How do you find the amplitude of a point on a standing wave?

Question

For any standing wave, how do you find the amplitude at a given point?

Answer 1

Depends on the type of wave and what you are talking about.

First, if you are just talking mathmatics, the amplitude at the nodes is zero. You then find the ampltude between the two nodes and the amplitude of every other point can be determined as if it were a sine wave, i.e., x=Maxamp*sin (theta) where theta goes from 0 to pi as you travel from node to node.

If you need to manually determine it, use an Ocilliscope if you can. If not -- say it is a guitar string you are measuring -- make some sort of sensing devise to see how far up it vibrates. Or take a picture -- make sure the camera is steady and hold the appeture open for at least several vibration, and maybe put a graph beneath the vibrating string -- you'll see a blur on the photo which will also show you the max amplitude at all points. (Remember that the string is changing direction at the max amplitude which will mean it will spend more time there and give you a clearer picture).

Answer 2

With a well calibrated osilloscope!