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:

[tex]X=24.1decibels[/tex]

Step-by-step explanation:

From the question we are told that:

Loudness function [tex]L= 10 log_{10} R[/tex]

Sound of a person [tex]S_p=80\ decibels\ or 10^8[/tex]

Number of persons talking [tex]n=20 people[/tex]

Generally the Relative intensity for 20 people is mathematically given by

Relative intensity for[tex]R_{20}=[/tex][tex]20*10^8[/tex]

Relative intensity for[tex]R_{20}=[/tex][tex]20^8[/tex]

Generally the loudness for 20 people is mathematically given by

[tex]L_{20}= 10 log_{10} R[/tex]

[tex]L_{20}= 10 log_{10} 20^8[/tex]

[tex]L_{20}= 10 (8 log_{10} 20)[/tex]

[tex]L_{20}= 104.1 decibels[/tex]

Therefore increase in loudness X is given as

[tex]X=104.1-80=-52.90[/tex]

[tex]X=24.1decibels[/tex]

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