The transverse displacement of a string (clam | vedclass

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(A) The standard equation for a standing wave is $y(x,t) = A \sin(kx) \cos(\omega t)$.Comparing this with the given equation $y(x,t) = 0.6 \sin \left(

Vedclass · Accepted Answer

$648$

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(A) The standard equation for a standing wave is $y(x,t) = A \sin(kx) \cos(\omega t)$.Comparing this with the given equation $y(x,t) = 0.6 \sin \left( \frac{2\pi}{3}x ight) \cos (120\pi t)$,we get angular frequency $\omega = 120\pi \, rad/s$ and wave number $k = \frac{2\pi}{3} \, m^{-1}$.The wave speed $v$ is given by $v = \frac{\omega}{k} = \frac{120\pi}{2\pi/3} = 180 \, m/s$.The linear mass density $\mu$ is $\mu = \frac{M}{L} = \frac{3.0 	imes 10^{-2} \, kg}{1.5 \, m} = 2 	imes 10^{-2} \, kg/m$.The wave speed in a string is related to tension $T$ by $v = \sqrt{\frac{T}{\mu}}$,so $T = \mu v^2$.Substituting the values: $T = (2 	imes 10^{-2} \, kg/m) 	imes (180 \, m/s)^2 = 2 	imes 10^{-2} 	imes 32400 = 648 \, N$.

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