In addition to the great information presented so far, allow me to borrow a little bit from the high speed digital world too.... The physical construction of the opamp ICs and digital logic ICs in the high speed logic world are not much different... Inside there are bond wires, usually thinner than a human hair. These bond wires are typically made of gold or aluminum and hook up the "silicon" chip from the "bonding pad" on the chip to the black plastic molded package pin/frame that ultimately gets soldered to the PCB...
Since these bond wires are skinny, they can be inductors when high current, especially at high frequency, is trying to be shoe-horned through the skinnyness.... This causes (in the high speed digital world) ground bounce, where the local "ground" potential on the IC chip bond pad will actually rise up (due to the inductance bucking the current feeding through it and increasing voltage at the bonding pad on the IC to compensate as an inductor would normally do). When the "ground" reference of the IC rises up, the logic thresholds go wonky and then a 1 is not a 1 and a 0 is not a 0, so the logic gate acts erratically and turns not into an AND gate or an OR gate, but into a MAYBE gate
Also keep in mind that since digital is "square waved" (except at really high freqs, it becomes rounded and more of a high freq analog problem) there is a lot of high frequency harmonics above the fundamental and the age-old debate of slew rate slowing down in FPGAs since you may not need all the harmonics (and power to maintain the harmonics) to represent a 1 or 0 on a receiving chip..
Capacitance, as mentioned previously is the "inverse" impedance of inductance and they can cancel each other out yielding a purely resistive load, in this case to the power supplies with a decoupling scheme. This can be seen in a Smith Chart (a conformal mapping of impedances from the complex plane) as used for RF circuit design, but I submit that it can be used for audio too... Power Utility companies do the exact same thing too, where a large industrial factory with lots of industrial sized (inductive load) motors will have banks of capacitors outside the factory that the utility company can switch in and out (remotely) to keep the power factor on the utility grid near 1.0 (purely resistive).
Another borrowed concept from the high speed digital realm is that the return current (up at higher frequencies) likes to take the path of least INDUCTANCE... This means that the return current likes to flow mostly under the sourcing current copper trace even if the return current has an entire ground plane to flow through... The main issue is that most ground planes may broken up where there is a gap where the source current copper trace goes over a split plane due to some component having to make the ground plane be split or else there would be a design rule violation in the manufacturing of the PCB house's manufacturing capabilities.... Some tricks include "stitching" capacitors across the two splits to compensate for the increase in inductance with the split plane (decoupling the inductance from the circuit)...
So in addition to the stray impedances (inductive or resistive) on the sourcing traces on the circuit board, there are also funny things that can happen at higher frequencies inside the IC.... Can you guarantee that RF won't get into the IC if no decoupling is used (or a particular style of decoupling is used over a different style of decoupling)? The op-amp could have some high out of band frequencies near the audio band that could be just heating up the output transistors, causing them to draw more current and bounce the rails a little bit? Of course it is always good to limit the bandwidth perhaps of the op-amp with a parallel capacitor in the FB, and the decoupling capacitors can do the rest...
Another thought, it just came to me (I dunno if this is true and maybe someone may care to correct me if I am wrong) is that PSRR may not be useful (or reduced) when swinging the outputs near the rails since the output transistors are "wide open throttle" (WOT?) so it is all up to the decoupling caps at that point (and perhaps the feedback?)... I have obsessed previously over linear voltage regulation and they are typically not able to quiet down noise for the standard LM317s and the like throughout the entire audio band getting into the AM radio band.... for another A/D D/A design I have on the drawing board I have been trying to keep the power quiet so that it does not modulate into the A/Ds PSRR etc.... The typical voltage regs are great at quieting line frequencies and some of their harmonics though for a linear (non-switching) supply...
The good news is that if making a PCB, it is easy enough put footprints of capacitors everywhere in the various decoupling schemes and not stuff them onto the board if it does call for it...
Sorry for the tome
Cheers,
-chris
