#$&* course PHY 232 If your solution to stated problem does not match the given solution, you should self-critique per instructions athttp://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.
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Given Solution: `aThe beat frequency is the difference in the frequencies, in this case 277 Hz - 262 Hz = 15 Hz. One ocatave reduces frequency by half, so two octaves lower would give frequencies 1/4 as great. The difference in the frequencies would therefore also be 1/4 as great, resulting in a beat frequency of 1/4 * 15 Hz = 3.75 Hz. ********************************************* Question: What frequency is received by a person watching an oncoming ambulance moving at 110 km/h and emitting a steady 800-Hz sound from its siren? The speed of sound on this day is 345 m/s. What frequency does she receive after the ambulance has passed? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: According to Doppler shift: f ' = (c + v_r) / (c - v_s) * f When the ambulance approaches and the receiver stands still: f ' = (345 m/s + 0) / (345 m/s - 30 m/s) * 800 Hz = 876 Hz. When the ambulance has already passed: f ' = (345 m/s + 0) / (345 m/s - (- 30 m/s)) * 800 Hz = 736 Hz confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ confidence rating #$&*: (Type in a number from 0 to 3, indicating your level of confidence in your solution. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 3 means you are at least 90% confident of your solution, or that you are confident you got at least 90% of the solution 2 means that you are more that 50% confident of your solution, or that you are confident you got at least 50% of the solution 1 means that you think you probably got at least some of the solution correct but don't think you got the whole thing 0 means that you're pretty sure you didn't get anything right) Response: 3 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): (If you believe your solution matches the given solution then just type in 'OK'. Otherwise explain in your own words how your solution differs from the given solution, and demonstrate what you did not originally understand but now understand about the problem and its solution.) OK ------------------------------------------------ Self-critique Rating: (If you believe your solution matches the given solution then just type in 'OK'. Otherwise evaluate the quality of your self-critique by typing in a number between 0 and 3. 3 indicates that you believe you have addressed all discrepancies between the given solution and your solution, in such a way as to demonstrate your complete understanding of the situation. 2 indicates that you believe you addressed most of the discrepancies between the given solution and your solution but are unsure of some aspects of the situation; you would at this point consider including a question or a statement of what you're not sure you understand 1 indicates that you believe you understand the overall idea of the solution but have not been able to address the specifics of the discrepancies between your solution and the given solution; in this case you would normally include a question or a statement of what you're not sure you understand 0 indicates that you don't understand the given solution, and/or can't make a reasonable judgement about whether or not your solution is correct; in this case you would be expected to address the given solution phrase-by-phrase and state what you do and do not understand about each phrase) OK
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Given Solution: The general formula for the Doppler shift is f ' = (c + v_r) / (c - v_s) * f where v_r is the velocity of the receiver, v_s the velocity of the source, and c the speed of sound. f is the frequency of the source, f ' the frequency observed by the receiver. v_r is considered positive if the receiver is moving in the direction of the source, and v_s is considered positive if the source is moving in the direction of the receiver. In this case, the receiver is presumably stationary, while the source (the ambulance) is moving at 110 km/h = 110 * 1000 m / (3600 s) = 30 m/s. The received frequency is thus f ' = (345 m/s + 0) / (345 m/s - 30 m/s) * 800 Hz = 876 Hz. After the ambulance has passed, it is no longer approaching the source and its velocity is negative. In this case we have f ' = (345 m/s + 0) / (345 m/s - (- 30 m/s)) * 800 Hz = 736 Hz. 36. Two eagles fly directly toward one another, the first at 15.0 m/s and the second at 20.0 m/s (both relative to the air). Both screech, the first one emitting a frequency of 3200 Hz and the second one emitting a frequency of 3800 Hz. What frequencies do they receive if the speed of sound is 330 m/s? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: According to Doppler shift: f ' = (c + v_r) / (c - v_s) * f when the receiver is approaching the source, first eagle is the receiver and second is the source: f ' = (330 m/s + 20 m/s) / (330 m/s - 15 m/s) * 3200 Hz = 3556 Hz first eagle is the receiver and second is the source and the source is approaching the receiver: f ' = (330 m/s + 15 m/s) / (330 m/s - 20 m/s) * 3800 Hz = 4230 Hz confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ confidence rating #$&*:: (Type in a number from 0 to 3, indicating your level of confidence in your solution. