Answer:
The value is [tex]\beta_f = 84.95 \ dB[/tex]
Explanation:
From the question we are told that
The intensity level of the shout of a single person is [tex]\beta = 48.1 \ dB[/tex]
The number of fans is [tex]n = 4841[/tex]
Gnerally intensity level is mathematically represented as
[tex]\beta = 10 log * \frac{I}{I_o }[/tex]
Here [tex]I_o[/tex] is the minimum intensity of sound human ear can pick and the value is
[tex]I_o = 1 * 10^{-12} \ W/m ^2[/tex]
when [tex]\beta = 48.1 \ dB[/tex]
[tex]48.1 = 10 log * \frac{I}{ 1 * 10^{-12}}[/tex]
=> [tex]4.81 = log ( \frac{ I}{ 1 * 10^{-12}} )[/tex]
taking antilog of both sides
[tex]64565.42 = \frac{I}{ 1 *10^{-12}}[/tex]
=> [tex]I = 6.457 *10^{-8} \ W/m^2[/tex]
Generally the intensity for the whole fans is mathematically represented as
[tex]I_f = n * I[/tex]
=> [tex]I_f = 4841 * 6.457 *10^{-8 }[/tex]
=> [tex]I_f = 0.0003126 \ W/m^2[/tex]
Gnerally the intensity level for the whole fans is mathematically represented as
[tex]\beta_f = 10 log [ \frac{I_f }{I_o } ][/tex]
=> [tex]\beta_f = 10 log [ \frac{ 0.0003126 }{1*10^{-12}}[/tex]
=> [tex]\beta_f = 84.95 \ dB[/tex]
