Recent content by Rumo

Homework Statement \rho_0, c_0 is the mean density, the mean speed of sound in the ideal gas. Is the following correct? c(\rho)=c_0\left(\frac{\rho}{\rho_0}\right)^{\frac{\kappa-1}{2}} Homework Equations p = const * \rho^\kappa, c=\sqrt{\frac{\partial p}{\partial \rho}} The Attempt at...

But in this case, it is not a coordinate transformation! It is a moving spherical standing wave. I still use the same coordinates to differentiate. x, y, z, t. not x, y, z', t'!

Thanks for your reply! Isn't the lorentz transformation transforming the spatial and time coordinates? Hence, I would use the chain rule to show the invariance. The Φ would not be important at all, just a solution to the wave equation. It would describe how Φ would look like from the point of...

I calculated this with Mathematica. I would have uploaded the notebook, but I can't. Hence I made a screenshot. You can calculate this easily with any program of your choice. Just replace c with w/k.

This thread is not about the lorentz invariance of the wave equation: \frac{1}{c^2}\frac{\partial^2\Phi}{\partial t^2}-\Delta \Phi = 0 It is about an interesting feature of a standing spherical wave: A\frac{\sin(kr)}{r}\cos(wt) It still solves the wave equation above, when it is boosted in...