Here is a tricky one (for me) that uses linear mass density and two masses. I don't really know which to do so I did both! 1. The problem statement, all variables and given/known data An object can be hung from a string (with linear mass density μ=0.00200kg/m) that passes over a light pulley. The string is connected to a vibrating arm (of constant frequency f), and the length of the string between the vibrating arm and the pulley is L=2.10m. When the mass m of the object is either 25.0kg or 36.0kg, standing waves are observed; no standing waves are observed with any mass between these values, however. What is the frequency of the vibrating arm? What is the largest object mass for which standing waves could be observed? In the picture, there is a vibrating sinusoidal transverse wave with 3 periods. 2. Relevant equations I used μ=T/v2, v=fλ, and T=m*9.81m/s2. 3. The attempt at a solution First I found the wavelength, λ=2.1m/3=0.7m. Next, I found the tensionS... Using 25kg and 36kg. T=25*9.81=245.25N OR T=36*9.81=353.16N. With these tensions, I found the velocitieS μ=245.25/v2=350.2m/s OR μ=353.16/v2=420.2. Always fun getting two different solutions, right? Finally, found the frequencies using these velocities and my wavelength. f=350.2/.7=500.3Hz OR f=420.2/0.7=600.3Hz. I don't know which one to pick :( Also, I had no idea where to begin for the second part of the question, so if you could give me a hint for that, it would be greatly appreciated.