The strings of a violin are tuned to the tones G, D, A, and E, which are separated by a fifth from one another. That is, f(D) = 1.5f(G), f(A) = 1.5f(D) = 440 Hz, and f(E) = 1.5f(A). The distance between the two fixed points, the bridges at the scroll and over the body of the instrument, is 30 cm. The tension on the E string is 90 N.

(a) What is the mass per meter of the E string?

(b) To prevent distortion of the instrument over time, it is important that the tension on all strings be the same. Find the masses per meter of the other strings.