Question

the loudness, L, measured i in decibels (Db), of a sound intencity, I, measured in watts per square meter, is defined as L=10logI/I0, where I0=10^-12 and is the least intense sound a human ear can hear. what is the approximate loudness of a rock concert with a sound intensity of 10^-1

Answer 1

The approximate loudness of a rock concert with a sound intensity of 10⁻¹

is 110 Db.

Loudness

Since the loudness L measured in decibel (Db) of a sound intensity I is given by

L = 10㏒(I/I₀) where

• I = intensity of sound and
• I₀ = least intense sound human ear can hear = 10⁻¹².

Since we want to determine  the approximate loudness of a rock concert with a sound intensity of 10⁻¹. So, I = 10⁻¹

Loudness of the rock concert

So, substituting the values of the variables into L, we have

L = 10㏒(I/I₀)

L = 10㏒(10⁻¹/10⁻¹²)

L = 10㏒10¹¹

L = 11 × 10㏒10

L = 110㏒10

L = 110 (since ㏒10 = 1)

So, approximate loudness of a rock concert with a sound intensity of 10⁻¹

is 110 Db.

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