Standing Wave Frequencies in Wire & Pipe: Similarities & Differences

[PremedBeauty]

-Look up or derive the frequencies of the standing waves of a length of wire, L, clamped at the ends and under tension.
-What are the similarities and differences between a vibrating string and a resonating pipe?
-Does the diameter of the wire matter?
-Does the diameter of the pipe matter?

-first question, I don't know how to derive it.
-The pipe is hollow and the forces acting upon it will be different because the inside is space. The forces will need to overcome the structural strength of the tube.The wire is a solid cylinder. Thus the vibration can travel throughout easier.
-The diameters will make a difference dependent upon the force of the vibration,The diameter of the string also affects the frequency of the string. A thicker diameter vibrates slower, causing the pinch in the string to travel slower. This results in fewer cycles per second, which is a lower frequency so yes.
-I'm thinking the similar answer goes to the pipe as well.

please check these answers.

 

[berkeman]

Moved from Advanced Physics to Intro Physics.

I believe that for the pipe, they are talking about resonance of air standing waves in the pipe, not the pipe bending and resonating itself like a wire does.

And as for the equation that describes waves on a string or wire, you can find that at wikipedia.org or most Intro Physics books under simple harmonic motion (SHM).