- #1

jaumzaum

- 434

- 33

For example, I was taught any wave can be written in the form:

$$y=f(x-vt)$$

But here the velocity is variable, so can we still write the above equation?

Also, will the amplitude remain constant?

I will write the result I got, but I don't know if they are correct, can anyone help me figure this out?

For the wave:

$$x=\frac{gt^2}{4}$$

$$\alpha=w\sqrt{4x/g}-wt+\phi$$

$$y=A sin(w\sqrt{4x/g}-wt+\phi)$$

For the stationary wave:

$$y_{stationary}=2A sin(w\sqrt{4x/g}+\phi) cos(wt)$$