(a) By what factor is one sound more intense than another if the sound has a level 17.0 dB higher than the other?
(b) If one sound has a level 32.0 dB less than another, what is the ratio of their intensities?
To answer both questions, we need to understand how sound intensity is related to decibels (dB).
(a) To determine the factor by which one sound is more intense than another, given a level difference of 17.0 dB, we can use the formula:
Intensity ratio = 10^(dB difference / 10)
In this case, the dB difference is 17.0 dB. Plugging it into the formula:
Intensity ratio = 10^(17.0 dB / 10)
= 10^(1.7)
Calculating this using a calculator or software, the intensity ratio is approximately 50.12.
Therefore, one sound is approximately 50.12 times more intense than the other.
(b) To find the ratio of the intensities when one sound has a level that is 32.0 dB less than the other, we again use the formula:
Intensity ratio = 10^(dB difference / 10)
In this case, the dB difference is -32.0 dB (negative because it is less than the other sound). Plugging it into the formula:
Intensity ratio = 10^(-32.0 dB / 10)
= 10^(-3.2)
Calculating this using a calculator or software, the intensity ratio is approximately 0.00501.
Therefore, the ratio of the intensities is approximately 0.00501.