To find the equation of the sinusoidal wave, we need to determine several properties of the wave:

Wave Velocity (v):

Given that the wave travels a distance of 1.2 cm in 0.3 seconds, the velocity $ v $ can be computed as:

$ v = \frac{\text{distance}}{\text{time}} = \frac{1.2 \, \text{cm}}{0.3 \, \text{s}} = 4 \, \text{cm/s} $

Wave Number (k):

The wave number $ k $ is calculated using the wavelength $ \lambda = 7.5 \, \text{cm} $:

$ k = \frac{2\pi}{\lambda} = \frac{2\pi}{7.5} = \frac{4\pi}{15} \approx 0.83 $

Angular Frequency ($\omega$):

Angular frequency $ \omega $ is related to the wave number and velocity by the equation $ v = \frac{\omega}{k} $, thus:

$ \omega = vk = 4 \times \frac{4\pi}{15} = \frac{16\pi}{15} \approx 3.35 $

Wave Equation:

The general form for a sinusoidal wave traveling in the positive x-direction is:

$ y = A \cos(kx - \omega t) $

Given the maximum displacement (amplitude $ A $) of the wave is 2 cm, the equation becomes:

$ y = 2 \cos(0.83x - 3.35t) \, \text{cm} $

This equation accurately describes the sinusoidal wave given the provided parameters.