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Two speakers and radiate sound uniformly in all directions. The sound speed is 340 m/s The power output from speaker A is 8.00 watt and from B it is 2.00 watt. ...

Question

Two speakers and radiate sound uniformly in all directions. The sound speed is 340 m/s The power output from speaker A is 8.00 watt and from B it is 2.00 watt. Both speakers are vibrating in phase at a frequency of 170 Hz. A listener is 4.00 m - 3.00 m- standing at point C between A and B, and is 4.00 m away from A and 3.00 m from B. (a) Determine the intensity (powerlarea) at C from speaker A if speaker B is turned off. (b) Whatis the corresponding intensity level in dB as youjust obtained

Two speakers and radiate sound uniformly in all directions. The sound speed is 340 m/s The power output from speaker A is 8.00 watt and from B it is 2.00 watt. Both speakers are vibrating in phase at a frequency of 170 Hz. A listener is 4.00 m - 3.00 m- standing at point C between A and B, and is 4.00 m away from A and 3.00 m from B. (a) Determine the intensity (powerlarea) at C from speaker A if speaker B is turned off. (b) Whatis the corresponding intensity level in dB as youjust obtained in (a)2 (0 dB 10-"2WIm?) (c) Determine the intensity at € when both speakers are turned on. (hint: consider interference effect) Use three significant figures for this problem (HtBA= (AIAZE/F ?) (2/3/5 pts)



Answers

Two loudspeakers, $A$ and $B,$ radiate sound uniformly in all directions in air at $20^{\circ} \mathrm{C}$ . The acoustic power output from $A$ is $8.00 \times 10^{-4} \mathrm{W}$ , and from $B$ it is $6.00 \times 10^{-5} \mathrm{W}$ . Both loudspeakcrs are vibrating in phase at a frequency of 172 $\mathrm{Hz}$ (a) Determine the difference in phase of the two signals at a point $C$ along the line joining $A$ and $B, 3.00 \mathrm{m}$ from $B$ and 4.00 $\mathrm{m}$ from $A(\mathrm{Fig} .16 .46)$ . (b) Determine the intensity and sound intensity level at $C$ from speaker $A$ if speaker $B$ is turned off and the intensity and sound intensity level at point $C$ from speaker $B$ if speaker $A$ is turned off. (c) With both speakers on, what are the intensity and sound intensity level at $C ?$

This question were given that there is a speaker a and then is one mostly could be and did there at two meter distance apart. And there is a queue point here, which is that distance one meter from the speaker. And there is a point b here which is have distance X. So the remaining distances two minus x. So let's say to relent is and because it was two meter, so we will use this as a variable here for the moment. So for Pat, eh? We have frequency equals two, two zero sis hunch. We can find out the land off this wave so the land becomes mellow city over frequency, which is equality for four meter second, which is sound wave velocity in air over two zero six hours, which is it caused to one point six seven meters. So that's the prevalent off the sound which is produced by the speakers. The questions is about the destructive interference and constitution different. So for destructive interference, we should have just doing defendants. We should have the butt defense should be, But difference should be toe end plus one over lambda by two. Just the road multiple off the Lambda where and can be zero one two Don't, don't don't. And for constructive interference we should have d apart Different speedy should be And Lambda where and can be zero one two Don't don't So let's find out the past defense first So but difference should be close to We have got violent elf and this is X So this is l minus X No, my part defense becomes, Let's say this is Delta So l minus X miners. This becomes L minus two X or ex becomes l minus Delta and or two for the safety of interference. We already found her there for any question Jiro and equals to Jiro so D. But difference should be equals to land a by two. So my del tile should be lambda by two. So using this situation, you find out that Dan Tile equals point eight three five meter. So this gives us X equals two point five eight meter and for and equals two minus one. We can also find out the DealTime Jessica's appoint a three five meter, which gives us X equals to one point for two meter. So these are two values which makes the difference into the destructive interference. So let's go to the park. Be here. This was part eh? To Mr by beena for constructive interference, we can have any cause to one or any question minus one. So for dental also, we can have any question Jiro just the delta and will be cause, which is a trivial Justin. They should be caused to sit the same point, which is not possible. So then tell it calls to lander, which is of course, to one point six seven meter which gives us X equals two point one centimeter and for any cause to minus one, we have del del equals two minus one point six centimeter or X equals to one point three two for a speaker A and B. So these this access out of the just one point in time that this means that this is the point one point two. And for this we have point once and point one centimeter. That means that this is the point. Frank wants him. So these are two points. This this one in the second point. Similarly, the same for the destructive interference. We have two points. This one and this one and the question. See, the sense is that why no, the usual? Because we to use at home. I know what they produce is some kind of just the independence of the cast of independence. There isn't but police easy and say well, because the speakers, which we have at home, are very big, are very big and men. It produces some kind of the They're here, so it produces a wave in much, much broader way or having the Lambda may be the same. But the sound wave within at every point is all almost same, so we don't have any kind of destructive interests for constructive interference. That's it.

