The wave function (this is the wave function in mechanical waves. It is not the wave equation, which is derived from this wave function. Neither is this the wave function for quantum mechanics!) is given as: \begin{align} y(x,t)&=A\cos(kx \pm \omega t + \phi) \end{align} (where $k$ is the wavenumber, $x$ is the position, $A$ is the amplitude, $\omega$ is the angular frequency, $t$ is the time, and $\phi$ is the phase difference)
From my knowledge, the $\pm$ in front of $\omega t$ is to account for wave direction. However, mathematically, I am unable to intuitively understand or even picture why this $\pm$ sign in front of $\omega t$ (which accounts for the time dependency of the wave function) should account for direction. Hence, may I know the connection between this $\pm$ sign and the direction of the wave propagation? Thank you!
