# How come Einstein's mass-energy relationship is basically apparent in the string wave equation?

My physics teacher claimed to derive $E=mc^2$ by manipulating the equation for the speed of a standing wave on a string. A commonly known fact about the string wave equation is that speed can be calculated by $c^2=\frac{T}{\mu}$ where $\mu$ is the mass per unit length of the string. "Since Fds is energy we can work out $E = mc^2$". I feel like this is cheating. In fact, I know this is cheating but still, why does it work so well in terms of the units for energy? Isn't this just a funny coincidence?

• – AccidentalFourierTransform Feb 10 '17 at 14:16
• These aren't really related. We already know that kinetic energy is generically quadratic in velocity, just by dimensional analysis. But $E = mc^2$ says there's an extra contribution to the energy even when objects aren't moving at all! – knzhou Feb 10 '17 at 16:36

• @rpfphysics I'm not sure I understand what coincidence you're talking about. If you're relating mass to energy then you need to multiply by a speed squared to make the units work. Another example would be the expression for kinetic energy: you have energy on one side and mass on the other, and you're multiplying the mass by a speed squared ($v^2/2$). – Jold Feb 10 '17 at 17:20