Loudness is psychological response to a sound. It depends on both the intensity and the frequency of the sound. As a rule of thumb, a doubling in loudness is approximately associated with an increase in sound level of 10 dB. (this rule of thumb is relatively inaccurate at very low or very high frequencis.) If the loudness of the machines in illustration 6. is to be doubled, how many machines at the same distance from the worker must be running?

Explanation

To solve the problem of how many machines must be running to double the loudness, we can follow these steps:

### Step 1: Understand the Relationship Between Loudness and Decibels
According to the problem, doubling the loudness is associated with an increase of approximately 10 dB in sound level. This means if we want to achieve a loudness that is twice as loud, we need to increase the sound level by 10 dB.

**Hint:** Remember that the decibel scale is logarithmic, which means that each increase of 10 dB represents a tenfold increase in intensity.

### Step 2: Use the Formula for Sound Level
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