An audio amplifier is a voltage gain device. The output voltage is a multiple of the input voltage, regardless of input frequency UNLESS THE LOAD DRAWS SO MUCH CURRENT THAT THE AMPLIFIER'S VOLTAGE DROP UNDER SUCH MOMENTARY OVERLOADS. Power 'P' delivered to the load is P=V²/R where 'V' is the instantaneous amplifier output voltage and 'R' is the magnitude of the speaker impedance (which varies with frequency). A Volume control sets the gain of the system. THIS IS TOO ESOTERIC TO CONSIDER, BUT IT'S TRUE: ACTUALLY, ANY SUCH SYSTEM IS COMPOSED OF GAIN BLOCKS OF FIXED GAIN, AND THE VOLUME CONTROL(S) ATTENUATE(S) THE OUTPUT(S) OF INDIVIDUAL SECTIONS.

Regardless of speaker impedance the amplifier output stage is rated at a certain MAXIMUM current.

Over the operating range of the amplifier all input frequencies at a given level will result in the same output voltage from the amplifier (commonly called "flat" response) UP TO THE POINT OF OVERLOAD. The output current at a given frequency depends on the magnitude of the speaker impedance at that frequency AND THE AMPLIFIER'S ABILITY TO SUPPLY THE CURRENT DEMANDED BY THE LOAD. For a typical dynamic loudspeaker system the magnitude of impedance varies wildly by frequency.

I'm not sure if I like this analogy, but here goes:

The accelerator of a motor vehicle adjusts power delivered to the wheels. One would use a different setting on level, up hill, or down hill roads in order to maintain a constant speed.

In our audio power amplifier, delivering 100W to a bass driver would probably be satisfying, depending on efficiency and acoustics. In most situations, delivering 100W into a tweeter driver at high frequencies would result in tweeter destruction and potential glass shattering.