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Phy 202
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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The SHM of the left-hand end of a long string is given by y = 1.08 cm * sin ( ( 4 `pi rad/s) t ). This motion induces a traveling wave in the string. The string has tension 27 Newtons and mass per unit length is 13 grams / meter. Explain how we know there is energy in the wave, and find how much energy there is in 13.3 meters of this wave.
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I do not understand how we determine the amount of energy in the wave. I know you can find velocity by using v = square root of (T/m/L)). So in this case v = square root of (27/(.013kg/meter)) = 45.6m/s
The SHM is (I believe) y=1.08cm * sin ((4pi rad/s)(13.3m - 45.6m/s * t))
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How do you go from that formula to finding energy?
self-critique rating
@& Every point on the string undergoes simple harmonic motion with the same amplitude and the same frequency as the left-hand end.
The maximum velocity of a point moving in SHM with amplitude 1.08 cm and frequency 4 pi rad / sec is (4 pi rad / sec) * 1.08 cm = 13 cm / sec, approximately.
Every particle in the string has a total energy (consisting of its KE and is PE) which is at certain instants equal to its maximum PE and at certain other instants to its maximum KE. It follows that the total energy in a segment of the wave is equal to the KE that segment would have if it was all moving at the maximum velocity.
So you would figure out the mass of 13.3 meters of string, and the KE of that mass if it was moving at the maximum velocity 13 cm/s.
It's important to understand that the entire length of string is not all moving at this velocity; however every particle has the same total energy it would if it was moving at this speed.
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#$&*
Phy 202
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** **
** **
The SHM of the left-hand end of a long string is given by y = 1.08 cm * sin ( ( 4 `pi rad/s) t ). This motion induces a traveling wave in the string. The string has tension 27 Newtons and mass per unit length is 13 grams / meter. Explain how we know there is energy in the wave, and find how much energy there is in 13.3 meters of this wave.
** **
I do not understand how we determine the amount of energy in the wave. I know you can find velocity by using v = square root of (T/m/L)). So in this case v = square root of (27/(.013kg/meter)) = 45.6m/s
The SHM is (I believe) y=1.08cm * sin ((4pi rad/s)(13.3m - 45.6m/s * t))
** **
How do you go from that formula to finding energy?
self-critique rating
@& Every point on the string undergoes simple harmonic motion with the same amplitude and the same frequency as the left-hand end.
The maximum velocity of a point moving in SHM with amplitude 1.08 cm and frequency 4 pi rad / sec is (4 pi rad / sec) * 1.08 cm = 13 cm / sec, approximately.
Every particle in the string has a total energy (consisting of its KE and is PE) which is at certain instants equal to its maximum PE and at certain other instants to its maximum KE. It follows that the total energy in a segment of the wave is equal to the KE that segment would have if it was all moving at the maximum velocity.
So you would figure out the mass of 13.3 meters of string, and the KE of that mass if it was moving at the maximum velocity 13 cm/s.
It's important to understand that the entire length of string is not all moving at this velocity; however every particle has the same total energy it would if it was moving at this speed.
*@
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