The equation of a transverse wave propagating | vedclass

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(C) The standard equation of a transverse wave is $y = A \sin(kx + \omega t)$.Comparing this with the given equation $y = 3 \sin(4x + 200t)$, we get:W

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$0.2$

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(C) The standard equation of a transverse wave is $y = A \sin(kx + \omega t)$.Comparing this with the given equation $y = 3 \sin(4x + 200t)$, we get:Wave number $k = 4 \ m^{-1}$Angular frequency $\omega = 200 \ rad \ s^{-1}$The wave speed $v$ is given by $v = \frac{\omega}{k} = \frac{200}{4} = 50 \ m/s$.The speed of a transverse wave on a stretched string is also given by $v = \sqrt{\frac{T}{\mu}}$, where $T$ is the tension and $\mu$ is the linear mass density.Squaring both sides, we get $v^2 = \frac{T}{\mu}$, which implies $\mu = \frac{T}{v^2}$.Substituting the given values $T = 500 \ N$ and $v = 50 \ m/s$:$\mu = \frac{500}{(50)^2} = \frac{500}{2500} = \frac{1}{5} = 0.2 \ kg \ m^{-1}$.Thus, the linear density of the string is $0.2 \ kg \ m^{-1}$.

The equation of a transverse wave propagating on a stretched string is given by $y = 3 \sin (4x + 200t)$, where $x$ and $y$ are in metres and the time $t$ is in seconds. If the tension applied to the string is $500 \ N$, the linear density of the string is: (in $kg \ m^{-1}$)

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