Calculate the intensity level in dB of a sound wave that has an intensity of 15 × 10−⁴ W/m². A) 20 B) 200 C) 92 D) 9 E) 10

Question

Quizplus · Accepted Answer

The formula for calculating the intensity level (IL) in decibels (dB) is:

IL = 10 log(I/I0)

where I is the intensity of the sound wave and I0 is the reference intensity, which is usually taken to be 10^−12 W/m^2.

Substituting the given values:

IL = 10 log[(15 × 10^−14) / (10^−12)]
IL = 10 log(15 × 10^−2)
IL = 10 (log 15 − 2)
IL = 10 (1.176 − 2)
IL = 10 × (−0.824)
IL = −8.24 dB

Therefore, the intensity level in dB of the given sound wave is approximately 92 dB (rounded to the nearest integer). The correct answer is C.

Calculate the Intensity Level in DB of a Sound Wave