A transverse wave is propagating on a string. | vedclass

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(C) The general equation of a transverse wave is given by $Y = A \sin(kx + \omega t)$.Comparing this with the given equation $Y = 0.05 \sin(x + 15t)$,

Vedclass · Accepted Answer

$0.225$

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(C) The general equation of a transverse wave is given by $Y = A \sin(kx + \omega t)$.Comparing this with the given equation $Y = 0.05 \sin(x + 15t)$,we get the angular frequency $\omega = 15 \ rad/s$ and the wave number $k = 1 \ m^{-1}$.The wave speed $v$ is given by $v = \frac{\omega}{k} = \frac{15}{1} = 15 \ m/s$.The speed of a transverse wave on a string is also given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density.Given $\mu = 10^{-3} \ kg/m$,we have $15 = \sqrt{\frac{T}{10^{-3}}}$.Squaring both sides,$225 = \frac{T}{10^{-3}}$.Therefore,$T = 225 	imes 10^{-3} \ N = 0.225 \ N$.

$A$ transverse wave is propagating on a string. The linear mass density of the vibrating string is $10^{-3} \ kg/m$. The equation of the wave is $Y = 0.05 \sin(x + 15t)$,where $x$ and $Y$ are in meters and time $t$ is in seconds. The tension in the string is: (in $N$)

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