When a sound's intensity increases by a factor of 10, its decibel reading increases by how many decibels?

If sound intensity increases by a factor of 10, the decibel reading increases by 10.

Explanation:

Decibel scale:

In order to express levels of sound meaningfully in numbers that are more manageable, a logarithmic scale is used, rather than a linear one. This scale is the decibel scale. every increase of 3 dB represents a doubling of sound intensity.

Increase in decibel scale is given by the formula:

n = 10*log(Increased Intensity of sound/Original Intensity of Sound

n = 10*log(I/I₀)

In our case the sound intensity increases by a factor of 10. So I/I₀ increased by 10 times and will be 10 I/I₀

n = 10*log(10 I/I₀)

n = 10*log(10) + 10log(I/I₀)

n = 10 + 10*log(I/I₀)

This shows that the decibel reading is increased by 10 points.

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