the possible modes of the string have
f = (n/2L)sqrt(T/u)
where n is an integer, L is the length of the string, T its tension, and u the density. You know T=mg, tension is provided only by the hanging mass. You also know f is fixed by the resonator attached, f=120Hz. The only variables are m and n.
If the two given masses m1 and m2 work, but nothing in between does, then they must be adjacent harmonics - one is n and the other is (n+1).
Plug that into the above equation separately for both masses, set equal, and you can find n. Once you have n, you know everything in the equation above except u ...
Isn't v equal to sqrt(T/u)? If so, the equation
ReplyDeletef = (nv/2L)sqrt(T/u)
has v in it twice. Is this correct?
no ... fixed
ReplyDeleteWhen I plug n into the equation with the lighter mass, I get the wrong answer. When I plug n+1 in with the larger mass, I get the wrong answer. But if I plug n+1 in with the lighter mass, I get the answer you provided. Do I have my pairs switched up here?
ReplyDelete