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(C) The standard equation for a progressive wave is $x = A \sin(\omega t + ky)$.Comparing the given equation $x = 1.2 \sin(314t + 12.56y)$ with the st

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$0.5 \, m, -ve \, y$-direction

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(C) The standard equation for a progressive wave is $x = A \sin(\omega t + ky)$.Comparing the given equation $x = 1.2 \sin(314t + 12.56y)$ with the standard form,we get the wave number $k = 12.56 \, 	ext{rad/m}$.The wavelength $\lambda$ is given by the formula $\lambda = \frac{2\pi}{k}$.Substituting the value of $k$ and $\pi \approx 3.14$:$\lambda = \frac{2 	imes 3.14}{12.56} = \frac{6.28}{12.56} = 0.5 \, 	ext{m}$.Since the term inside the sine function is $(314t + 12.56y)$,the positive sign between the $t$ and $y$ terms indicates that the wave is traveling in the negative direction of the axis associated with the variable $y$.Therefore,the wave is traveling in the $-ve \, y$-direction.

The equation of a progressive wave is given by $x = 1.2 \sin(314t + 12.56y)$. What are the wavelength and the direction of the wave?

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