Calculating Amplitude of a Wave at x = 6 cm | Dynamics Explained

[chukie]

For the wave shown in this drawing, what is the amplitude at x = 6 cm?
[Hint: Remember that the wave will be moving. So even though there presently is an node at x = 6 cm, this will change at a later time.]


I put 0 cm as the answer but I got it wrong and I don't understand why it's not zero. Could someone please help me?

 

[mukundpa]

I think you need to understand the difference between the amplitude and the instantaneous displacement of the particle.

 

[Moetasim]

I can help clarify the concept of amplitude and its calculation for a wave at a specific point. The amplitude of a wave is defined as the maximum displacement of a particle from its equilibrium position. In this case, the wave is shown as a transverse wave, where the particles move perpendicular to the direction of the wave's propagation.

At x = 6 cm, the wave shown in the drawing has a node, which is a point of zero displacement. However, this does not mean that the amplitude is zero. As the wave moves, the particles at x = 6 cm will eventually reach a maximum displacement from their equilibrium position. This maximum displacement is the amplitude of the wave at that point.

To calculate the amplitude at x = 6 cm, we need to consider the wave's properties and use the wave equation, A = y_max - y_min, where A is the amplitude, y_max is the maximum displacement of the wave, and y_min is the minimum displacement of the wave.

Since the wave is shown as a simple harmonic wave, we can assume that the maximum displacement and minimum displacement are equal in magnitude but opposite in direction. This means that the amplitude at x = 6 cm is half of the distance between the crest and the trough of the wave at that point.

In conclusion, the amplitude at x = 6 cm is not zero, but half of the distance between the crest and the trough of the wave at that point. I hope this explanation helps in understanding the concept of amplitude and its calculation for a wave at a specific point.