# Standing waves rate of change

nil1996
Equation of standing waves→ y=Asinkxcosωt

What do i get if i differentiate the above equation with respect to "x" ?
Do i get the rate of change of amplitude when i put t=0?

NihalSh
when you differentiate it with respect to x, then you get slope of the curve/wave at a given instant ##\frac{dy}{dx}=slope##.

NihalSh
rate of change of amplitude is velocity, ##\frac{dy}{dt}=##velocity of particle

nil1996
Lets consider a string oscillating in fundamental frequency. In the wave equation if i put t=0 the i will get a snapshot of the wave in which all particles will be at their amplitudes. Now if i differentiate the equation that is y=Asinkx i will get something like $\frac{dy}{dx}$=Akcoskx and i think this will be the rate of change of amplitude on the string. Isn't it right?

nil1996
rate of change of amplitude is velocity, ##\frac{dy}{dt}=##velocity of particle

I want to say how much the amplitude changes as i move forward on x-axis.

NihalSh
I want to say how much the amplitude changes as i move forward on x-axis.

Yes, you can say that!!