What Are Longitudinal Standing Waves and How Do They Work?

[hidemi]

Homework Statement

How to know the answer is E?
Thanks!

Relevant Equations

None

 

[berkeman]

Welcome to PF.

What are your thoughts? Think of a transverse standing wave first -- what does the string or water look like one quarter period after the peaks are the highest?

 

[hidemi]

Welcome to PF.

What are your thoughts? Think of a transverse standing wave first -- what does the string or water look like one quarter period after the peaks are the highest?

Hi Berkeman,
The water is the longitudinal wave, while the string travel is the traverse wave.
That's all I know, how can I continue and match the option E above?

 

[rsk]

Assume that the starting picture shows the particles at their maximum displacement. Now picture the sin/cosine graph and move on one quarter cycle from that maximum. Where are they now?

 

[Steve4Physics]

Homework Statement:: How to know the answer is E?
Thanks!
Relevant Equations:: None

View attachment 277358

The best approach (in my opinion) is to have a mental image and conceptual understanding of what is happening in a standing wave.

Note: In the video below, if you click the ‘cog-wheel’ at the bottom of the YouTube screen, you can set the playback speed to slow, so it’s easier to follow what’s going on.

Start with a transverse standing wave - watch an animation carefully, e.g.

If you’ve ‘got it’, you should be able to say what the shapes are at the start, after ¼ of a cycle, after ½ a cycle, after ¾ of a cycle and after a full cycle.

EDIT 3: When you're happy with transverse standing waves, do the same for longitudinal ones. Here is a suitable animation:
You might be able to find better ones.

 

[robphy]

Here's another set of visualizations:
http://physics.bu.edu/~duffy/HTML5/transverse_standing_wave.html
http://physics.bu.edu/~duffy/HTML5/longitudinal_standing_wave.html

 

[hidemi]

Thanks all of you!
I finally understand :)