You and your team are designing a tunable, single-tone, acoustic emitter. One end of a string is connected to a post on the top of a frictionless inclined plane. The string supports a mass at rest below, on the surface of the plane. The angle of the incline relative to the horizontal (θ) is adjustable. The length of the string is L = 35.0 cm, and the mass per unit length of the string is λ = 5.28 × 10^–3 kg/m.

(a) When θ = 17.0°, the plucked string is supposed to emit a fundamental frequency of f = 212 Hz. What value of the mass (M) is needed under these conditions?

(b) What is the full frequency range of the device (i.e., by changing the angle)?

(c) With the mass calculated in part (a), to what value should you set θ so that the fundamental frequency is 330 Hz?