The intensity of sound is measured in decibels (dB) on a logarithmic scale. The formula to calculate the increase in intensity level in decibels when the intensity of a sound is doubled can be determined using the logarithmic relationship:
ΔL = 10 * log10(I2/I1)
Where: ΔL is the increase in intensity level in decibels I2 is the doubled intensity I1 is the initial intensity (faintest audible sound)
In this case, if the intensity of the louder sound is double the intensity of the faintest audible sound, I2 = 2 * I1. Substituting this into the formula, we get:
ΔL = 10 * log10((2 * I1) / I1) = 10 * log10(2)
Using a calculator, we can determine the value of log10(2) to be approximately 0.301. Therefore:
ΔL ≈ 10 * 0.301 ≈ 3.01
So, when the intensity of a sound is doubled (compared to the faintest audible sound), the intensity level increases by approximately 3.01 decibels.