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The intensity ofa certain sound your eardrum 0.()35 WIm.Calculale the rale at which sound energy hits your eardrum. Assume that the ared ol your eardrum about 47 mm...

Question

The intensity ofa certain sound your eardrum 0.()35 WIm.Calculale the rale at which sound energy hits your eardrum. Assume that the ared ol your eardrum about 47 mm ?What power output P required from point source that is 2.6 m away in order t0 crcatc the same intensity your eardrum?

The intensity ofa certain sound your eardrum 0.()35 WIm. Calculale the rale at which sound energy hits your eardrum. Assume that the ared ol your eardrum about 47 mm ? What power output P required from point source that is 2.6 m away in order t0 crcatc the same intensity your eardrum?



Answers

The intensity of a certain sound at your eardrum is $0.0030$ $\mathrm{W} / \mathrm{m}^{2} .$ (a) Calculate the rate at which sound energy hits your eardrum. Assume that the area of your eardrum is about $55 \mathrm{~mm}^{2}$. (b) What power output is required from a point source that is $2.0 \mathrm{~m}$ away in order to create that intensity?

In this question. We need to calculate the energy delivered to the your job each second at normal tone. Okay, so solution be using, uh, power. It goes to intensity times era. Okay, So how long is equal to the intensity, which is 10 to the minus six. What's familiar square, and then the area off the ear drum. Okay, so pi r Square. So the diameter is 8.4. Mm. So the region is 4.2. Mm. So come out to meet us. That's what we have. Then para square and calculate this. You get 25 times 10 to the minus 11. What? Okay. And then the energy delivered in one second. Okay, is just p times Delta T whether Delta t is one second. So the answer is 5.5 times 10 to the minus 11. What? Okay, so this is the answer for this question. That's all

Uh, once again welcome to a new problem. Was still dealing with sound waves. He assumed that's a Sinus oId Oh, off course. We do know that when you talk about sound waves, you have compressions rare factions. So this is this is how the sound waves move so there, Longitudinal, as opposed to Sinus idol. But for compasses off explaining sound with. Sometimes you might use the thesis sine waves so you might use assignments. It so happens that when they move on, the sound that you get from your ear is a based off vibrations. So if you listening right there and that's you hear inside of it, it is going to be an ear drum. And so the sound is traveling up until you, um, and these pressure on your ear drum So this is your ear drum on? It's very delicate. If it gets destroyed, then you're pretty much messed up in terms off your hearing, Um, levels. So in this sense, assumed that the intensity for this round way of his two point over times 10 to the negative three uh, gone once from meters squared, eso assumed That's you, um, you sound with his coming up on tool up until you hear. Of course, that's the pressure level. So when you hear something, it means that these these pressure on on inside of you here Oh, on these are These are your decibels. So you know the measurement measurement of sound. It's coming up until you, um and sometimes you might not feel comfortable. Okay, You might not feel comfortable. And that happens. That happens sometimes. S o. Let's assume that we have some sound. You know, let's assume you have sound, uh, that it's it's coming up until you hear and the units for measurement for this sound. This one here is what's once Amita squid off course. You're going to hear other units along the way. You'll hear people talk about Desi bells and other pressure units for sound. But for now, assume you're dealing with the intensity being two point all times 10 to the negative three. What's for me to sweat? And then your year drum. So this is your ear drum right here. So gonna assume that it's secular in nature and it has a diameter d off, uh, six point all millimeters damage. Is this distance right here? Um and of course, at this point was saying, If the sound is troubling up until your ear drum, you know what's the energy involved? We defined energy as Aziz work or force times distance, different ways of defining energy capacity. You know, it's the capacity to do work. So if your energy if your energy you're looking at your energy and you're listening to the sound for time period off. One minute you're asking yourself what's gonna be the energy involved in this process. So the you know the intensity we know the Oh, damn it. A, which is six millimeters. We're going to change that to, uh, meters. Of course, we can always get the radius from this. The radius is half the damage, so it's three millimeters. That's all radius. Uh, and if we change that too, two leaders one meter is Samos 1000 millimeters. So this becomes 3.0 times 10 to the negative three meters. That's your radius. The time period that this happens T is in minutes. So it's one minute, but one minute has 60 seconds. So we changed that two seconds. Um, and soul, these are the units were dealing with want to find What's the energy? What's the value of the energy that's get gets transferred to your ear? Drum your drum. Assuming it's secular, the area itself is a pyre square. That's the area of your ear drums. So this is the same spy times The radius were really change that too Meters three times 10 to the negative three meters and we square that. So this is 28.3 times 10 to the negative. Six meters squared. Um, that's the Now that's the area. So the energy that's gonna get into your ear e it calls to are the intensity times the area times the time are the disarmament. The intensity turns the area times the time that this happens. So this is 2.0 time. Stand to the negative three. What's the meters squared? And then multiply that by the area, which is 28.3 time. Stand to the negative six meters squared and then finally we have the time, which is 60 seconds. So this becomes the same month. E energy becomes a 3.39 times 10 to the They gave nine jewels three points 39 times stand to the negative angels. Or, you could say 3.39 Michael jewels. You want to call it that? Ah, 3.39 micro jewels. But, you know, we don't have to do my cordials. We could just leave it us in terms of jewels. We don't need Michael. Its energy units of energy is always comfortable in jewels, so that's what we're dealing with. So once again, you know, we had a problem where there was sound traveling, and it's longitudinal gets to you hear office is a lot of pressure going on what they want to find. What's the energy as the sound gets to your ear drops well, given the intensity of two point no times 10 to the negative three. I will also given the diameter six. That helps us get the radius. We change it two meters off the drum and then using the radius, we compute the area off the bedroom. And now that we have the area on the intensity with the time period off 60 seconds, we end up with 3.392 Instead of negative nine jewels, I hope you enjoy the problem. Feel free to send any questions or comments and have a wonderful day

Number 42 has an ear drum human ear drum that has a radius. I guess we're assuming a circular ear drum has a radius of four millimeters and they wouldn't have the energy per second that your drum gets when the sound is at the threshold. A hearing and when a sound is a threshold of pain energy per second, that's power. That's what power is. I mean, that's what What is a jeweled per second. So if we can find power and that's what the definition of intensity is, how much power per area? So, um, at the threshold of hearing, you can look at that up on the table, the intensity is 10 minutes 12. We've been using that a lot. We're looking for the power in the area. We'll just the area of a circle to buy. I mean, pi r squared. I'm gonna have to put that in. Meters four millimeters would be 0.4 meters when I was cross multiply. So the threshold of hearing I get a power of 5.3 times 10 to the negative 17 and that would be watts on them worth threshold of pain. You can look that up on the table in the book intensity is one. So same equation intensity. Well, you could make that a one intensity, which is one pretty cool. The power per area and the area is still pi r squared coast multiply. And at the threshold of pain, I get that the tower is oh, 5.0 times 10 to the negative. Let me wants. So I guess over here I should have kept just two significant figures also.

In this question. There are two parts in party. We want to calculate the power captured by one year at zero decibels. Okay, so in part, A will be using, um, power equals two i times aim. So the power captured is equal to I know times eight because at zero decibels, zero decibels correspond to I go to I know which is and to the minus 12 watts per meter square. Okay. And then the So we have the I not to be 10 to the minus trial. And then, uh, area is high kinds Regis Square. The radius is 3.5, and then Okay. You calculate this, you get, um, 3.8 times 10 to the minus 17. What? Okay, So this is the answer for party, then? Maybe we want to find the energy captured during one hour after listening to a lecture delivered at 60 decibels. Okay, So the energy you'll be using a formula using equals to p times delta t. And we know that he is the intensity times area. And then times delta t Okay, So the energy captured is equal to so the intensity and 60 dispose is, uh yes, I also need to use I equals two. I know times 10 to the data by 10. Okay, so I know is 10 to the minus trough and then beta 60. So we have 10 to the 60 divide by 10, and then the area is pi times 3.5 times 10 to the ministry square, and then the delta T is one hour, so we have 3600 seconds. Okay? And you calculate days you get, uh, 1.4 times 10 to the minus seven Jews. Okay, so this is the answer for part B, and that's all.


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