course Phy 242 When is Test I due by? {jʥĈxsxםassignment #011
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17:21:13 Query introductory set six, problems 15-18 how do we determine the energy of a standing wave given the amplitude and frequency of the wave and the mass of the string?
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RESPONSE --> First, find the maximum velocity. vmax = 'omega*A This works because 'omega is the frequency * 2'pi. Then you multipled by the amplitude to give you the maximum velocity of this wave. Now that we have the maximum velocity we can determine the Kinetic Energy of the wave by: KE = 0.5*m*v^2 KE = 0.5*m*('omega*A)^2 KE= 0.5*m*(2 * 'pi * f * A)^2
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17:21:31 STUDENT ANSWER AND INSTRUCTOR RESPONSE: Energy = 2*pi^2*m*f^2*A^2 INSTRUCTOR RESPONSE: ** You should understand the way we obtain this formula. We assume that every point of the string in in SHM with amplitude A and frequency f. Since the total energy in SHM is the same as the maximum potential or the max kinetic energy, all we need to do is calculate the max potential energy or kinetic energy of each point on the string and add up the results. Since we know mass, frequency and amplitude, we see that we can calulate the max kinetic energy we can get the result we desire. Going back to the circular model, we see that frequency f and amplitude A imply reference point speed = circumference / period = circumference * frequency = 2 `pi A f. The oscillator at its maximum speed will match the speed of the reference point, so the maximum KE is .5 m v^2 = .5 m (2 `pi A f)^2 = 2 `pi^2 m f^2 A^2. **
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RESPONSE --> Understood.
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17:23:58 If the ends of two strings are driven in phase by a single simple harmonic oscillator, and if the wave velocities in the strings are identical, but the length of one string exceeds that of the other by a known amount, then how do we determine whether a given frequency will cause the 'far ends' of the strings to oscillate in phase?
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RESPONSE --> I am not sure how to go about doing this problem but I will be sure to study the answer.
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17:26:20 ** the question here is whether the far ends of the strings are at the same phase of motion, which occurs only if their lengths differ by exactly one, two, three, ... wavelengths. So we need to find the wavelength corresponding to the given frequency, which need not be a harmonic frequency. Any frequency will give us a wavelength; any wavelength can be divided into the difference in string lengths to determine whether the extra length is an integer number of wavelengths. Alternatively, the pulse in the longer string will be 'behind' the pulse in the shorter by the time required to travel the extra length. If we know the frequency we can determine whether this 'time difference' corresponds to a whole number of periods; if so the ends will oscillate in phase **
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RESPONSE --> I understand that even though the velocities are the same to get the ends to osicillate at the same time involves are ability to change the ""pulse"" so that the time to travel the extra distance is there.
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course Phy 242 When is Test I due by? {jʥĈxsxםassignment #011
......!!!!!!!!...................................
17:21:13 Query introductory set six, problems 15-18 how do we determine the energy of a standing wave given the amplitude and frequency of the wave and the mass of the string?
......!!!!!!!!...................................
RESPONSE --> First, find the maximum velocity. vmax = 'omega*A This works because 'omega is the frequency * 2'pi. Then you multipled by the amplitude to give you the maximum velocity of this wave. Now that we have the maximum velocity we can determine the Kinetic Energy of the wave by: KE = 0.5*m*v^2 KE = 0.5*m*('omega*A)^2 KE= 0.5*m*(2 * 'pi * f * A)^2
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17:21:31 STUDENT ANSWER AND INSTRUCTOR RESPONSE: Energy = 2*pi^2*m*f^2*A^2 INSTRUCTOR RESPONSE: ** You should understand the way we obtain this formula. We assume that every point of the string in in SHM with amplitude A and frequency f. Since the total energy in SHM is the same as the maximum potential or the max kinetic energy, all we need to do is calculate the max potential energy or kinetic energy of each point on the string and add up the results. Since we know mass, frequency and amplitude, we see that we can calulate the max kinetic energy we can get the result we desire. Going back to the circular model, we see that frequency f and amplitude A imply reference point speed = circumference / period = circumference * frequency = 2 `pi A f. The oscillator at its maximum speed will match the speed of the reference point, so the maximum KE is .5 m v^2 = .5 m (2 `pi A f)^2 = 2 `pi^2 m f^2 A^2. **
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RESPONSE --> Understood.
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17:23:58 If the ends of two strings are driven in phase by a single simple harmonic oscillator, and if the wave velocities in the strings are identical, but the length of one string exceeds that of the other by a known amount, then how do we determine whether a given frequency will cause the 'far ends' of the strings to oscillate in phase?
......!!!!!!!!...................................
RESPONSE --> I am not sure how to go about doing this problem but I will be sure to study the answer.
.................................................
......!!!!!!!!...................................
17:26:20 ** the question here is whether the far ends of the strings are at the same phase of motion, which occurs only if their lengths differ by exactly one, two, three, ... wavelengths. So we need to find the wavelength corresponding to the given frequency, which need not be a harmonic frequency. Any frequency will give us a wavelength; any wavelength can be divided into the difference in string lengths to determine whether the extra length is an integer number of wavelengths. Alternatively, the pulse in the longer string will be 'behind' the pulse in the shorter by the time required to travel the extra length. If we know the frequency we can determine whether this 'time difference' corresponds to a whole number of periods; if so the ends will oscillate in phase **
......!!!!!!!!...................................
RESPONSE --> I understand that even though the velocities are the same to get the ends to osicillate at the same time involves are ability to change the ""pulse"" so that the time to travel the extra distance is there.
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