Standing waves

  1. 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?
  2. jcsd
  3. when you differentiate it with respect to x, then you get slope of the curve/wave at a given instant ##\frac{dy}{dx}=slope##.
  4. rate of change of amplitude is velocity, ##\frac{dy}{dt}=##velocity of particle
  5. 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?
  6. I want to say how much the amplitude changes as i move forward on x-axis.
  7. Yes, you can say that!!
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