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 3 means you are at least 90% confident of your solution, or that you are confident you got at least 90% of the solution 2 means that you are more that 50% confident of your solution, or that you are confident you got at least 50% of the solution 1 means that you think you probably got at least some of the solution correct but don't think you got the whole thing 0 means that you're pretty sure you didn't get anything right) Response: 3 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): (If you believe your solution matches the given solution then just type in 'OK'. Otherwise explain in your own words how your solution differs from the given solution, and demonstrate what you did not originally understand but now understand about the problem and its solution.) OK ------------------------------------------------ Self-critique Rating: (If you believe your solution matches the given solution then just type in 'OK'. Otherwise evaluate the quality of your self-critique by typing in a number between 0 and 3. 3 indicates that you believe you have addressed all discrepancies between the given solution and your solution, in such a way as to demonstrate your complete understanding of the situation. 2 indicates that you believe you addressed most of the discrepancies between the given solution and your solution but are unsure of some aspects of the situation; you would at this point consider including a question or a statement of what you're not sure you understand 1 indicates that you believe you understand the overall idea of the solution but have not been able to address the specifics of the discrepancies between your solution and the given solution; in this case you would normally include a question or a statement of what you're not sure you understand 0 indicates that you don't understand the given solution, and/or can't make a reasonable judgement about whether or not your solution is correct; in this case you would be expected to address the given solution phrase-by-phrase and state what you do and do not understand about each phrase) OK
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Given Solution: The general formula for the Doppler shift is f ' = (c + v_r) / (c - v_s) * f where v_r is the velocity of the receiver, v_s the velocity of the source, and c the speed of sound. f is the frequency of the source, f ' the frequency observed by the receiver. v_r is considered positive if the receiver is moving in the direction of the source, and v_s is considered positive if the source is moving in the direction of the receiver. Let's assume that the first eagle is the source and the second the receiver. In this case, the receiver is approaching the source at 20 m/s, while the source is approaching the receiver at 15 m/s, and the source is emitting frequency 3200 Hz. The received frequency is thus f ' = (330 m/s + 20 m/s) / (330 m/s - 15 m/s) * 3200 Hz = 3556 Hz, approx. In the second case the first eagle is the receiver, the second the source. The source is approaching the receiver at 20 m/s, the receiver approaching the source at 15 m/s, so f ' = (330 m/s + 15 m/s) / (330 m/s - 20 m/s) * 3800 Hz = 4230 Hz, approx. ********************************************* Question: `qquery gen phy problem 12.46 speakers 1.8 meters apart, listener three meters from one and 3.5 m from the other **** gen phy what is the lowest frequency that will permit destructive interference at the location of the listener? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: for destructive interference to occur, the path difference is an odd multiple of half of the wavelength with dx as the path difference and L as Lambda which is wavelength: L=2*'dx =2(3.5m-3.0m) =1m Frequency = speed of sound/L Frequency=343m/s/1m=343 Hz This is the lowest frequency in which the destructive interference can occur. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ confidence rating #$&*: (Type in a number from 0 to 3, indicating your level of confidence in your solution. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 3 means you are at least 90% confident of your solution, or that you are confident you got at least 90% of the solution 2 means that you are more that 50% confident of your solution, or that you are confident you got at least 50% of the solution 1 means that you think you probably got at least some of the solution correct but don't think you got the whole thing 0 means that you're pretty sure you didn't get anything right) Response: 3 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): (If you believe your solution matches the given solution then just type in 'OK'. Otherwise explain in your own words how your solution differs from the given solution, and demonstrate what you did not originally understand but now understand about the problem and its solution.) OK ------------------------------------------------ Self-critique Rating: (If you believe your solution matches the given solution then just type in 'OK'. Otherwise evaluate the quality of your self-critique by typing in a number between 0 and 3. 3 indicates that you believe you have addressed all discrepancies between the given solution and your solution, in such a way as to demonstrate your complete understanding of the situation. 