You are trying to overhear a juicy conversation, but from your distance of 15.0 m, it sounds like only an average whisper of 20.0 dB. How close should you move to the chatterboxes for the sound level to be 60.0 dB?

Video transcript

Hey everyone. Alright in this video we are going to be working with sound intensity and different positions um or sound intensity level. It's another word for volume that's given in decibels. So television set is located on a table 10 m away from you. It plays music. You hear the music at an average of 15 decibels. At what position measured from the tv set? Will you hear the music at a sound level of 30 decibels? Okay, so we know that for our first distance R one is 10 m and that sound intensity at 10 m or beta one is decibels. We are looking for the distance R two where the sound level will be decibels. So let's first recall our sound intensity level equation. So delta beta equals decibels times the log Of I two over I one. We're also going to need our intensity equation so recall I equals power over area where area recall can be given as or pi r squared. Now that are, is really what we're looking for because we are given are one and we are solving for R two. So up here we are given um the sound level to sound level one, so delta beta is just beta two minus beta one or 30 minus 15 decibels, which gives us 15 decibels. So we're gonna take this first equation here and we are going to Saul or I two over. I won kind of as a total value or as a singular value. So we know we have 15 decibels equals decibels times the log of I two over I one. We're gonna divide each side by 10 decibels. 1.5 equals the log of I two over I one. We need to remember some log math here. This can be rewritten as I to over I one equals 10 to the 1.5. Plug that into our calculators and we get 31.62 is the value of I two over I one. Let's go up to our intensity equation and remember focusing on this part where we are going to solve for our So I to over I one is equal to P 2/4 pi R two squared over. P 1/4 pi R one squared. The power is the same same tv set those cancel for pie is a constant. Those cancel. And so we can rewrite I to over. I won as R one squared over R two squared. We can plug that back into this equation over here where we have 31.62 equals R one squared is 10 m. So 10 m squared over. R two squared. Let's multiply both sides by our two squared and divide both sides by 31.26. So that we can get our R2 all by itself. And that comes out to the square root of 100 or 10 squared over 31. At 1.78 m. Looking at our options or answers. That does match it is answer C. Alright, that's all for this video, folks. We'll see you in the next one.