The linear mass density of a vibrating string | vedclass

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(A) The standard equation of a transverse wave is $y = A \sin(kx + \omega t)$.Comparing this with the given equation $y = 0.021 \sin(x + 30t)$,we get

Vedclass · Accepted Answer

$0.12$

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(A) The standard equation of a transverse wave is $y = A \sin(kx + \omega t)$.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 tension $T$ in a string is related to the linear mass density $\mu$ and wave speed $v$ by the formula $T = \mu v^2$.Given $\mu = 1.3 	imes 10^{-4} \ kg/m$,we have $T = (1.3 	imes 10^{-4}) 	imes (30)^2$.$T = 1.3 	imes 10^{-4} 	imes 900 = 1.3 	imes 0.09 = 0.117 \ N$.Rounding to two decimal places,the tension is approximately $0.12 \ N$.

The linear mass 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 approximately: (in $N$)

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