Question

A whisper has an intensity level of about 15 dB. What is the corresponding intensity of the sound?

a) 10⁻¹² W/m²
b) 10⁻¹⁵ W/m²
c) 10⁻¹⁸ W/m²
d) 10⁻²⁰ W/m²

Answer 1

The corresponding intensity of a whisper with an intensity level of 15 dB is 10⁻¹⁵ W/m².OPTION C

Step-by-step explanation:

The intensity of a sound is measured in watts per meter squared (W/m²). The intensity level of a sound is measured in decibels (dB). The relationship between the intensity level (ß) and intensity (I) is given by the equation ß = 10 log₁₀(I/I₀), where I₀ is the threshold intensity of sound.

In this case, the intensity level of the whisper is 15 dB. To find the corresponding intensity, we can rearrange the equation to solve for I. So, 15 = 10 log₁₀(I/I₀).

By substituting ß = 15 and I₀ = 10⁻¹² W/m² into the equation, we get:

15 = 10 log₁₀(I/10⁻¹²)

1.5 = log₁₀(I/10⁻¹²)

I/10⁻¹² = 10¹.⁵

I = 10⁻¹² × 10¹.⁵

I = 10⁻¹²⁻⁰.⁵

I = 10⁻¹²⁻⁰.⁵ = 10⁻¹⁵ W/m².