A wave equation which gives the displacement | vedclass

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(D) The standard wave equation is given by $y = a \sin(\omega t + kx)$.Comparing the given equation $y = 0.001 \sin(100t + x)$ with the standard form:

Vedclass · Accepted Answer

Travelling with a velocity of $100 \ m/s$ in the negative $x$-direction

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(D) The standard wave equation is given by $y = a \sin(\omega t + kx)$.Comparing the given equation $y = 0.001 \sin(100t + x)$ with the standard form:$1$. Angular frequency $\omega = 100 \ rad/s$. Since $\omega = 2\pi f$,the frequency $f = \frac{100}{2\pi} = \frac{50}{\pi} \ Hz$.$2$. Wave number $k = 1 \ m^{-1}$. Since $k = \frac{2\pi}{\lambda}$,the wavelength $\lambda = 2\pi \ m$.$3$. Wave velocity $v = \frac{\omega}{k} = \frac{100}{1} = 100 \ m/s$.$4$. Since there is a positive sign between the $t$ and $x$ terms $(100t + x)$,the wave is travelling in the negative $x$-direction.Therefore,the correct option is $(d)$.

$A$ wave equation which gives the displacement along $y$-direction is given by $y = 0.001 \sin(100t + x)$,where $x$ and $y$ are in meters and $t$ is time in seconds. This represents a wave:

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