Basic Waves Question, but can't visualize.

[Beeza]

Alright, I'm stuck working with the "Engineering for Engineers and Scientists" workbooks, and the textbook, from what I understand, doesn't explain the concept behind waves very well.

I know that a longitudinal wave has "particle" displacement in the direction of wave propagation. Is the displacement of every particle in the wave equal? For instance, a particle near the "outer" end of the wave is displaced by a maxiumum of 2cm from its equillibrium position, while at that same instance of time, the particles in the middle of the wave are under compression. At a later point in time (when the particles originally being compressed are no longer being compressed), do those particles that were being compressed earlier also have a displacement of 2cm from their equillibrium position?

I'm trying to picture a slinky in my mind, but I always have trouble with these conceptual questions and typically find the math easier to work with

 

[nrqed]

Alright, I'm stuck working with the "Engineering for Engineers and Scientists" workbooks, and the textbook, from what I understand, doesn't explain the concept behind waves very well.

I know that a longitudinal wave has "particle" displacement in the direction of wave propagation. Is the displacement of every particle in the wave equal? For instance, a particle near the "outer" end of the wave is displaced by a maxiumum of 2cm from its equillibrium position, while at that same instance of time, the particles in the middle of the wave are under compression. At a later point in time (when the particles originally being compressed are no longer being compressed), do those particles that were being compressed earlier also have a displacement of 2cm from their equillibrium position?

I'm trying to picture a slinky in my mind, but I always have trouble with these conceptual questions and typically find the math easier to work with

It's tough to explain without pictures to show you! When I teach this, I show computer animations to my students. Without that, it's almost impossible to explain clearly.

If you look at each particle as a function of time, it will oscillate back and forth from -A to +A (as measured from its equilibrium position)

If you take a snapshot at a given time, there will be particles which are the farthest to the left from their equilibrium position (all are at -A as measured from their equilibrium position). All those particles are at the same value of x at that time (I am imagining a wave moving along x, let's say in a gas, so there are many particles all at any given value of x). Now, the particles a bit to the left of those first particles are at a bit more than -A (say $-A + \delta$ as measured from *their* equilibirum position). And so on as we move along the wave.

One key point: the displacement is always measured with respect to the equilibrium position of a particle. In the case of a longitudinal wave, the equilibrium position varies from particle to the next (as we move along the x axis).

So at any given time, there are particles which are at all possible displacement from their own equilibirum positions, displacements ranging from -A to +A.

Now, be careful when you think about pressure (region of compression, etc). At any given time, the zone of highest pressure correspond to points where the particles have zero displacement (they are at their equilibrium position). The same is true for zones of lowest pressure. They correspond to particles which are at their equilibrium position.

It's hard to explain. Feel free to keep asking!

 

[Beeza]

Thank You! I understand it now, but it's still hard to picture in my head. I can't really follow it until I look at the graphs and see the sinusoidal waves moving between +A and -A.

I originally thought of it as you explained, but then my intuition and trying to picture a slinky oscillating started to lead me to believe differently.
This workbook is beating me to death with snapshot and history graphs of waves and predicting one graph from looking at the other.

 

[arildno]

To gain a useful picture of a longitudinal wave, consider the propagation of a 1-D density disturbance:

At a particular moment, the particles in one region will be more compressed than they are in the equilibrium state, whereas in an adjoining region, the particles will be more sparsely distributed.

 

[EnergyHobo]

Transverse waves look exactly like a graph of the sine trig function. You can visualize this by taking a long rope on the ground and flip it back and forth (like a snake).

Longitudinal waves is exactly like the slinky. Each point is pushing the next point so-to-speak. Sound waves are like this.

Hope this helps.

 

[PeterO]

Alright, I'm stuck working with the "Engineering for Engineers and Scientists" workbooks, and the textbook, from what I understand, doesn't explain the concept behind waves very well.

I know that a longitudinal wave has "particle" displacement in the direction of wave propagation. Is the displacement of every particle in the wave equal? For instance, a particle near the "outer" end of the wave is displaced by a maxiumum of 2cm from its equillibrium position, while at that same instance of time, the particles in the middle of the wave are under compression. At a later point in time (when the particles originally being compressed are no longer being compressed), do those particles that were being compressed earlier also have a displacement of 2cm from their equillibrium position?

I'm trying to picture a slinky in my mind, but I always have trouble with these conceptual questions and typically find the math easier to work with

Have a look at the animations on this page. [link below]

Once you are viewing, concentrate on a single dot in the animation.

the maximum displacement of the particles is the same, but the particlces do not all have maximum displacement at the same time.

You can see the way particles go in a transverse wave as well, as well as a couple of other complicated waves.


http://www.kettering.edu/physics/drussell/Demos/waves/wavemotion.html