Suppose, I have a a rod hung by two wires on both ends. Now I add some additional mass on the rod, at some point which is not at the center. It has been told to me that, if I use a tuning fork to excite both the wires, the first one will vibrate at the fundamental frequency and the second one at the first overtone.
I had a minor disagreement
My point was, since the same tuning fork is used, the frequency should be the same in both cases. However, the first wire is vibrating at it's fundamental frequency, and second one is vibrating at the first overtone, so, the tension in the first wire should be more
since f=n/2l sqrt{T l /m}2
In the first wire, f_1=1/2l sqrt{T_1 l/m}, in the second wire it is f_2=2/2l sqrt{T_2 l/m}.
Now I've argued that the same tuning fork excites both wires so f_1 = f_2, and thus T_1>T_2
is that line of reasoning correct ?
