A transverse wave is shown in the diagram. What is the amplitude of the wave?
Okay, so in this question, we’ve been given a graph. And on this graph, we can see displacement plotted on the vertical axis and the time plotted on the horizontal axis. And what we’ve been told is that this diagram is showing a transverse wave. In other words, if we imagine that we’ve got, say, a particle of some sort at this position which we will say is its equilibrium or resting position before the wave came along. Then the graph is telling us that at a time of zero seconds, the particle is displaced from its original position about 1.2 metres in the downward direction. And then as time progresses, we see how the displacement of this particle, say, changes over time. In other words, at a time of 0.5 seconds, we see that the particle is positioned here. At a time of one second, the particle is here, and so on and so forth.
Now, we’ve been asked to find the amplitude of the wave. So, to help answer this question, we can recall that the amplitude of a wave is defined as the maximum displacement of a medium undergoing oscillations as measured from the equilibrium position. Now, in this particular case, what we’re imagining is that the medium undergoing oscillations is this particle here. It doesn’t have to be a particle of course, but that’s how we’re imagining it. And the amplitude of this particle’s oscillations is simply the maximum displacement of this particle from its equilibrium position, which is where the particle would be if there were no wave. In other words, that corresponds to a displacement of zero metres.
So, if we can look along our graph, we can say that the equilibrium position is zero displacement for the particle. And to find the amplitude, we need to find the maximum displacement. In other words, what’s the furthest this supposed particle is displaced from its equilibrium position? And we can see that the largest possible displacement is this displacement here, in other words, when the particle is displaced this amount from its equilibrium position. And that particular displacement happens to have a value of 1.5 metres.
And note that the particle is displaced in both directions from its equilibrium position. In this case, we’re imagining that an upward displacement is positive and a downward displacement is negative. Meaning that a displacement down in this direction of 1.5 metres is the displacement of the same magnitude, but the opposite direction due to the negative sign. And so, we could use this measurement to find the amplitude of our wave also. We just need to be careful that an amplitude is given as a positive value because we only care about the magnitude or size of the maximum displacement when finding the amplitude.
And so, using either this value or this value, we can see that the magnitude or size of the maximum displacement of this wave is 1.5 metres.