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Answer on Acoustics Question for kaitm

Question #2280
A grade-school teacher insists that the the overall sound level in his classroom not exceed 64 dB at his location. There are 25 students in his class. If each student talks at the same intensity level, and they all talk at once, what is the highest sound level at which each one can talk without exceeding the limit? answer in Db(decibels)
Expert's answer
The formula for adding many incoherent sound sources is

<img src="/cgi-bin/mimetex.cgi?L_%7B25%7D%20=%2010%20%5Ccdot%20%5Clog_%7B10%7D%5Cleft%20%28%2025%20%5Ccdot%2010%5E%7BL/10%7D%20%5Cright%20%29%20dB%20=%2064%20%5C%20dB%20%5C%5C%206.4%20=%20%5Clog_%7B10%7D25+%20L/10%20=%201.4%20+%200.1%20L;%20%5C%5C%20L%20=%2050%20%5C%20dB." title="L_{25} = 10 \cdot \log_{10}\left ( 25 \cdot 10^{L/10} \right ) dB = 64 \ dB \\ 6.4 = \log_{10}25+ L/10 = 1.4 + 0.1 L; \\ L = 50 \ dB.">

Answer: The highest sound level should be of 50 dB.

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