2 indicates that you believe you addressed most of the discrepancies between the given solution and your solution but are unsure of some aspects of the situation; you would at this point consider including a question or a statement of what you're not sure you understand 1 indicates that you believe you understand the overall idea of the solution but have not been able to address the specifics of the discrepancies between your solution and the given solution; in this case you would normally include a question or a statement of what you're not sure you understand 0 indicates that you don't understand the given solution, and/or can't make a reasonable judgement about whether or not your solution is correct; in this case you would be expected to address the given solution phrase-by-phrase and state what you do and do not understand about each phrase) OK
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Given Solution: `aSTUDENT SOLUTION: To solve this problem, I first realize that for destructive interference to occur, the path difference is an odd multiple of half of the wavelength(ex. 1/2, 3/2, 5/2). I used Fig.12-17 in the text to help visualize this problem. Part (A) of the problem asks to calculate the lowest frequency at which destructive interference will occur at the point where two loudspeakers are 2.5m apart and one person stands 3.0m from one speaker and 3.5m from the other. The text states that 'destructive interference occurs at any point whose distance from one speaker is greater than its distance from the other speaker by exactly one-half wavelength.' The path difference in the problem is fixed, therefore the lowest frequency at which destructive interference will occur is directly related to the longest wavelength. To calculate the lowest frequency, I first have to calculate the longest wavelength using the equation 'dL ='lambda/2, where `dL is the path difference. 'lambda=2*'dL =2(3.5m-3.0m)=1m Now I can calculate the frequency using f=v/'lambda. The velocity is 343m/s which is the speed of sound. f=343m/s/1m=343 Hz. Thus, the lowest frequency at which destructive interference can occur is at 343Hz. Keeping in mind that destructive interference occurs if the distance equals an odd multiple of the wavelength, I can calculate (B) part of the problem. To determine the next wavelength, I use the equation 'dL=3'lambda/2 wavelength=2/3(3.5m-3.0m) =0.33m Now I calculate the next highest frequency using the equation f=v/wavelength. f^2=343m/s/0.33m=1030Hz. I finally calculate the next highest frequency. 'del L=5/2 'lambda wavelength=0.20m f^3=343m/s/0.2m=1715 Hz. INSTRUCTOR EXPLANATION: The listener is .5 meters further from one speaker than from the other. If this .5 meter difference results in a half-wavelength lag in the sound from the further speaker, the peaks from the first speaker will meet the troughs from the second. If a half-wavelength corresponds to .5 meters, then the wavelength must be 1 meter. The frequency of a sound with a 1-meter wavelength moving at 343 m/s will be 343 cycles/sec, or 343 Hz. The next two wavelengths that would result in destructive interference would have 1.5 and 2.5 wavelengths corresponding to the .5 m path difference. The wavelengths would therefore be .5 m / (1.5) = .33 m and .5 m / (2.5) = .2 m, with corresponding frequencies 343 m/s / (.33 m) = 1030 Hz and 343 m/s / (.2 m) = 1720 Hz, approx. **** **** gen phy why is there no highest frequency that will permit destructive interference? ** You can get any number of half-wavelengths into that .5 meter path difference. ** STUDENT COMMENT: After reading the solution I understand the formula I am supposed to use a bit better, but I am still kind of confused about the concept of destructive interference. INSTRUCTOR RESPONSE: As you change position the relative alignment of 'peaks' and 'valleys' change. Sometimes peaks from one path arrive at the same time as peaks from the other (in which case valleys will arrive with valleys), and the interference is constructive. Sometimes peaks from one path arrive at the same time as valleys from the other, and the interference is destructive. When one path is a whole number of wavelengths longer than the other, peaks meet peaks and the waves reinforce. When one path is a half a wavelength longer than the other, peaks meet valleys and the waves cancel; the same happens when one path is half a wavelength plus a whole number of wavelengths longer than the other. STUDENT QUESTION I got the lowest frequency fine. And I was on the right track with my reasoning. But which way do you suggest to solve problems like this: your way, or the students solution. INSTRUCTOR RESPONSE The two solutions are completely equivalent. If you really understand it one way, you'll understand it the other. However in the interest of time, you should pick one. Whichever way makes more sense to you, that's the way you should think of it. ********************************************* Question: `qgen phy what must happen in order for the sounds from the two speakers to interfere destructively, assuming that the sources are in phase? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The condition for the two sounds to interfere destructively is that the path difference must be an integer number of wavelengths + ½ wavelength. