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Suppose the above two graphs describe a wave, then I've a couple of conceptual questions that I don't fully understand.

1) Is there an analogy that I can use to imagine the graphs?

For GRAPH 1 I generally think about the Simple harmonic motion, A bob oscillating up and down along the y-axis and if we keep on rolling a sheet of paper in the direction of the x-axis we will end up getting GRAPH 1, but what about GRAPH 2?

2) What are the maximum variables that can be inferred from both the graphs? By variables, I mean, quantities such as wavelength, wave velocity, frequency etc.

I know that the amplitude on both the graphs is the same (why?). From GRAPH 1 we can get the frequency, time period and the wavelength, and, therefore, the wave velocity. Does GRAPH 2 allow us to calculate anything else apart from amplitude?

3) By looking at both the graphs, can we claim that the wave is transverse or longitudinal and if so then why?

Frankly, as I mentioned earlier, I can't fully visualize the second graph and so, I don't have an answer to this question. Please help

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1 Answer 1

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First, I'm going to assume that above the first graph is a caption that goes something like "the variation with time $t$ of the displacement $y$ of the string at $x=0$". That's the only way it really makes sense.

1) If you think of simple harmonic motion for the first graph, you will get the right picture but I don't follow the rolling paper because you want the bob to be stationary in the x-direction. Since it just moves up and down over time, the graph shows its displacement from equilibrium $y=0$.

For graph 2, it should be even easier. Think of plucking a string - you get an image like shown in the graph 2, but moving all over the place. Now take a picture of the string (at $t=0$), and you will get exactly the graph 2 shown.

2) The frequency is related to the time, so the top graph will tell you the frequency (looks like $T=0.25$ ms so $f=4$ MHz). You cannot find the wavelength unless you know the speed of the wave (using $\lambda=v/f$). But graph two is a physical representation of the wave as a function of distance, so peak-to-peak will give you the wavelength. It looks like $\lambda=3$ cm to me.

The amplitude is the same because you are graphing the displacement of a single wave. Regardless of if you at constant $x$, changing time $t$ (graph 1) or constant $t$, changing $x$ (graph 2), the maximum displacement of the wave will be the same.

3) transverse and longitudinal refer to the displacement of the wave relative to the direction of motion. From the second graph it's clear that this wave is moving along the positive $x$ direction. The displacement is at right angles to that (in the $y$ direction), so this wave is transverse. A longitudinal wave vibrates in the same direction it moves, like a sound wave.

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