Measuring Wave Speed: Reference Frame Considerations

[Pushoam]

In the wave equation$\frac {\partial^2 \psi} {\partial x^2}=\frac{1}{v^2}\frac{\partial^2 \psi}{\partial t^2}\tag{1}$, v is the speed of the wave propagation.
With respect to which reference frame is this speed measured( in general)?

 

[jedishrfu]

What is the context of your question, classical physics, relativity or quantum mechanics?

 

[Pushoam]

classical physics and relativity

 

[jedishrfu]

What do you think v represents for each one then?

 

[Pushoam]

What do you think v represents for each one then?

v represents speed of the wave propagation.
For example, if we take wave on a string, then the speed is measured from the lab frame.
But how do we know that the speed should be measured from the lab frame( just by knowing the wave equation)?
And why can't we decide the reference frame in case of electromagnetic waves?