OK, well, in response to this little arguement, I've broken out my Year 12 Physics textbook from last year and there seems to be some confusion among you guys regarding the difference between sound intensity and sound level. The reson for this is that human hearing percieves sounds in a way that is rather mathematically odd, with an increase of ten times the intensity resulting in an increase in the sound
level (percieved by the human ear) of 10 decibels, meaning a human doesn't hear the sound as being 10 times louder, even though it it is ten times more
intense, which is due to the manner in which the human ear operates.
What is true, however, is that if you double the distance to the source of the sound, you quarter the intensity, rather than halving it (as it is indeed given by I = 1/r
2). A doubling of sound intesnity will increase the sound
level (in decibels) by about 3 dB, so if you double the distance (and thus quarter the intensity), the sound level will decrease by 6 dB... What the book doesn't seem to say, however, is how much quiter a decrease of 6 dB sounds to the human ear, though according to this website...
http://www.gcaudio.com/resources/howtos/loudness.html...we percieve an increase of 10 dB (meaning an increase of ten times the intensity) as being roughly twice as loud and a 20 dB increase as four times as loud...
The bottom line here is that, laptop and thomas, neither of you is exactly right.
Laptop, it is indeed neccessary to put in ten times the power (as intensity is given by Watts per square metre) to make a sound the human ear will percieve as being ten times louder, but doubling the distance to the source of a sound
will not make it sound twice as quiet (as the sound level will decrease by 6 dB every time the distance doubles, not 10), 'nor will doubling the distance halve the intensity (it will quarter it).
Thomas, your statement is correct with respect to sound
intensity (how much actual power-per-unit-area there is), but as far as the human ear is concerned, standing 2 metres away from the source of the sound will
not cause it to sound four times as loud than if you were standing 4 metres away (even though the intensity has indeed increased by 4 times, as you need the intensity to increase by 10 times to raise the level by 10 dB and thus make it sound twice as loud).
I hope that helps clear things up... I also hope I haven't gotten anything wrong here... :-/