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History of the Wave Equation

  • Thread starter Musa Ali
  • Start date
  • #1
3
0
Hi,

We were recently testing out waves on a string and completing a lab based on it, and I wanted to provide background information on how the equation v=fλ was formulated. I would greatly appreciate it if someone could direct me to a source on it.

Thanks.
 

Answers and Replies

  • #2
259
2
Let me first tell you that in general the equation you wrote down isn't called the wave equation. The wave equation looks like ##c^{2}\nabla^{2} f = \frac{\partial^{2} f }{\partial t^{2}}##. Anyway the equation you talk about doesn't really have such a history as you might think - it's very easy to reason. The velocity of something is given by ##v=\frac{\Delta x}{\Delta t}## right? Well let's consider the ##\lambda=\Delta x##, what is the corresponding time? It's just what we define to be the period ##T## of the wave, namely, how much times it takes for one wavelength to pass. And so we have ##v=\frac{\lambda}{T}##. The fraction ##\frac{1}{T}## corresponds to the frequency ##f## and so we arrive at ##v=\lambda f##
 

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