The loudness L, in bels (after Alexander Graham Bell), of a sound of intensity I is defined to be
L = log I/I0,
Where I0 is the minimum intensity detectable by the human ear (such as the tick of a watch at 20 ft under quiet conditions) if a sound is 10 times as intense as another, its loudness is 1 bel greater than that of the other. If a sound is 100 times as intense as another, its loudness is 2 bels greater, and so on. The bel is a large unit, so a subunit, the decibel, is generally used. For L, in decibels, the formula is
L = 10 log I/I0.
Find the loudness, in decibels, of each sound with the given intensity.
SOUND INTENSITY
a) Jet engine at 100 ft ............1014 ∙ I0
b) Loud rock concert.............1011.5 ∙ I0
c) Train whistle at 500 ft ..........109 ∙ I0
d) Normal conversation ..........106.5 ∙ I0
e) Trombone ........................1010 ∙ I0
f) Loudest sound possible ......1019.4 ∙ I0