The sound of bad filter caps - hum and ghost notes.
A lot of amps, both tube and solid state, will experience failure in electrolytic caps, particularly ones made during the "Capacitor plague" era of the early 2000s. When they fail, they can no longer smooth out the source power, so the rectifier hum of 100 or 120 Hz comes through the speaker. This differs from the low 50 or 60 cycle hum from filament grounding problems or the higher frequency sounds of line noise. Additionally, you may hear "Ghost notes" or intermodulation distortion combining the notes you are playing with the hum and creating additional tones that sound harsh and dissonant. This is what to listen for.
One thing I forgot to mention in the video is that you may experience "Motorboating" which is where your amp will just sound like a low speed diesel engine very loudly (at full volume essentially.) This is caused by gain stages feeding back into each other with the phase shifted by coupling caps. This will generally be caused by cap failures that are between stages, not the ones right off the rectifier like this video shows.