The decibel (dB) is a logarithmic unit used to express the ratio of one intensity to another. It does not directly represent the absolute intensity of a sound but rather compares it to a reference intensity. To determine the corresponding intensity of a sound given its intensity level in decibels, we need the reference intensity.
In acoustics, the reference intensity used is often defined as the threshold of hearing, which is approximately 10^(-12) watts per square meter (W/m^2). Therefore, we can calculate the corresponding intensity of a sound in watts per square meter (W/m^2) using the formula:
I = I₀ × 10^(L/10),
where I is the intensity of the sound, I₀ is the reference intensity (10^(-12) W/m^2), and L is the intensity level in decibels.
Let's calculate the corresponding intensity of a whisper with an intensity level of 15 dB:
I = (10^(-12) W/m^2) × 10^(15/10) ≈ (10^(-12) W/m^2) × 3.162 ≈ 3.162 × 10^(-12) W/m^2
Therefore, the corresponding intensity of the whisper is approximately 3.162 × 10^(-12) watts per square meter (W/m^2).