# A recording engineer is in a soundproof room that is 44 dB quieter than outside. If the sound...

## Question:

A recording engineer is in a soundproof room that is {eq}44\ \rm{dB} {/eq} quieter than outside. If the sound intensity in the room is {eq}1.2 \times 10^{-10}\ \rm{W/m}^2 {/eq}, what is the intensity outside?

## Decibels

Decibels are an acoustic comparison measure that determines the relationship on the logarithmic scale between the measured intensity and a reference intensity, commonly attributed to the human listening threshold. Mathematically this relationship is presented as,

{eq}\beta_0 = 10log\left( \dfrac{I}{I_0} \right) {/eq}

Here,

{eq}I = \text{Intensity}\\ I_0 = \text{Reference Intensity} {/eq}

## Answer and Explanation: 1

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The sound Intensity inside the room is

{eq}I_i = 1.2 \times 10^{-10} W/m^2 {/eq}

The sound intensity level inside room can be given by

{eq}\beta_i...

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