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More Ways to Use This Stuff

Here's the formula for computing decibel levels:

dB = 10 log( I / 10^( -12 ) ) ... the dB is decibels ... the 10^( -12 ) is the intensity of the softest sound a healthy human ear can detect ... the I is the intensity of the sound

* intensity is measured in
       watts / meter^( 2 )

Here's an example:

You're at a rock concert and you  measure the sound intensity at
100 w / m^( 2 ) .  Do you need ear plugs?

       Well, the threshold of pain is about 130-135 dB...

dB = 10 log( 100 / 10^( -12 ) )

       Put that calculator down!  We can do this by hand...

= 10 log( 10^( 2 ) / 10( -12 ) ) = 10 log 10^( 2 - ( -12 ) ) ... =10 log( 10^( 14 ) ) = 10 log to the base 10( 10^( 14 ) ) ... the log to the base 10 and the 10 cancel out ... = 10 * 14 = 140 dB

Grab some earplugs!

YOUR TURN:  (no calculator!)

You measure the intensity of a sound to be 10,000
w / m^( 2 ) .  What's the intensity in decibels?