Answer to Question #173410 in Physics for Kenan

Question

A heavy machine in the factory produces a sound intensity level of 130 dB in relation to the audibility threshold. Determine the level of sound intensity that will be produced by two such machines that would work simultaneously.

Answer 1

The sound intensity level of a single machine is

$$\beta_1=10\log_{10}\frac{I}{I_0}.$$

In this equation, I₀ is the audibility threshold equal to 10^-12 W/m².

So, for a single machine,

$$I=I_0·10^{\beta_1/10}.$$

For two similar machines working simultaneously:

$$\beta_2=10\log_{10}\frac{2I}{I_0}=10\log_{10}\frac{2I_0·10^{\beta_1/10}}{I_0}=\\\space\\ =10\log_{10}[2·10^{\beta_1/10}]=133\text{ dB}.$$