Question - by how many decibels is a 1000 watt amplifier louder than a 10 watt amplifier?
Potentially this could be a trick question. The answer could be 0 dB, meaning that they are both the same loudness. It would be the correct answer if they were both set to the same gain, within the range of the 10 watt amplifier to handle comfortably.
The answer could also be that the 10 watt amplifier could be louder. Indeed, if the 10 watt amplifier were set to a gain such that it had started to distort on peaks, and the 1000 watt amplifier were set the same gain where it obviously wouldn't distort, then the 10 watt amplifier would sound louder. Distortion makes a sound seem louder than it would be if measured by a meter.
But let's suppose that we feed the two amplifiers with the same signal and turn the gain of each up to the maximum that can be handled without distortion.
So the 1000 watt amplifier is sending out 1000 watts and the 10 watt amplifier is sending 10 watts. The question becomes by how many decibels is 1000 watts louder than 10 watts?
It's not so much the answer that is important. It's whether you have an instinctive feeling for these quantities.
To many people, particularly those who have no specialized knowledge of sound engineering, that 1000 watts must be shatteringly louder than 10 watts. But this is not necessarily so...
Play some music through your mixing console and set the output fader to -20 dB. Set the volume control of your amplifier so that the monitor level is quiet but still comfortably listenable as background.
Now raise the fader. Keep on raising it gradually until you reach 0 dB. Now you have the difference between 10 watts and 1000 watts. The 1000 watt amplifier is 20 dB louder.
It is plainly an obvious difference, but maybe not quite as much as you expected.
Getting a feeling for decibels is important in sound. Make it a habit always to observe the amount of dB you are changing by, each time you move a fader. Listen and learn.