the relation:
$\lambda=\frac{2\text{l}}{\text{m}}$
where,
n = Number of nodes in the wire
For fundamental node, n = 1:
$\lambda=2\text{l}$
$\lambda=2\times0.875=1.75\text{m}$
The speed of the transverse wave in the string is given as:
$\text{v}=\text{v}\lambda=45\times1.75=78.75\text{m/s}$
$\text{T}=\text{v}^2\mu$
$=(78.75)^2\times4.0\times10^{-2}=248.06\text{N}$
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