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(D) The standard wave equation for a wave traveling in the negative $x$-direction is $y = A\sin(kx + \omega t + \phi_0)$.Comparing the given equation

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Both $(b)$ and $(c)$

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(D) The standard wave equation for a wave traveling in the negative $x$-direction is $y = A\sin(kx + \omega t + \phi_0)$.Comparing the given equation $Y = A\sin(10\pi x + 15\pi t + \frac{\pi}{3})$ with the standard form,we identify the angular frequency $\omega = 15\pi\,rad/s$ and the wave number $k = 10\pi\,rad/m$.The wave velocity $v$ is given by $v = \frac{\omega}{k} = \frac{15\pi}{10\pi} = 1.5\,m/s$. Since the signs of the $x$ and $t$ terms are both positive,the wave travels in the negative $x$-direction.The wavelength $\lambda$ is given by $\lambda = \frac{2\pi}{k} = \frac{2\pi}{10\pi} = 0.2\,m$.Thus,both statements $(b)$ and $(c)$ are correct.

$A$ wave represented by the given equation $Y = A\sin(10\pi x + 15\pi t + \frac{\pi}{3})$,where $x$ is in meters and $t$ is in seconds. The expression represents:

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