In the first part of this question, destructive difference happens. Diffidence happens then the difference to the point is equal to when you do plus in into number. And in this case, the part difference is good too. Two minus X minus X is going to tu minus two x. This part difference because to the A go for auditions, then there will be a destructive difference. So can right through my stoics. It's good. I wonder what do bless in Linda Further garbage? Basically, yeah, Flamingo from this Sunday became far. Far enough to find a variant. Valiant is equal to redirected by Who? Couldn't see this spirit stranded for before we were persecuted, derided by frequencies. Given it is true. 06 hertz we get. We're identical to 1.67 m from the before of difference, which was two minus two X is it could go. Who knew a cool Klis in? We'll declare by them. You really quit this question, too. In addition, forex, which comes to the X equal to one minus whenever four limbed up, minus one over cool and Linda student values off and the indiscretion we get executed toe one minus one were fought into. We'll keep like 1.67 minus one worku and with deep lately, 1.67 we get duty off accessible to zero point 58 five me too minus zero. Put 85 and and its purpose, it'll exit will do. Was it a point five 8 to 5 and even End is going to minus one. The X is a good girl. One point for one, even five 32 There will come a good second park, this question and the second barker's you know, constructive difference. Interference occurs it appointment. The difference is a good do and Linda, and in this situation, what difference is equal to do? Minus X minus X. It's good to Gu. Minus drinks. Once again, Real addict, musical F lender and limb guys could go. We do every day if these 300 ft before the Taper skin doing by. If it's cruz it off. Sixers. When we do at this, we get limb rising. Photo. 1.67 m ups for which was too much to X is equal to in Linda from this question weekend from in the Question for X, which is good. Go Xa Goto one minus manure. Go. And Linda really accepted that. You off. Then Bring in this question. Exit little one, minus one Work. Do him multiply by with one point 67. Then you get excellent photo. One minus zero point. Hey, three life. And so here, when n is equal to zero X will be equal to 0.1 65 m when it is a good one. Then X we could toe Judy the invisible to fund. Then execute Cruz in apartment 65 m and an ethical to minus one. Then you will get extra critical. 1.835 m and given and physical. 20 10 you get. The only affects is going toe 1 m. So this is the answer off. Over signalled Berg this question

