Question

While at a party, you pull up a sound intensity level app on your phone (everyone does stuff like that, right?), and it reads 83 dB . You look around and count 32 people talking. If you assume that each person contributes the same amount of noise, determine the sound intensity level of one of those people talking.

Answer 1

To solve this problem it is necessary to apply the concepts related to Sound Intensity. The unit most used in the logarithmic scale is the decibel and mathematically this is expressed as

$\beta_{dB} = 10log_{10}\frac{I}{I_0}$

Where,

$\beta_{dB}$= Sound intensity level in decibels

I = Acoustic intensity on the linear scale

$I_0 =$ Hearing threshold

According to the values, the total intensity is 32 times the linear intensity and the value in decibels is 83dB

So:

$10log_{10}(\frac{32I}{I_0}) = 83$

$10log(\frac{I}{I_0})+10log(32) = 83$

$10log(\frac{I}{I_0})= 83-10log(32)$

$10log(\frac{I}{I_0})= 67.948dB$

Therefore the sound intensity due to one person is 67.948dB