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

Answer:

$X=24.1decibels$

Step-by-step 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

$X=104.1-80=-52.90$

$X=24.1decibels$