Question

Where I is the intensity of a given sound and I0 is the threshold of hearing intensity. What is the intensity, in decibels, [I(dB)], when I = 10 Superscript 32 Baseline (I Subscript 0)?

Answer 1

`I(db)=320`

Explanation:

Given

`I(db)=10\log((I)/(I_o))`

`I = 10^(32)(I_o)`

Required

Determine
`I(dB)`

We have:

`I(db)=10\log((I)/(I_o))`

Substitute
`I = 10^8(I_o)`

`I(db)=10\log((10^(32)(I_o))/(I_o))`

`I(db)=10\log(10^(32))`

Apply law of logarithm

`I(db)=10*32\log(10)`

`\log(10) = 1`

So:

`I(db)=10*32*1`

`I(db)=320`