Let's start with some simple concepts. Your source, whether it be a tape player, dvd, or a cd player has a maximum rated output voltage. That output is too weak to directly power a speaker, so in turn it's sent to an amplifer, which well... amplifies that signal and sends that along to your speaker.
What the "gain knob" does is matches the amplifier's input sensitivity to the maximum output of your source. Simply put, it prevents your headunit from overdriving your amplifier by telling your amp what is the max voltage/signal that it can expect from your headunit. At that point, your amp will achieve maximum power output without being overdriven into distortion/damage.
So if your headunit is capable of 4v, and you set the amp's gains to 4v then your amp will make max power when your headunit sends it a 4v signal. Sending it anything more than 4v will cause excess distortion and heat, since you're now exceeding the maximum power rating for your amp. On the other hand, setting the gains to 8v when you're headunit's max output is only 4v will cause your amp to never reach maximum power output.
Now, take a look at the following song:
This shows you the amplitude levels of the song over time. Notice that it fluctuates quite a bit, with some parts obviously much louder than others.
The ratio between the average level of the entire song and it's loudest point is called the "crest factor".
You can see that there's a problem here. If we were to set our amp's gain to the max output of our headunit, the only time our amplifier would be making it's max power output would be during those few, brief moments in the song when the amplitude is at it's peak. We can clearly see that for most portions of the song, the average amplitude is considerably lower than it's peak resulting in a large portion of our amp's power output being wasted. Remember that a doubling of power is equivalent to 3db of gain. Imagine that your typical song has a crest factor of 12db or more, and you can easily imagine the considerable waste of power if your gains were to be set in such a manner. For a 16w amp, you would only be outputting an average 1w... with volume set to max on your headunit.
So what can we do? Generally, I prefer to set my gains by ear. I set the gains at a lower output level than what my headunit is capable of producing, up until the point I can "hear" the amplifier distorting. At that point I back off a bit. Now the amplifier is still going to distort, but only on those very brief high amplitude peaks in the music. Everyone's ears are different. It's best to choose a song with a high crest factor to ensure the least amount of amplifier distortion with the widest range of music, and to let your ear be the judge of what distortion levels are audible to you. This way, you can be sure to utilize as much of our amp's power output as possible.
Also consider the practical fact that as you turn up the gains on your amp, you generally begin to pickup more hiss/noise. Having a more powerful amp will allow you to keep the gains down, and thus reduce noise.
Regardless, with music it's fairly obvious that your amp does not constantly output it's maximum continuous power output. Looking at the example song above, the amplitude fluctuates quite a bit. So when people claim their speakers are taking the full rated output of their amp's on a continuous basis, it's probably not true.
Also, bear in mind that we rarely use one speaker in our setups. We have mids, tweeters, and subs. Generally, the power output to tweeters and mids is fairly low. Those huge spikes you see in the music are bass tones. This is because our ears are less sensitive to bass frequencies, so when recording a low frequency and a higher frequency tone of the same spl, the low frequency tone is going to have much higher amplitude.
For anyone curious to get a more realistic measure of how much power is needed or used, I suggest using 0db sine waves to test your system. Hook up a voltmeter across the terminals of your tweeter or mid and play the sine wave. You'll be surprised to find how little power it takes to get your speaker extremely loud above 200hz. Usually a few watts at 1m on your typical tweeter at 3khz is enough to cause pain.
What the "gain knob" does is matches the amplifier's input sensitivity to the maximum output of your source. Simply put, it prevents your headunit from overdriving your amplifier by telling your amp what is the max voltage/signal that it can expect from your headunit. At that point, your amp will achieve maximum power output without being overdriven into distortion/damage.
So if your headunit is capable of 4v, and you set the amp's gains to 4v then your amp will make max power when your headunit sends it a 4v signal. Sending it anything more than 4v will cause excess distortion and heat, since you're now exceeding the maximum power rating for your amp. On the other hand, setting the gains to 8v when you're headunit's max output is only 4v will cause your amp to never reach maximum power output.
Now, take a look at the following song:

This shows you the amplitude levels of the song over time. Notice that it fluctuates quite a bit, with some parts obviously much louder than others.
The ratio between the average level of the entire song and it's loudest point is called the "crest factor".
You can see that there's a problem here. If we were to set our amp's gain to the max output of our headunit, the only time our amplifier would be making it's max power output would be during those few, brief moments in the song when the amplitude is at it's peak. We can clearly see that for most portions of the song, the average amplitude is considerably lower than it's peak resulting in a large portion of our amp's power output being wasted. Remember that a doubling of power is equivalent to 3db of gain. Imagine that your typical song has a crest factor of 12db or more, and you can easily imagine the considerable waste of power if your gains were to be set in such a manner. For a 16w amp, you would only be outputting an average 1w... with volume set to max on your headunit.
So what can we do? Generally, I prefer to set my gains by ear. I set the gains at a lower output level than what my headunit is capable of producing, up until the point I can "hear" the amplifier distorting. At that point I back off a bit. Now the amplifier is still going to distort, but only on those very brief high amplitude peaks in the music. Everyone's ears are different. It's best to choose a song with a high crest factor to ensure the least amount of amplifier distortion with the widest range of music, and to let your ear be the judge of what distortion levels are audible to you. This way, you can be sure to utilize as much of our amp's power output as possible.
Also consider the practical fact that as you turn up the gains on your amp, you generally begin to pickup more hiss/noise. Having a more powerful amp will allow you to keep the gains down, and thus reduce noise.
Regardless, with music it's fairly obvious that your amp does not constantly output it's maximum continuous power output. Looking at the example song above, the amplitude fluctuates quite a bit. So when people claim their speakers are taking the full rated output of their amp's on a continuous basis, it's probably not true.
Also, bear in mind that we rarely use one speaker in our setups. We have mids, tweeters, and subs. Generally, the power output to tweeters and mids is fairly low. Those huge spikes you see in the music are bass tones. This is because our ears are less sensitive to bass frequencies, so when recording a low frequency and a higher frequency tone of the same spl, the low frequency tone is going to have much higher amplitude.
For anyone curious to get a more realistic measure of how much power is needed or used, I suggest using 0db sine waves to test your system. Hook up a voltmeter across the terminals of your tweeter or mid and play the sine wave. You'll be surprised to find how little power it takes to get your speaker extremely loud above 200hz. Usually a few watts at 1m on your typical tweeter at 3khz is enough to cause pain.