Answer to Question #103006 in Physics for Nyx

Question

The sound level produced by one singer is
84.2 dB.
What would be the sound level produced
by a chorus of 43 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 43 singers is 43I. In decibels, this intensity will be equal to:

$$X=10\log_{10}\frac{43I}{I_0}$$

$$X=10\log_{10}40 +10\log_{10}\frac{I}{I_0}=10\log_{10}40 +X_0$$

$$X=10\log_{10}40 +84.2=100.2\ dB$$