The equation of a wave on a string of linear | vedclass

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(D) The standard wave equation is $y = A \sin(2\pi(\frac{t}{T} - \frac{x}{\lambda}))$. Comparing this with the given equation $y = 0.02 \sin[2\pi(\fra

Vedclass · Accepted Answer

$6.25$

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(D) The standard wave equation is $y = A \sin(2\pi(\frac{t}{T} - \frac{x}{\lambda}))$. Comparing this with the given equation $y = 0.02 \sin[2\pi(\frac{t}{0.04} - \frac{x}{0.50})]$,we get the time period $T = 0.04 \, s$ and wavelength $\lambda = 0.50 \, m$.The wave speed $v$ is given by $v = \frac{\lambda}{T} = \frac{0.50}{0.04} = 12.5 \, m/s$.The tension $T_{tension}$ in the string is related to the linear mass density $\mu$ and wave speed $v$ by the formula $T_{tension} = \mu v^2$.Given $\mu = 0.04 \, kg \cdot m^{-1}$,we have $T_{tension} = 0.04 	imes (12.5)^2 = 0.04 	imes 156.25 = 6.25 \, N$.

The equation of a wave on a string of linear mass density $0.04 \, kg \cdot m^{-1}$ is given by: $y = 0.02 \, \sin \left[ 2\pi \left( \frac{t}{0.04} - \frac{x}{0.50} \right) \right]$. The tension in the string is ..... $N$.

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