So here in this problem were given that two identical speakers connected to the same amplifier on the frequency range of the amplifier is between 300 to 600 Hutz on their three parts in the Croatian. In the a part, we have to tell that you are standing somewhere near the speakers and you are able to hear the minimum intensity sound. And we have to tell that why we're able to hear the minimum intensity sound. So the reason behind this question, the concept behind discussion is the destructive interference. So destructive interference takes place when the waves came together in such a manner that they completely cancel out each other on for destructive indifference for destructive indifference to occur. The path difference for the two sources must be a half integral. A number off wavelength that means are two minus our one. This is a part difference. It should be quills. Tow em plus one divide by two times Linda. So the point where you're standing should satisfy the condition for destructive interference to hear the minimum intensity. So this was a solution for the part? A. Now in the part B, they're saying that one of the speaker is moved 39.8 centimeters. So let me write this. Any of the speakers moved 39 point 8 70 widow on were able to hear the maximum intensity sound Andrea little that What is the frequency for this sound? So here we are able toe here the maximum sound insert intensity on it indicates that the speaker is moved at a distance equal toe half wavelength from the previous position to satisfy the condition off. Constructive interference on the condition for constructive interference is are two minus. Our one is equals to sometimes Linda Onda, lender by two. For the given, conditions should be equals to 39.8 centimeters. From here, Linda will be equals to 79.6 centimeter. And if we get the answer in meters will get 0.79 six Mito. Now the equation for the frequency we know it is equals to frequencies equals toe we over the lindo that is a violent this visa speed of flight on speed of flight. We know it is 3 40 m per second on the value of lambda is zero point 796 m. So from her frequency will be equals to 4 27 hoods. So therefore the frequency is equals to 4. 27 hurts. So this is required Answer for the be part. Next I will be solving the C part now in the sea part. We have to tell that how much closer to you from the position in the part B that we have calculated must the speaker We moved to the next position so that we can hear the maximum intensity sound so the distance would be equal to the wavelength that we calculated earlier. So, Linda, that we calculated earlier was 79.6 centimeters. And if you're right, answers and meter will get 0.796 m. So this is the distance that the speaker should be moved so that the we hear the maximum intensity sound. So I hope you have understood the problem. Thank you

Two identical loudspeakers. Air located at a different 20.2 m away. There's too little off speaker driven by the same empty flash and play fire. The frequency of sound produced by the loudspeaker is 7 84. Hearts feed off. Sounding air is 3 44 m per second and the distance between the two say distance between the two. Loudspeaker is 2 m, so the wavelength will be Lambda physical too. Or 3 44 upon 7 84. That is their 0.43 it it Mito Mm. Yeah, this is pick a one B hair speaker A distances to meter find. See, this is find peace. Distance from Speaker. We took peace X here I e saw f p is equal toe loot over a squared plus x square. So a P minus BP is BP is float over X square plus x square minus thanks. So here, from the condition off destructive interference route over s square plus X square minus X is equal. Tow em plus one upon to Linda. So a square plus X square is equal to x plus M plus half Linda squaring on both side s square plus X square is equal to X square. That's twice I am blessed Half one Lambda X plus and plus half square Linda Square. Yeah, so no ex physical too s square upon tow. Am less Have Who's Linda minus M Pless Half hole square, Lambda Square one Toy and Bless half Linda So Mexico Toe Square E boy am less half lim down minus hand Let's half lambda the front Do This is a question one. So for Mexico toe sort of X equal to 9.1 m and Chemical tau zero em is equal to one X equal to 2.71 m where I am a culture to x equal to 1.27 meter chemical toe three x equal 2.534 m I am called to forest X equal to 0.26 Mito now off for the second plan For constructive indifference You do it over a squared plus X squared minus X tickle toe M Linda. The route over square plus X square is equal to X plus m lambda squaring The both side s square plus X square is equal to X square plus two Isom Lambert X plus m squared member square so twice, and lambda X equal toe square minus and square Linda, square the distances from bes Mexico Little s Square Oh, yeah, Twice. Um, Lambda minus m lambda off this equation toe now for chemical toe one X is for pine tree for meter. I am equal to two x is 1.84 m mm ical toe three x 0.861 m on chemical toe four Exists there a point to 62 m. Thank you. Now, if there is no destructive interference along the line busy than substituting X equal to zero and m equal to zero in the question one that is ex ical Toe s square upon twice I am blessed Half lambda minus AM plus half lambda have fun to X is zero square one lambda minus lambda pond for so square Linda is limbed up on four. So Lambda Square is a world forest square. The four Lambda is yeah to s. Now let us calculate d low frequency if iss new upon lambda. No, upon lamb dyes to isis and newest 3 44 m for a second. Upon to and to Mr That is 86. Hard step for low frequencies 86 hearts


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