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

Answer:

$I(db)=320$

Step-by-step explanation:

Given

$I(db)=10\log(\frac{I}{I_o})$

$I = 10^{32}(I_o)$

Required

Determine $I(dB)$

We have:

$I(db)=10\log(\frac{I}{I_o})$

Substitute $I = 10^8(I_o)$

$I(db)=10\log(\frac{10^{32}(I_o)}{I_o})$

$I(db)=10\log(10^{32})$

Apply law of logarithm

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

$\log(10) = 1$

So:

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

$I(db)=320$