Logarithmic question using decibels?
Restaurant conversation is about 45 dB. If ordinary conversation is 100 times greater than restaurant conversation, how loud is ordinary conversation?
Using the formula: L = 10log (I/I0) for decibels.
Could someone show me step by step how to solve this so I can learn how? Thank you!
- chauncyLv 74 years agoFavorite Answer
L = 10 log (I/Io)
where L = loudness, I = intensity and Io is a reference intensity level.
Let the intensity of restaurant conversation = Ir and of ordinary conversation = Ioc
45 = 10 log (Ir/Io)
log (Ir/Io) = 4.5
Ir/Io = 10^4.5
Ir = Io * 10^4.5
Ioc = 100 * Io * 10^4.5 = Io * 10^6.5
Ioc/Io = 10^6.5
The loudness of ordinary conversation = 10 log (Ioc/Io)
= 10 log (10^6.5)
= 10 * 6.5
Note: The letters o, r and oc are subscripts.
Io is the intensity when L = 0.
If I = Io then L = 10 log (Io/Io) = 10 log 1 = 10 * 0 = 0