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Question

(A) The standard equation for a traveling wave is given by $y(x, t) = a \sin(\omega t - kx)$.Given equation: $y(x, t) = 0.03 \sin(2\pi t - 0.01\pi x)$

Vedclass · Accepted Answer

$200$

Vedclass · Answer

(A) The standard equation for a traveling wave is given by $y(x, t) = a \sin(\omega t - kx)$.Given equation: $y(x, t) = 0.03 \sin(2\pi t - 0.01\pi x)$.Comparing the given equation with the standard form,we identify the wave number $k$ as the coefficient of $x$:$k = 0.01\pi$.We know that the wave number $k$ is related to the wavelength $\lambda$ by the formula $k = \frac{2\pi}{\lambda}$.Substituting the value of $k$:$0.01\pi = \frac{2\pi}{\lambda}$.Solving for $\lambda$:$\lambda = \frac{2\pi}{0.01\pi} = \frac{2}{0.01} = 200 \ m$.

$A$ wave travels in a medium according to the equation of displacement given by $y(x, t) = 0.03 \sin \pi (2t - 0.01x)$,where $y$ and $x$ are in metres and $t$ is in seconds. The wavelength of the wave is .... $m$.

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