The linear density of a vibrating string is 1 | vedclass

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(A) The wave equation is given by $Y = A \sin(kx + \omega t)$.Comparing this with the given equation $Y = 0.021 \sin(x + 30t)$,we get the angular freq

Vedclass · Accepted Answer

$0.117$

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(A) The wave equation is given by $Y = A \sin(kx + \omega t)$.Comparing this with the given equation $Y = 0.021 \sin(x + 30t)$,we get the angular frequency $\omega = 30 \, rad/s$ and the wave number $k = 1 \, m^{-1}$.The wave speed $v$ is given by $v = \frac{\omega}{k} = \frac{30}{1} = 30 \, m/s$.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 $\mu = 1.3 	imes 10^{-4} \, kg/m$.Substituting the values: $30 = \sqrt{\frac{T}{1.3 	imes 10^{-4}}}$.Squaring both sides: $900 = \frac{T}{1.3 	imes 10^{-4}}$.$T = 900 	imes 1.3 	imes 10^{-4} = 1170 	imes 10^{-4} = 0.117 \, N$.

The linear density of a vibrating string is $1.3 \times 10^{-4} \, kg/m$. $A$ transverse wave is propagating on the string and is described by the equation $Y = 0.021 \, \sin(x + 30t)$,where $x$ and $y$ are measured in meters and $t$ in seconds. The tension in the string is ..... $N$.

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