Answer to Question #104893 in Physics for marland

Question

The sound level produced by one singer is
76.6 dB.
What would be the sound level produced
by a chorus of 18 such singers (all singing at
the same intensity at approximately the same
distance as the original singer)?
Answer in units of dB.

Answer 1

If the intensity of sound produced by one singer is I, then the intensity of sound of 18 singers is 18I. In decibels, this intensity will be equal to:

$$X=10\log_{ 10}\frac{18I}{I_0} ​$$

$$X=10\log_{ 10}18+10\log_{ 10}\frac{I}{I_0}=10\log_{ 10}18+X_0$$

$$X=10\log_{ 10}18+76.6=89.2\ dB$$