Exploring Standing Wave Speed: Understanding the Concept and Formula in Physics

[ahaanomegas]

My Friend and I were discussing standing waves and I made problem about speed, inspired off a concept taught in my Physics book: $v = \sqrt {\frac {F_T}{m/L}}$. My Friend asked a very valid question: "How in the whole can you defined speed of a standing wave when it's not changing position?" - He understands the formula but not what velocity in a standing wave means. And he stumped me on it. I couldn't find an answer to that question.

Can you?

 

[AlephZero]

You can think of a standing wave as the superposition of two traveling waves moving in opposite directions.

For example $\cos(x - vt)$ and $\cos (x + vt)$ are two traveling waves, and their sum is $\cos(x - vt) + \cos(x + vt) = 2\cos x \cos(vt)$ which is a standiing wave.