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Arithmetic Mean

The noise lev...

Question

The noise level in a classroom in absence of the teacher is 50 dB when 60 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

$β_{A} = 10 l o g_{10} (\frac{50 I}{I_{0}})$

$β_{B} = 10 l o g_{10} (\frac{100 I}{I_{0}})$

$\Rightarrow β_{B} - β_{A}$

$= 10 l o g_{10} (\frac{100 I}{I_{0}}) - 10 l o g_{10} (\frac{50 I}{I_{0}})$

$= 10 l o g (\frac{100 I}{50 I})$

$= 10 l o g_{10} 2 = 3$

So, $β_{A} = 50 + 3 = 53 d B$

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