# Frequency of third harmonic

**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.

http://ift.tt/1forfzq

## Leave a comment