1. The problem is to understand the mathematical representation of a wave. 2. A common formula for a sinusoidal wave is: $$y = A \sin(kx - \omega t + \phi)$$ where: - $A$ is the amplitude (maximum displacement), - $k$ is the wave number related to wavelength by $k = \frac{2\pi}{\lambda}$, - $\omega$ is the angular frequency related to period by $\omega = \frac{2\pi}{T}$, - $t$ is time, - $x$ is position, - $\phi$ is the phase constant. 3. This formula describes how the wave oscillates in space and time. 4. Important rules: - The wave repeats every wavelength $\lambda$ in space. - The wave repeats every period $T$ in time. - The amplitude $A$ determines the height of the wave peaks. 5. For example, if $A=1$, $\lambda=2\pi$, $T=2$, and $\phi=0$, then: $$k = \frac{2\pi}{2\pi} = 1$$ $$\omega = \frac{2\pi}{2} = \pi$$ 6. So the wave equation becomes: $$y = \sin(x - \pi t)$$ 7. This means the wave moves along the $x$-axis with time $t$, oscillating between -1 and 1. This is a basic explanation of a wave function.