1. The problem statement, all variables and given/known data
A yarn of material that cannot dilate, length L, mass m and elastic constant K is trapped and stretched with negligible tension between the two supports A and B attached to the ends of the metal bar, CD, whose coefficient of expansion varies linearly from to , increasingly with temperature in the range of interest of the question. Determine the frequency of the third harmonic that is established in the rope when heated ΔT.
3. The attempt at a solution
[itex]\alpha _{eq} = \dfrac{\alpha 1 + \alpha 2}{2}[/itex]
Since the metal bar expands, separation between A and B increases. This creates a tension in the string. The change in length is given by LαΔT.
F = KLαΔT
Frequency of third harmonic = 4v/2L
where [itex]v=\sqrt{\dfrac{FL}{m}} [/itex]
If I substitute the value of F, the answer comes out to be wrong.
A yarn of material that cannot dilate, length L, mass m and elastic constant K is trapped and stretched with negligible tension between the two supports A and B attached to the ends of the metal bar, CD, whose coefficient of expansion varies linearly from to , increasingly with temperature in the range of interest of the question. Determine the frequency of the third harmonic that is established in the rope when heated ΔT.
3. The attempt at a solution
[itex]\alpha _{eq} = \dfrac{\alpha 1 + \alpha 2}{2}[/itex]
Since the metal bar expands, separation between A and B increases. This creates a tension in the string. The change in length is given by LαΔT.
F = KLαΔT
Frequency of third harmonic = 4v/2L
where [itex]v=\sqrt{\dfrac{FL}{m}} [/itex]
If I substitute the value of F, the answer comes out to be wrong.
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