Standing waves rate of change

  • Thread starter nil1996
  • Start date
  • #1
301
7
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?
 

Answers and Replies

  • #2
199
15
when you differentiate it with respect to x, then you get slope of the curve/wave at a given instant ##\frac{dy}{dx}=slope##.
 
  • #3
199
15
rate of change of amplitude is velocity, ##\frac{dy}{dt}=##velocity of particle
 
  • #4
301
7
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 [itex]\frac{dy}{dx}[/itex]=Akcoskx and i think this will be the rate of change of amplitude on the string. Isn't it right?
 
  • #5
301
7
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.
 
  • #6
199
15
I want to say how much the amplitude changes as i move forward on x-axis.

Yes, you can say that!!
 

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