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

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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.

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nil1996 said:I want to say how much the amplitude changes as i move forward on x-axis.

Yes, you can say that!

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.

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.

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.

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.

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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