Question

What is the decibel level of the noise from a firecracker with intensity 10^-4 watts per square inch? Use a logarithmic model

to solve.

Answer 1

80 db

Explanation:

D=10log(I10−12)

Substitute in the intensity level, I, and then simplify to find

DD=10log(10−410−12)=10log(108).

Since log108=8, simplify to find

DD=10⋅8=80.

The decibel level is 80dB.

Answer 2

`\large \boxed{\text{110 db}}`

Explanation:

The intensity β of a sound wave in decibels is given by the formula

`\beta = 10 \log \left ((I)/(I_(0)) \right)`

and I₀ = the reference intensity (10⁻¹² W/m²)

Data:

I = 10⁻⁴ W·in⁻²

Calculations:

1. Convert watts per square inch to watts per square metre

`\text{Sound level} = \frac{10^(-4)\text{ W}}{\text{1 in}^(2)} * \left(\frac{\text{39.37 in}}{\text{1 m}}\right )^(2) = 1.5 * 10^(-1) \text{ W$\cdot$m}^(-2)`

2. Convert the intensity to decibels.

`\beta = 10 \log \left ((1.5 * 10^(-1))/(1* 10^(-12)) \right) = 10\log(1.5 * 10^(11)) = 10 * 11 = \textbf{110 db}\\\text{The sound intensity of the firecracker is $\large \boxed{\textbf{110 db}}$}`