Answer: When the power intensity of a sound increases, the change in decibels can be calculated using the logarithmic formula for sound intensity:
Step-by-step explanation:
Change in decibels (dB) = 10 * log10(I2/I1)
where I2 is the new intensity and I1 is the original intensity.
In this case, the sound intensity increases by a factor of 500, so I2 = 500 * I1.
Plugging this into the formula, we get:
Change in decibels (dB) = 10 * log10(500 * I1/I1)
Simplifying further:
Change in decibels (dB) = 10 * log10(500)
Using a calculator, the logarithm of 500 is approximately 2.7.
Therefore, the change in decibels is:
Change in decibels (dB) = 10 * 2.7
Change in decibels (dB) = 27
So, the change in decibels is 27 dB when the power intensity of the sound is 500 times greater.