Draw the history graph D(x = 4.0 m, t) at x = 4.0 m for the wave shown in FIGURE EX16.4.

Question

Snapshot graph showing displacement vs. position at t=0s for a wave in fluid mechanics.

Accepted Answer

Welcome back everyone. We are given this below graph of a wave at time equal to zero seconds here. And we are tasked with making the displacement versus time graph at the position of 16 m. So first let me set up a graph here. Our displacement versus time graph, we'll need a positive and negative vertical axis as well as a horizontal axis too. So our vertical axis is going to be displacement and then our horizontal axis will be time here. Now, I'm just gonna label this and our unit for time is going to be second. So let's take an observation at our shot here. We can see that at position 16 here, the wave has not arrived yet. There is no displacement, the wave or the front edge of the wave is currently at a position of eight m. So the remaining travel time is going to be 16 m minus eight m, which gives us eight m. Now, we are told that the velocity of the wave is four m per second. From this, we can figure out how much time it will take for the wave to reach our position here, we have eight m divided by four m per second. What this gives us is that it will take two seconds for the wave to arrive. Now, what will happen at two seconds? Well, as you see from the front edge hitting our position, the wave goes upwards. So our, our wave is going to make an upward displacement here, which I will signify by this arrow. Now, as you can see by looking at the initial intervals of our wave, this period right here is 0.5 seconds. So at 2.5 seconds, we will reach a maximum of our wave. And at another 0.5 seconds later, a K a total of three seconds, we will start making our downward displacement, adding another 0.5 seconds to that. At 3.5 seconds, we will reach a minimum and at four seconds, we will then go back to zero. So what we can do then is we can trace this exact behavior on our displacement versus time graph. So nothing will happen until we reach two seconds and then it will go up and at 2.5, it'll be maximum. So then it will start going down at 3.5, there will be a minimum, then it will go back up to four and it will just ride out as the wave passes our position here. Wonderful. So this is what our wave should look like. Let's scroll down to see our answer. Choices and as you can see what we have described is exactly what is reflected in answer choice. A thank you all so much for watching. I hope this video helped. We will see you all in the next one.

Draw the history graph D(x = 4.0 m, t) at x = 4.0 m for the wave shown in FIGURE EX16.4.

Verified Solution

Key Concepts

Wave Properties

History Graphs

Snapshot vs. History Graphs