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(A) The standard equation of a plane progressive wave is $y = A \sin(\omega t - kx)$.Comparing the given equation $y = 0.1 \sin \left( 200\pi t - \fra

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$100 \ Hz, 1.7 \ m, 170 \ m/s$

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(A) The standard equation of a plane progressive wave is $y = A \sin(\omega t - kx)$.Comparing the given equation $y = 0.1 \sin \left( 200\pi t - \frac{20\pi x}{17} \right)$ with the standard equation:$1$. Angular frequency $\omega = 200\pi \ rad/s$. Since $\omega = 2\pi n$,we have $2\pi n = 200\pi$,which gives frequency $n = 100 \ Hz$.$2$. Wave number $k = \frac{20\pi}{17} \ rad/m$. Since $k = \frac{2\pi}{\lambda}$,we have $\lambda = \frac{2\pi}{k} = \frac{2\pi}{20\pi/17} = 1.7 \ m$.$3$. Wave speed $v = \frac{\omega}{k} = \frac{200\pi}{20\pi/17} = 170 \ m/s$.Thus,the frequency,wavelength,and speed are $100 \ Hz, 1.7 \ m, 170 \ m/s$ respectively.

$A$ plane progressive wave is represented by the equation $y = 0.1 \sin \left( 200\pi t - \frac{20\pi x}{17} \right)$,where $y$ is displacement in $m$,$t$ is in seconds,and $x$ is the distance from a fixed origin in meters. The frequency,wavelength,and speed of the wave respectively are:

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