How to get string between two certain strings in Swift?

Question: Two strings at different lengths and linear densities are joined together. They are stretched so that the tension in each...

• Question: Two strings at different lengths and linear densities are joined together. They are stretched so that the tension in each string is 190.0 N. The free ends are fixed in place. Find the lowest frequency that permits standing waves in both strings with a node at the junction. The standing wave pattern in each string may have a different number of loops. 3.75 m 1.25m _________________===================== 6*10^-2 kg/m 1.5*10^-2 kg/m (this is kinda what the picture looks like if it helps but it seems really confusing on the computer) Equations I should use (there may be others): f=nv/2L (n1v1)/2L1=(n2v2)/2L2 Other information I am given: L1=3.75 L2=1.25 n1=? n2=? v1=? v2=? (m/L)=6.00x10^-2 kg/m (m/L)2=1.50x10^-2 kg/m I need to create a ratio between n1 and n2. I don’t understand how I get v and then how to find a ratio between n1 and n2.

• Answer:

  You did well, but forgot a basic equation v= sqrt(T/d) where T is the Tension in string and d is the linear density We have T=190.0 N. and d for both strings So the equation for lowest frequency at node becomes (n1v1)/2L1=(n2v2)/2L2 = n1*sqrt(T/d1)/2L1 = n2sqrt(T/d2)/2L2 So n1/n2 = sqrt(d2/d1)L2/L1 => n1/n2 =sqrt (1.5/6) *(1.25/3.75)=1/2 * 1/3 = 1/6 So, now you got your ratio. Remember v= sqrt(T/d) from now, it will help in most cases.