I simulated and built a Class AB amplifier recently, which is powered straight from a +-20V lab power supply. When testing, I noticed that there was a dip in the amplifier's frequency response at around 15kHz.
After some research, I realized this was due to the resonant frequency of the PSU - PSU cable - power capacitor RLC circuit. If I model my 0.5m power cable as a 1uH inductor, and use my 100uF power caps in the equation:
$$f_r = \frac{1}{2\pi\sqrt{LC}}$$
I get a resonant frequency of 15.9kHz, which is mostly spot on. Simulations confirm (with variation of the capacitor value) that this resonance is what I am noticing.
How do professional audio amplifiers solve this problem? By making the power capacitors small, the resonant frequency is increased above the audio range, however there is bad distortion at the output. The capacitors can also be made really big to push this frequency below the audible range, however this requires a massive 100F capacitor for a resonant frequency of 15.9Hz. I don't believe audio amplifiers implement this.
For car amplifiers, pretty long (1m+) cables are run directly from the 12V battery of a car into the amplifier. How are these amplifiers designed to allow a variable length of power cables at their supply?