Answer to Question #279497 in Physics for Anonymous005

Question

How does the fundamental frequency of a standing wave on a string vary with string length? What is an experiment I can do to prove a relation between the two. This is for an IB internal assessment topic I chose. Any equations I can use to model the relation as well?

Answer 1

The fundamental frequency is inversely proportional to the length L:

$$f=\frac{v}{2L}.$$

Alternatively, you can use this equation:

$$f=\frac12\sqrt{\frac{TL}{m}}.$$

The experiment: for the given tension (use a weight of a known mass) and mass of string, adjust the length and observe how the frequency changes.