What is the rate of change of amplitude for standing waves with respect to x?

[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!