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Question 9How many times is 4OdB louder than its reference? Give your answer asa ratioMoving another question will save this response...

Question

Question 9How many times is 4OdB louder than its reference? Give your answer asa ratioMoving another question will save this response

Question 9 How many times is 4OdB louder than its reference? Give your answer asa ratio Moving another question will save this response



Answers

SOUND If the intensity of a sound from one source is 10,000 times that of another, how much more is the decibel level of the louder sound than the quieter one?

We will use the decibel formula and it's given that I said two is equal to 1000 times I sub one. And so let's let do you want equal 10 times log uh, ice of one divided by isis zero and D to physical to 10 times log of ice up to over ice and zero. And therefore de tu minus D one is equal to 10 times log of I to over I zero Martus 10 log I went over I zero. If we use our log properties, we get that detailed honesty. One is equal to 10 times law. Uh, I two divided by i zero to Bata bhai. I won over I zero Evan, let's simplify so way bring down, do you two months t one and that equals 10 log I two over I would and because, um earlier we said that I said to is equal to 1000 times ice of one. I can now say that de to modesty. One is equal to 10 times love of 1000. I won over I want which is equal. Teoh 10 blawg 1000 can rewrite the 1000 as 10 cute and then so that that is just 10 times three, which is equal to 30. So the solution is 30 decibels

So in this problem we're being asked how many times more intense as a sound that measures 120 decibels than the sound that measures 110 decibels. Well, remember from problem number 51 the formula defined decibels of a certain amount of intensity is equal to 10 times the log of I Divided by ice of zero. So in this case we need to substitute these values into both formulas. So when we have 100 and 20 decibels, that would be 100 and 20 equal to 10 times the log of I divided by ice of zero. And for the 110 decibels, that would be 110 equal to 10 times the log of I divided by ice of zero. So in this case we have to find the value of I. So in our first equation, I'm going to start by dividing both sides by 10, so the 10s will cancel. So we have 12 equal to log of I divided by ice of zero. So the next thing we're going to do is we're gonna convert this an exponential form. Remember if you have a log base B of X equal to Y. In exponential form, it's B to the Y equals X. So if we apply this to our formula and don't forget if you don't see a base, it's based 10. So if we apply this to our formula will have 10 to the 12 is equal to I divided by ice of zero. Well, in both of our problems, I sub zero is going to be the same. So that ice of zero essentially cancels out. So we have 10-12 or actually you know what we'll do? We'll multiply it on both sides because most of the time intensity is getting multiplied by I subzero. So like I said, we'll go ahead and multiply both sides of our equation by ice of zero. So have 10 to 12 times ice of zero is equal to I. Now we're going to solve our second equation the same way we'll begin by dividing both sides by 10, So we'll have 11 equal to the log of I divided by ice of zero. Keep in mind it has based 10. So we can rewrite it as 10 to the 11th power equal to I divided by ice of zero. And then we'll multiply both sides of our equation by ice of zero, which means that 10 to the 11th time size of zero is equal to. Uh Well like I mentioned before, our eyes of zeros are the same. So essentially we just have to compare 10 to the 12 divided by 10 to 11 to figure out how many times more loud is. Well, remember when we divide like basis, we simply subtract the exponents. Well, 12 minus 11 is one. So that would mean we'd have 10 to the first power, which is just 10, Which means it would be 10 times as loud or as intense.

Okay, So, given her answers from previous questions are fireworks. I'm intensity we're talking was 10 or is it the power of 13? And our concert was 10. Race to seven and 1/2. And they're asking for, um, the difference in the intensities. In other words, they're asking us to do the ratio. So if I did that, that would be a 10 2 of 13 over 10 7.5. And if you remember anything about thes like bases, I could do that. It's 10 to the 13 minus 7.5, which would give me, um, an answer of 10 uh, to the 5.5 times greater. And this would be for our, um, fireworks that it was 10 to the 55.5 times greater and intensity than that of the concert.

Hello students. In this question, we have to determine approximately how many times louder is better than equals 200 decibel sound from better to equals to 60 decibel sound. So the difference in the sound level delta beta, it is equal to one minus beta two, which is equal to 100 decibel minus 60 decibels. Okay, so from here after solving we will get that 40 decibel and this can be rearranged to write as delta beta equals two. Former player by 10 decibels, which can be compared with and more player bait and disable. So from here after comparing and comes out to be four. So hence the affected by which the Beethoven is louder is equals to the power end, so N is equal to hear for so hence we can say that 16, So hence we can say that Beethoven is beatable or we can directly right as 100 decibel is 16 times louder, 16 times louder, then 60 decibel. Okay, so this becomes the answer for this problem. Okay, thank you


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