- #1
utkarshakash
Gold Member
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Homework Statement
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.
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.