QJEEM24Ph240a: JEE Main 2024 Physics - Class 11 JEEM24Ph240a Solution: A plane progressive wave is given by . The frequency of the…

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.

The general form of a wave equation is:

where:

• $A$ is the amplitude of the wave.
• $f$ is the frequency of the wave.
• $t$ is the time variable.
• $k$ is the wave number, defined as $\frac{2 \pi}{\lambda}$ where $\lambda$ is the wavelength.
• $x$ is the spatial variable.
• $\phi$ is the phase constant.

By comparing the given wave equation with the general form, we have:

We observe that the term $2 \pi(330t - x)$ corresponds to $2 \pi ft - kx$ in the general form.

From this, it is clear that:

• $2 \pi ft \rightarrow 2 \pi \cdot 330 t$
• Therefore, $f = 330$ Hz

So, the frequency of the wave is 330 Hz.

Thus, the correct answer is:

Option C: 330 Hz