Question

Use the formula L= 10 log 10 R, where Is the loudness of a sound and R is the sound's relative intensity. to find out how much louder 20 people talking would be than one person talking. Suppose the sound of one person talking has a relative intensity of 80 decibels.

Answer 1

`X=24.1decibels`

Explanation:

From the question we are told that:

Loudness function
`L= 10 log_(10) R`

Sound of a person
`S_p=80\ decibels\ or 10^8`

Number of persons talking
`n=20 people`

Generally the Relative intensity for 20 people is mathematically given by

Relative intensity for
`R_(20)=`
`20*10^8`

Relative intensity for
`R_(20)=`
`20^8`

Generally the loudness for 20 people is mathematically given by

`L_(20)= 10 log_(10) R`

`L_(20)= 10 log_(10) 20^8`

`L_(20)= 10 (8 log_(10) 20)`

`L_(20)= 104.1 decibels`

Therefore increase in loudness X is given as

`X=104.1-80=-52.90`

`X=24.1decibels`