Answer to Question #105774 in Physics for Zhyla

Question

In a factory, 30 noisy machines produce a decible rating of 90dB. How many machines must be removed aiming to decrease the decible level to 80 dB?

Answer 1

If the intensity of sound produced by one machine is I, then the intensity of sound of 30 machines is 30I. In decibels, this intensity will be equal to:

$$90=10\log_{10}{\frac{30I}{I_0}}$$

$$80=10\log_{10}{\frac{nI}{I_0}}$$

$$90-80=10=10\log_{10}{\frac{30I}{I_0}}-10\log_{10}{\frac{(30-x)I}{I_0}}$$

$$10=10\log_{10}{\frac{30}{30-x}}$$

$$x=27$$

27 machines must be removed.