Question

The decibel level of the sound of a subway train was measured at 92 dB. Find the intensity in watts per square meter (W/m2). (Give your answer in scientific notation, correct to one decimal place.)

Answer 1

Answer:

I = 1.58 x 10⁻³ watt/m²

Explanation:

Here, we will use the following formula:

$\beta = 10\ log_{10}(\frac{I}{I_o})$

where,

β = decibel level = 92 dB

I = Intenisty of sound in watt/m² = ?

I₀ = reference intensity = 10⁻¹² watt/m²

Therefore,

$92\ dB =10\ log_{10}(\frac{I}{10^{-12}\ watt/m^2} )$

$10^{9.2} = \frac{I}{10^{-12}}\ watt/m^2\\\\I = (1.58\ x\ 10^9)(10^{-12}\ watt/m^2)$

I = 1.58 x 10⁻³ watt/m²