The speed of a transverse wave on a long cylindrical steel string is given by
v=\sqrt{\frac{T}{M / L}}
where T is the tension in the string, M is the mass, and L is the length of the string. Ignore any string stiffness, and assume that it does not stretch when tightened.
Consider two steel strings of the same length, the first with radius r_{1} and a second thicker string with radius r_{2}=4 r_{1}. Each string is tightened to the maximum possible tension without breaking.
What is the ratio f_{1} / f_{2} of the fundamental frequencies of vibration on the two strings?
Answer Choices
A. 1
B. \sqrt{2}
C. 2
D. 2 \sqrt{2}
E. 4