Question 137: Waves

Question

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

Accepted Answer

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:
$$y = A \cos (2 \pi ft - kx + \phi)$$
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:
$$y = 2 \cos 2 \pi (330 t - x)$$
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

Answer

660 Hz

Answer

340 Hz

Answer

330 Hz

Answer

165 Hz

Waves

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

Choose the correct answer: