Amplitude and wavelength of longitudinal wave

[songoku]

Homework Statement

A wave is shown below. The dots represent the particles of the wave at a time t = 0 s, and the vertical lines represent the positions of the particles before the wave arrives. Find the amplitude and wavelength of the wave

Homework Equations

Not sure

The Attempt at a Solution

1. The vertical line is wavefront??
2. To find wavelength, I tried to find the distance between the center of adjacent compression (although I am not sure which one). Is the answer 24 m?
3. To find amplitude, I tried to find the distance between the end of first compression and the start of next compression. Is this method correct? I am also not sure which one is the distance. Is the answer 12 m?

Thanks

 

[scottdave]

Look at the points where the particle did not move at all (the dot is on the line). This is where the "sine wave" crosses zero. The distance between adjacent crossings is half a wavelength. Next, look and figure the maximum distance a particle gets displaced from its rest position.

 

[haruspex]

The vertical line is wavefront??

No. In case you have not figured it out from scott's answer, you are told the vertical lines are where the particles were before the wave came along. Therefore these are the rest positions. Each particle oscillates with some magnitude about its rest position.

You could draw it as a transverse wave if it makes it clearer. At each vertical line, find the dot that belongs to it. Imagine the dot being connected to its line, and hinged there, by a rigid horizontal rod. Rotate the rod anticlockwise 90 degrees so that the dot is now on its line. This converts the horizontal displacements of the longitudinal wave into vertical displacements, making a transverse wave.

 

[scottdave]

...You could draw it as a transverse wave if it makes it clearer. At each vertical line, find the dot that belongs to it. Imagine the dot being connected to its line, and hinged there, by a rigid horizontal rod. Rotate the rod anticlockwise 90 degrees so that the dot is now on its line. This converts the horizontal displacements of the longitudinal wave into vertical displacements, making a transverse wave.

Nice @haruspex pivoting the little rods to visualize the amplitude.

 

[songoku]

Look at the points where the particle did not move at all (the dot is on the line). This is where the "sine wave" crosses zero. The distance between adjacent crossings is half a wavelength. Next, look and figure the maximum distance a particle gets displaced from its rest position.

No. In case you have not figured it out from scott's answer, you are told the vertical lines are where the particles were before the wave came along. Therefore these are the rest positions. Each particle oscillates with some magnitude about its rest position.

You could draw it as a transverse wave if it makes it clearer. At each vertical line, find the dot that belongs to it. Imagine the dot being connected to its line, and hinged there, by a rigid horizontal rod. Rotate the rod anticlockwise 90 degrees so that the dot is now on its line. This converts the horizontal displacements of the longitudinal wave into vertical displacements, making a transverse wave.

I take the leftmost dot to find the maximum distance that a dot gets displaced. So I need to literally measure the distance between leftmost dot and leftmost vertical line using ruler and compared it to the scale of distance between two vertical lines?

 

[haruspex]

I take the leftmost dot to find the maximum distance that a dot gets displaced. So I need to literally measure the distance between leftmost dot and leftmost vertical line using ruler and compared it to the scale of distance between two vertical lines?

Yes. The drawing is rather rough - the vertical lines get closer together on the right - so I don't think much accuracy is required. You could just judge it by eye.

 

[songoku]

Thank you very much for the help haruspex and scottdave

 

[scottdave]

You are welcome. Like @haruspex said, this will be an approximation of the amplitude, so you probably should state that in your answer.
Something that I thought odd about the question: the lines represent the initial position, but then the displaced dots were at time t=0. Most people would expect that t=0 is the initial position, and that probably led to some confusion.

 

[songoku]

You are welcome. Like @haruspex said, this will be an approximation of the amplitude, so you probably should state that in your answer.
Something that I thought odd about the question: the lines represent the initial position, but then the displaced dots were at time t=0. Most people would expect that t=0 is the initial position, and that probably led to some confusion.

If the question asks to draw the positions of particles at time T/2, what will it be?

Let give numbers to the dots and vertical lines. Starting from the leftmost dot and line, the number will be dot 1, dot 2, etc and also line 1, line 2, etc. Dot 1 will be on line 1 at t = 0.

So, after T/2, dot 1 will be on the left side of line 1 by the same amount of horizontal distance? Dot 2 also will be on the left of line 2 by the same amount of horizontal distance as before? Dot 4 will stay at its place (still on line 4)?

 

[haruspex]

If the question asks to draw the positions of particles at time T/2, what will it be?

Let give numbers to the dots and vertical lines. Starting from the leftmost dot and line, the number will be dot 1, dot 2, etc and also line 1, line 2, etc. Dot 1 will be on line 1 at t = 0.

So, after T/2, dot 1 will be on the left side of line 1 by the same amount of horizontal distance? Dot 2 also will be on the left of line 2 by the same amount of horizontal distance as before? Dot 4 will stay at its place (still on line 4)?

That all sounds right.

 

[songoku]

Thank you very much