An audio amplifier is a voltage gain device. The output voltage is a multiple of the input voltage, regardless of input frequency. 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.

Regardless of speaker impedance the amplifier output stage is rated at a certain 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). The output current at a given frequency depends on the magnitude of the speaker impedance at that frequency. For a typical dynamic loudspeaker system the magnitude of impedance varies wildly by frequency.

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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.