Solid-state relay boards: Can they be used to switch audio signals?
A solid-state relay seems to be the totally wrong tool for the job. The image you posted shows it is intended to switch 240V AC. So it is designed to switch something like a 240V light on and off.

Relays in general are things designed to connect one thing to another (eg. power to a light). They just aren't designed to switch audio signals.


  I need to multiplex some audio signals in a mixer board, and I was already planning on using those solid-state relays before I learned all this


The expression "when the only tool you have is a hammer, everything looks like a nail" springs to mind.

There are chips designed to multiplex analog signals (as I describe on this page). That would be closer to what you need.

However that chip (the 74HC4067) is a "choose one input from many" sort of design. It isn't going to let you fade one audio signal in or out (neither would the relay for that matter).