The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as L = 10 lo

Question

1 month ago

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The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as L = 10 lo

g StartFraction I Over I 0 EndFraction, where I 0 = 10 Superscript negative 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?
A. 2 Db
B. 22 Db
C. 60 Db
D. 110 Db

Mathematics

2 answers:

Zina [12.3K] · Answer 1 · 2026-02-16T07:49:55+03:00

Zina [12.3K]1 month ago

7 0

Response: D. 110 Db

Step-by-step breakdown:

Svet_ta [12.7K] · Answer 2 · 2026-02-16T07:51:20+03:00

Response:

The estimated loudness level of a rock concert with a sound intensity of $10^{-1}$ measures 110 Db.

Step-by-step breakdown:

The loudness, L, represented in decibels (Db), resulting from a sound intensity, I, measured in watts per square meter, is given by: $L=10 log (\frac{I}{I_0})$

$I_0=10^{-12}$

We need to determine the approximate loudness of a rock concert featuring a sound intensity of $10^{-1}$ .

Thus, $I = 10^{-1}$

Substituting the values into the equation:

$L=10 log (\frac{10^{-1}}{10^{-12}})$

$L=10 log (10^{11})$

L=110 Db

Therefore, the estimated loudness of a rock concert with a sound intensity of $10^{-1}$ is 110 Db.