Question

A person standing a certain distance from an airplane with four equally noisy jet engines is experiencing a sound level of 145 dB . What sound level would this person experience if the captain shut down all but one engine?

Answer 1

Answer:

The sound level is 138.97 dB.

Explanation:

Given that,

Sound level L= 145 dB

We need to calculate the intensity

Using formula of sound intensity

$L=10\log(\dfrac{I}{I_{0}})$

Put the value into the formula

$145=10\log(\dfrac{I}{I_{0}})$

$\log(\dfrac{I}{I_{0}})=\dfrac{145}{10}$

$\log(\dfrac{I}{I_{0}})=14.5$

$\dfrac{I}{I_{0}}=10^{14.5}$

$I=10^{14.5}\times I_{0}$

$I=10^{14.5}\times10^{-12}$

$I=316.2$

We need to calculate the noise of one engine

Using formula of intensity

$I'=\dfrac{I}{4}$

Put the value into the formula

$I'=\dfrac{316.2}{4}$

$I'=79.05$

We need to calculate the intensity level due to one engine

Using formula of sound intensity

$L'=10\log(\dfrac{I'}{I_{0}})$

$L'=10\log(\dfrac{79.05}{10^{-12}})$

$L'=138.97\ dB$

Hence, The sound level is 138.97 dB