You live on a busy street, but as a music lover, you want to reduce the traffic noise. (a) If you install special soundreflecting windows that reduce the sound intensity level (in dB) by 30 dB, by what fraction have you lowered the sound intensity 1in W>m2 2?

Video transcript

Hey everyone. Alright, so this problem, we are working with sound intensity level. Let's go through and see what it's asking. We're looking, we're in a gathering hall. The walls of the hall, decrease the sound intensity level by 25 decibels. We need to determine the fraction by which the walls lower the sound intensity in watts per meter squared. So this problem, we're going to recall our sound intensity level equation, that's delta, beta equals 10 decibels times the log of I two over I one where I is your sound intensity back in the problem, they say, determine the fraction by which the walls lower the sound intensity. So we're looking at a difference of the eye to the second intensity as a fraction of I won the first intensity. So we're going to write that as I two equals X times Y one. We're going to solve for X. We know that the um sound intensity level was decreased by 25 decibels, so negative 25 decibels equals 10 decibels times the log of I two over I one. Now we know I two, we are rewriting I two as X X times I won. So we're going to put that into this equation here. X I one over I one and the initial intensity is canceled. So we'll divide these 10 decibels over to the other side, negative 2.5 equals the log of X. We need to remember some log math here and we can rewrite this equation as X equals 10 to the negative 2.5, plug that in and our answer is 3.16 times 10 to the negative third watts per meter squared. Look at our answer choices and that is answer B. Alright, that's all for this problem. We'll see you in the next video.