Sound and Music - Mission SM3 Detailed Help

If sound A is two times as intense as sound B, then sound A ____ sound B.


 
Every sound intensity has a unique deciBel rating. The deci of deciBel is a Greek prefix similar to the more familiar milli-, centi- and kilo- which commonly precedes units such as liter, gram and meter (for example, centimeter and kilogram). There are 10 deciBels in 1 Bel so the Greek prefix decimeans 1/10-th. The deciBel rating of a sound is 10 times the Bel rating of the sound. The Bel rating of a sound is the number of times greater that it's intensity is than the intensity of the threshold of hearing (1.0 x 10-12 W/m2) - expressed as a power of 10. See Math Magic section.


 
If one sound is 101 times more intense than a second sound, then its Bel rating is 1 Bel higher and its deciBel rating is 10 deciBels higher.
 
If one sound is 102 times more intense than a second sound, then its Bel rating is 2 Bels higher and its deciBel rating is 20 deciBels higher.
 
If one sound is 103 times more intense than a second sound, then its Bel rating is 3 Bels higher and its deciBel rating is 30 deciBels higher.
 
If one sound is 104 times more intense than a second sound, then its Bel rating is 4 Bels higher and its deciBel rating is 40 deciBels higher.


 
The deciBel rating (db) of a sound can be determined from the intensity (I) of the sound (in Watts/m2) using the formula:

db = 10 • log( I / 1.0 x 10-12W/m2)


 
A casual glance at the Math Magic section could be dangerous. (Then again a casual effort to learn anything in Physics could be anything from futile to dangerous.) The first line states that if one sound is 10 times more intense than another, then its deciBel rating is 10 deciBels higher. This may lead one to believe that sound A is 2 deciBels higher than sound B since it is two times the intensity. But don't be fooled! The deciBel scale does not work that way. Read on in the Formual Frenzy section and you will see that the deciBel scale is a logarithmic scale based on powers of 10. And a sound which is two times more intense is 100.301 times greater in intensity and only 3.01 deciBels higher.