Sound a measures 25 decibels and sound b is 8 times as loud as sound a. what is the decibel rating of sound b to the nearest integer?

55 decibels. Decibels is a logarithmic scale for power and is defined as 10 log(p1/p2). However, you need to be very precise in your language if you're speaking of decibels. For instance, a doubling of POWER means an increase of 3 decibels. a doubling of VOLTAGE means an increase of 6 decibels. And because of the ear's non-linear response to sound levels, a perceived doubling of LOUDNESS is an increase of 10 decibels. So the question mentioned loudness, I'll use the increase of 10 db per doubling of volume. 8 times is 3 doubling (2*2*2 = 8). So the increase in decibels is 3 * 10 = 30 decibels. So the decibel rating of a sound that sounds 8 times louder than a sound at 25 decibels is 25 + 30 = 55 decibels.