Question

A transverse periodic wave on a string with a linear mass density of 0.200 kg/m is described by the following equation $y = 0.05 \sin (420 t - 21.0 x)$ where x and y are in metres and t is in seconds. The tension in the string is equal to

Moderate

Solution

$V = \sqrt{\frac{T}{λ}} = \frac{ω}{k}$
$\Rightarrow T = \frac{ω^{2} λ}{k^{2}} = {(\frac{420}{21})}^{2} \times 0.2 = 80 N$

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