Do I need 10 gauge power cord if I have 10 gauge from panel?

I suspect the next trick in the evolution of the power cable argument is to cryogenically cool the cables, so they become superconducting. This should separate the physicists from the crowd. Not practical you say? Then the next best thing is to direct wire the power feed to the amps power switch to eliminate any resistance inherent in having a receptacle. Once your amp is open you may observe what gauge wire the factory thought was justified by their engineering staff. I'd be surprised if it was more than 14-gauge wire. 12 gauge would be overkill. Since the concern is really power density, rather than thinking in terms of resistance of the circuit, I would think it would be more appropriate to think in terms of conductance. Since I'm old school the units would be Mhos. Current teaching is Siemans as units. 

Let’s see  115v or 120v times

15 amps is 1725 to 1800 watts 

your wall outlet voltage might have some

wiggle room 

so yea you need a bigger cable to maximize your audio system 

Eventually frequency is impacted by gauge but not always in a good way.  I would be more concerned with downstream electronics not being able to blow a huge breaker when in distress.  Unless it is some one off like that monster Amp pictured I would not exceed 12 gauge 20 amp service for stereo gear.  For the huge 30 AMP monster AMP I would run dedicated circuit with dedicated breaker.  It already has a 30 AMP NEMA plug to prevent plugging into a standard 110 outlet.

It seems unlikely. Component power supplies are usually built with capacitors lage enough to store power beyond their staedy state demands, and supply power for transients much closer to the output devices than the power cord is.

When your why do people always think the power cord is the last 6 feet? If your amp draws the current wouldn't it technically be the first 6 feet? After all if your amp is plugged in and not powered on how much current is on the 15 or 20 amp circuit?