Consider the G string (196Hz) of a violin. It is ∼30 cm from bridge to nut (the fixed endpoints), and the tension in the string is ∼40 N.

(a) Infer the mass per unit length in the string and estimate its diameter. Hence estimate the strain in the string before being plucked. Estimate the strain’s increase if its midpoint is displaced through 3 mm.

(b) Now suppose that the string is released. Estimate the speed with which it moves as it oscillates back and forth.

(c) