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Find a clock that ticks. Then test to see which ear has the better hearing by covering one ear and finding how far away your open ear can hear the ticking; repeat f...

Question

Find a clock that ticks. Then test to see which ear has the better hearing by covering one ear and finding how far away your open ear can hear the ticking; repeat for the other ear. Notice also how the sensitivity of your hearing improves when you cup your ears with your hands.

Find a clock that ticks. Then test to see which ear has the better hearing by covering one ear and finding how far away your open ear can hear the ticking; repeat for the other ear. Notice also how the sensitivity of your hearing improves when you cup your ears with your hands.



Answers

What are the lowest and highest frequencies that an ear can detect when the sound level is 40 dB? (See Fig. 12$-$6.)

Number 90 a 0.48 grand pin is dropped from a height of 31 centimeters and it makes sound for 1.2 seconds. If all the mechanical energy and head up here is converting to sound energy, we want to find how far away you could hear that. Well, the threshold for hearing we know is 10 times 10 to the negative 12th. Um, so then that is power. And this is the distance away. Willpower is an energy per time. And that sound energy came from this gravitational potential energy. So this power is energy per time, and the energy is gravitational. So MGH her time is what this power is going to be. It's more than just insert my values. I know the intensity that you can barely hear be 10 to the negative 12. The power is gonna be MGH. So that is the mass, the pen in kilograms. So 0.0 oh, for a times G line 18 times the height in meters. It's a 0.31 all divided by the time which is 1.2 seconds. So that's the power that's still over for pie R squared and I'm solving for this are so if I multiply both sides by r squared, I want if I divide both sides Bye 10,012 Now I can solve this. So I'm taking that terms that jumps that divided by that and then also divided by this. And then I'll take the square root of both sides. And I got or was 98 33 meters. Oh, so you just say 9800 or I could say 9.8 kilometers.

So let's first understand what we are supposed to do in this. We are supposed to find the minimum distance off two speakers that we can resolve. A human ear can result when the spirit of sound these 3 40 meters per seconds. So let's say there are two speakers close by and you're standing right here. The sound will reach you. Let me enjoy that much better. The sound will reach you from these two speakers. So if these two speaker have the speaker had the sound which reaches you at, let's say this reaches you in two seconds and this reaches that 30 seconds, you can resolve it because as questions says, it's one. It should be one millisecond apart. On the other hand, if it is 2.9 seconds and this is three seconds, you can still resolve it. But if now we have 2.95 seconds and this is three seconds now, the time difference between them is 0.5 We cannot resolve this, so we need to find the distance between these two minimum distance, which we can resolve. So to do that, all we have to do is to find the distance which is well also team multiplied by time. So velocity is equal to 3 40 as we are given, multiplied by time, which is one milliseconds, which is strange power three seconds. So if you do this, you'll find the distance will be 30.34 meters. That is 34 centimeters. If these speakers are separated by the distance, less than 34 centimeters you cannot own a human deal cannot differentiate between these two speakers. So to resolve these two sounds distinctly, they must be at least this much distance apart.

Now, when you have an ear trumpet, insert off the affected area off your ear, being 0.5 centimeter square, you have an effective area off 900 centimeter square, over which sound from other sources is absorbed, which means you have an advantage off 900 by 0.5, which is 1800. So now you gained 1800 times more sound intensity done with a normal year, but off this, only 5% off. The sound is converted into electric impulse, which is fed into your ear a sound because of the 5% every agency, which means off this 1800 times only 500 kinds, which is 5% off the time is the actual intensity applicant amplification factor, which is 90. So truly speaking, the intensity when you have a near trumpet is 90 times more than the intensity of without an ear trumpet. So that is all we need. So if I not what your intensity corresponding to I know what were your decibel intensity? Correspond? Is your decibel intensity corresponding to the basic density? Some I not white and bar minus 12 on Peter is the decibel intensity corresponding tow the intensity with the year trumpet that would be into the best and lock to base and lock the vest on 90. I not bite. Inform ministry. This is without. This is just a normal year without a trumpet, and this is any year with a trumpet. Now we simply take the difference. Be Dominus. Beat or not is equally doe this time minus this time. Remember that long a minus lobby is locked A divided by B So we take the 10 common on locked based in log A minus. Lobby is love a divided by B so that 90 I no fight in a bar minus 12 divided by I not bite. In far minus 12 you can tell I not ended for mice. 12. On we get 10 locked based in 90 which turns out to be 19 going to fight. So the because of the trumpet, the sound you hear is 19.5 decibels. More simple as that. Now you could have used the other because off the decibel difference method you used once you know that the sound is 90 times stronger, you could have simply used can lock to the best and 90 and that will give you a 19 point file, and you automatically know that the sun is now 19.5 decibels higher. That is the usefulness of the metal.

Okay. It's when this question were concerned with the gain and decibels produced by a stethoscope. So let's write down the given so we can discuss how to do the problem. Um, so and we know that sound is transmitted 100 times is effectively I'm curious what that corresponds to mathematically 100 times power. What? I'll just write down 100 times question mark and come back to it. Um, and then we went to gain, um, if the gathering areas 15 centimeters squared. So I'll call that a one and, um and then it concentrates on to an ear drum to air drums, 0.9 centimeters squared, and I'll put at times too. Um, and the efficiency is 40%. So right now, I'm just gonna put this information aside. They think you can sort of, um, you can work with this information and so, uh, basically, we can assume that the power stays the same. Actually, I guess we want to assume that the efficiency is 40%. The power stays the same, though. Um, well, I guess we could say there's an initial power, and then the final power is only 40% of the initial power. And so you can say that I is p over a And so, um, we can get what? So we can have the intensity at the, um, sort of intake of the stethoscope, and then we can have enough it your drum, and so we don't really know the power. Um, so we could, but we can say an initial intensity is initial power over initial area. Final intensity is final power, which we can say is reduced by 40% of the original surrounded by area. Um, let me sync up my area one and two. So I call this all one. I'll call this all too. Okay, so too is at the years. And then one is at the opening of the stethoscope. So 111222 And we're concerned with, um, the game produced So, um, being, uh, is 10 db multiplied by 10 long 10 of I two over. I won. Okay, so now we can start plating in so we can do 10 10 db times a factor of log. I too. So that's gonna be P two were a two and I one is P one over a one and um P two is point for p one. So we can replace this with 10.4 and then a one over a two. Um, weaken. We just need to put everything into a calculator at this point? I guess so. They wanted to in a two are given. So we want to do, um 10 c Yes, 10 times the log. Oh, four times 15. And then we wanted to find all of that by when we have to remember that there's two of the area, so two times 20.9. So go ahead and put times two. And to see what we get, we get that the enhancement is by a factor of 5.23 db.


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