A plane progressive wave is given by $y=2 \cos 2 \pi(330 \mathrm{t}-x) \mathrm{m}$. The frequency of the wave is :

<p>To find the frequency of the plane progressive wave given by the equation $y = 2 \cos 2 \pi(330 \mathrm{t} - x) \mathrm{m}$, we start by analyzing the general form of a wave equation.</p> <p>The general form of a wave equation is:</p> $y = A \cos (2 \pi ft - kx + \phi)$ <p>where:</p> <ul> <li>$A$ is the amplitude of the wave.</li> <li>$f$ is the frequency of the wave.</li> <li>$t$ is the time variable.</li> <li>$k$ is the wave number, defined as $\frac{2 \pi}{\lambda}$ where $\lambda$ is the wavelength.</li> <li>$x$ is the spatial variable.</li> <li>$\phi$ is the phase constant.</li> </ul> <p>By comparing the given wave equation with the general form, we have:</p> $y = 2 \cos 2 \pi (330 t - x)$ <p>We observe that the term $2 \pi(330t - x)$ corresponds to $2 \pi ft - kx$ in the general form.</p> <p>From this, it is clear that:</p> <ul> <li>$2 \pi ft \rightarrow 2 \pi \cdot 330 t$</li> <li>Therefore, $f = 330$ Hz</li> </ul> <p>So, the frequency of the wave is 330 Hz.</p> <p>Thus, the correct answer is:</p> <p><strong>Option C: 330 Hz</strong></p>