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ confidence rating #$&*: (Type in a number from 0 to 3, indicating your level of confidence in your solution. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 3 means you are at least 90% confident of your solution, or that you are confident you got at least 90% of the solution 2 means that you are more that 50% confident of your solution, or that you are confident you got at least 50% of the solution 1 means that you think you probably got at least some of the solution correct but don't think you got the whole thing 0 means that you're pretty sure you didn't get anything right) Response: 3 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): (If you believe your solution matches the given solution then just type in 'OK'. Otherwise explain in your own words how your solution differs from the given solution, and demonstrate what you did not originally understand but now understand about the problem and its solution.) OK ------------------------------------------------ Self-critique Rating: (If you believe your solution matches the given solution then just type in 'OK'. Otherwise evaluate the quality of your self-critique by typing in a number between 0 and 3. 3 indicates that you believe you have addressed all discrepancies between the given solution and your solution, in such a way as to demonstrate your complete understanding of the situation. 2 indicates that you believe you addressed most of the discrepancies between the given solution and your solution but are unsure of some aspects of the situation; you would at this point consider including a question or a statement of what you're not sure you understand 1 indicates that you believe you understand the overall idea of the solution but have not been able to address the specifics of the discrepancies between your solution and the given solution; in this case you would normally include a question or a statement of what you're not sure you understand 0 indicates that you don't understand the given solution, and/or can't make a reasonable judgement about whether or not your solution is correct; in this case you would be expected to address the given solution phrase-by-phrase and state what you do and do not understand about each phrase) OK
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Given Solution: `a** The path difference has to be and integer number of wavelengths plus a half wavelength. ** STUDENT QUESTION The book tells me that for these two speakers to interfere destructively, the distance from one speaker has to be greater than its distance from the other speaker by one-half wavelength. Destructive interference would occur if the distance would equal 1/2, 3/2, 5/2, wavelengths. INSTRUCTOR RESPONSE That is correct. The given solution to the original problem says this as well. The book's explanation of course gives you a third option for the most appropriate way to think of the problem. In any case you need to understand why those path differences result in destructive interference. Once you're clear on that, a wide variety of interference problems become pretty straightforward. CRAB NEBULA PROBLEM? This Query will exit. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: Otherwise evaluate the quality of your self-critique by typing in a number between 0 and 3. 3 indicates that you believe you have addressed all discrepancies between the given solution and your solution, in such a way as to demonstrate your complete understanding of the situation. 2 indicates that you believe you addressed most of the discrepancies between the given solution and your solution but are unsure of some aspects of the situation; you would at this point consider including a question or a statement of what you're not sure you understand 1 indicates that you believe you understand the overall idea of the solution but have not been able to address the specifics of the discrepancies between your solution and the given solution; in this case you would normally include a question or a statement of what you're not sure you understand 0 indicates that you don't understand the given solution, and/or can't make a reasonable judgement about whether or not your solution is correct; in this case you would be expected to address the given solution phrase-by-phrase and state what you do and do not understand about each phrase) OK
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Given Solution: `a** The path difference has to be and integer number of wavelengths plus a half wavelength. ** STUDENT QUESTION The book tells me that for these two speakers to interfere destructively, the distance from one speaker has to be greater than its distance from the other speaker by one-half wavelength. Destructive interference would occur if the distance would equal 1/2, 3/2, 5/2, wavelengths. INSTRUCTOR RESPONSE That is correct. The given solution to the original problem says this as well. The book's explanation of course gives you a third option for the most appropriate way to think of the problem. In any case you need to understand why those path differences result in destructive interference. Once you're clear on that, a wide variety of interference problems become pretty straightforward. CRAB NEBULA PROBLEM? This Query will exit. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!