Question

What is the intensity of a sound with a sound intensity level (SIL) 67 dB, in units of W/m^2?

Answer 1

The intensity of sound (I) = 3.16 x 10⁻⁶ W/m²

Step-by-step explanation:

We have expression for sound intensity level (SIL),

`L=10log_(10)\left ( (I)/(I_0)\right )`

Here we need to find the intensity of sound (I).

`L=10log_(10)\left ( (I)/(I_0)\right )\\\\log_(10)\left ( (I)/(I_0)\right )=0.1L\\\\(I)/(I_0)=10^(0.1L)\\\\I=I_010^(0.1L)`

Substituting

L = 67 dB and I₀ = 10⁻¹² W/m² in the equation

`I=I_010^(0.1L)=10^(-12)* 10^(0.1* 65)\\\\I_0=10^(-12)* 10^(6.5)=10^(-5.5)=3.16* 10^(-6)W/m^2`

The intensity of sound (I) = 3.16 x 10⁻⁶ W/m²