Standing waves rate of change

In summary, the equation of standing waves is y=Asinkxcosωt and when differentiated with respect to x, it gives the slope or rate of change of the curve/wave at a given instant. The rate of change of amplitude is equal to the velocity of the particle. In the case of a string oscillating in fundamental frequency, differentiating the equation with respect to x will give the rate of change of amplitude on the string. This can also be interpreted as how much the amplitude changes as one moves forward on the x-axis.
  • #1
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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?
 
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  • #2
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
rate of change of amplitude is velocity, ##\frac{dy}{dt}=##velocity of particle
 
  • #4
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
NihalSh said:
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
nil1996 said:
I want to say how much the amplitude changes as i move forward on x-axis.

Yes, you can say that!
 

1. What is the definition of "Standing Waves Rate of Change"?

The Standing Waves Rate of Change is a measure of how quickly the amplitude of a standing wave changes over time. It is a key aspect of studying standing waves and is necessary for understanding their behavior.

2. How is the Standing Waves Rate of Change calculated?

The Standing Waves Rate of Change is calculated by taking the derivative of the standing wave equation with respect to time. This results in a value that represents the rate at which the amplitude of the standing wave is changing at any given point in time.

3. What factors affect the Standing Waves Rate of Change?

The Standing Waves Rate of Change is affected by several factors, including the frequency and amplitude of the standing wave, the properties of the medium in which the wave is traveling, and the boundary conditions of the system.

4. Why is the Standing Waves Rate of Change important in studying standing waves?

The Standing Waves Rate of Change is important because it provides insight into the behavior of standing waves. It allows us to determine how quickly the amplitude of the wave is changing, which can help us understand the energy transfer and stability of the wave.

5. How does the Standing Waves Rate of Change relate to the concept of resonance?

The Standing Waves Rate of Change is closely related to the concept of resonance. When the rate of change is at its maximum, it indicates that the standing wave is in resonance and the amplitude is increasing rapidly. On the other hand, a low rate of change may indicate that the wave is not in resonance and the amplitude is relatively stable.

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