PHY7C FNT2 - The end of FNT#1 and FNT#2 The end of FNT#1...

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The end of FNT #1 and FNT #2 August 14, 2005 The end of FNT #1 Question 8 a) How fast is the wave travelling? Which way is it going? These are both snapshots of the wave, and it is impossible to say for sure which way it is moving or how fast it is going. To see why, let us try and ask what happens to one of the peaks in the first graph: -0.1 -0.05 0 0.05 0.1 0 1 2 3 x [m] y(x) at t=0 sec [m] -0.1 -0.05 0 0.05 0.1 0 1 2 3 x [m] y(x) at t=1.0 sec [m] Where does this peak go at 1 second? Well, we cannot tell as all the peak s look exactly the same! Let us pick one peak at t = 0 seconds -0.1 -0.05 0 0.05 0.1 0 1 2 3 x [m] y(x) at t=0 sec [m] Peak Which peak is it in the t = 1 second picture? -0.1 -0.05 0 0.05 0.1 0 1 2 3 x [m] y(x) at t = 1 sec [m] Peak? The answer is that we cannot know, as all the peaks look the same. 1
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I working out this solution, I will present three different solutions 1. A solution based on choosing the closest peak 2. A solution based on choosing a different peak 3. Showing all the possible solutions If you were asked this on a quiz, the best idea is to pick a peak. Usually the closest peak is a good choice (as it leads to the smallest velocity). So I would suggest most people follow solution 1. Solution 1: Choose the closest peak We choose the closest peak for the reason that the wave has not gone very far in a small time (1 second). If I chose peaks further away the water peak would have moved further and the velocity would be bigger. We shall see at the end that the velocity that we get from this choice is “reasonable”. With this in mind, let us write down what we need to solve the problem Time Location of Peak t = 0 s 1.8 m t = 1 s 1.6 m As time gets later, this peak has moved to a smaller value of x . So the wave
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