Question

A noisy machine in a factory produces sound with a level of 80 dB. How many identical machines could you add to the factory without exceeding the 90-dB limit?

Answer 1

The number of identical machines that can be added to the factory without exceeding the 90-dB limit is 10.

Step-by-step explanation:

In order to determine how many identical machines could be added to the factory without exceeding the 90-dB limit, we need to understand the relationship between sound intensity levels and the number of machines.

Sound intensity levels are measured logarithmically in decibels (dB) and can be calculated using the formula:

dB = 10 * log10(I/I0)

Where I is the intensity of the sound and I0 is the reference intensity (generally set at 10-12 W/m2).

Assuming that all the machines have the same intensity, we can set up the following equation:

80 + 10 * log10(n) = 90

Where n is the number of machines we want to add. Solving for n:

10 * log10(n) = 10

log10(n) = 1

n = 10

Therefore, you can add 10 identical machines to the factory without exceeding the 90-dB limit.