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Finding Average Velocity

The noise lev...

Question

The noise level in a classroom in absence of the teacher is $50 d B$ when $50$ students are present. Assuming that on the average each student outputs same sound energy per second, what will be the noise level if the number of students is increased to $100$ ?

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Solution

Let the intensity of each student be $I$ .
According to the question
$β_{A} = 10 {log}_{10} \frac{50 I}{I_{0}}; β_{B} = 10 {log}_{10} (\frac{100 I}{I_{0}})$

$\Rightarrow β_{B} - β_{A} = 10 {log}_{10} \frac{100 I}{I} - 10 {log}_{10} (\frac{50 I}{I})$

$\Rightarrow β_{B} - 50 = 10 log (\frac{100 I}{50 I}) = 10 {log}_{10} 2 = 3$

So, $β_{A} = 50 + 3 = 53 d B$ .

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