Write phase of wave function in mathematical form https://www.youtube.com/watch?v=N-NI1EndSnk $$$\psi = A \times \sin\phi $$$ $$$\psi$$$ is wave function A is amplitude ================================================== Why does phase $$$\phi$$$ become $$$\phi = kx -\omega t$$$? ================================================== Notation of wave in physics way is that $$$f (x-vt)$$$ ================================================== Above one shows function $$$f(x)$$$ is moved towards right as much as distance $$$s=vt$$$ Moved $$$f(x)$$$ can be written as $$$f(x-vt)$$$ So, things which can be represented as $$$f(x-vt)$$$ can be considered as wave ================================================== $$$\sin 5 meter$$$ doesn't make sense $$$\sin 10 seconds$$$ doesn't make sense $$$\sin 5kilogram$$$ doesn't make sense $$$\pi$$$ in $$$\sin\pi$$$ should have just number ================================================== You had used $$$(x-vt)$$$ as kind of distance from above example You can use k to remove unit to use $$$(x-vt)$$$ inside of $$$\sin$$$ $$$\sin k(x-vt)$$$ ================================================== wavelength is most important characteristic and most important physical quantities in wave wavelength is very physical quantities which are related to periodicity of wave ================================================== If you pass $$$x+\lambda$$$ into $$$x$$$ from $$$\sin k(x-vt)$$$ value of $$$\sin k(x-vt)$$$ shoudln't change To achieve this, you should have $$$k\lambda = 2\pi$$$ Therefore, $$$k=\dfrac{2\pi}{\lambda}$$$ k is called wave number ================================================== $$$v = \dfrac{\lambda}{T} = f \lambda$$$ $$$\lambda$$$ is wavelength $$$T$$$ is one period $$$v$$$ is phase velocity of wave $$$f$$$ is number of vibrations Therefore, $$$kv = \dfrac{2\pi}{\lambda} \times f\lambda$$$ and finally $$$kv=2\pi f$$$ ================================================== $$$kv$$$ is called angular frequency $$$\omega$$$