Question Video: Understanding Transverse and Longitudinal Waves Physics

Video Transcript

A transverse wave is shown in the diagram. What is the amplitude of the wave?

To begin, we should recall that the amplitude of a wave is defined as the maximum displacement of the oscillating medium that the wave travels in. This oscillation is shown in the diagram. It’s a graph of displacement as a function of time. Notice the sinusoidal shape that’s indicative of transverse waves. The oscillations are centered around the horizontal axis of the graph. So a displacement of zero marks the wave’s equilibrium position. This is the baseline for measuring the displacement of the wave.

In this question, we want to find its maximum displacement or amplitude, which the medium reaches every time there’s a crest or trough in the waveform. We can see that there’s an equal amount of displacement in the positive and negative directions. But for easier reading on the vertical axis, let’s just focus on this first crest here. We know that it occurs at a time of one second. And to find the displacement at this moment, we trace the height of the crest directly over to the vertical axis.

Using this dashed horizontal line to help us take the proper reading from the scale, we can see that the crest is two of these small gray marks above 1.5 meters. Notice that five of these small gray marks occur over a range of 0.5 meters. Therefore, each of these small gray marks represents a tenth of a meter. This means that the amplitude of the wave spans one and a half meters plus two-tenths of a meter for a total of 1.7 meters. Thus, the amplitude of the transverse wave shown in the diagram is 1.7 meters.