What is the Relationship Between Intensity and Wattage?

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The relationship between intensity and wattage is logarithmic, with intensity being proportional to the square of the amplitude. To achieve a sound output that is twice as loud as a 20 W amplifier, a power of 80 W is required, while four times as loud would necessitate 320 W. This is based on the understanding that doubling the amplitude results in quadrupling the intensity. The discussion highlights the importance of decibels in measuring sound intensity. Understanding these relationships is crucial for selecting the appropriate amplifier power for desired sound levels.
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Homework Statement


OK, so this is a very basic question but i am uncertain what the relationship is. I know its logarithmic, but i don't know how to draw a conclusion. Here is the question:
If you want an amplifier which will give a sound output which is twice as lod as your present 20 W amplifier, what amplifier power should you buy? What if you wanted a sound output four times as loud?


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The Attempt at a Solution


I know that the relationship between Intensity and Wattage is logarithmic, but how do i draw a numeric conclusion?
 
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Are they looking for loudness or intensity?

The wattage of the amplifier is the maximum power it can supply to the signal.
The intensity a wave is the square of it's amplitude.
I suspect you are thinking of decibels.

If you double the amplitude, you get four times the intensity.
 
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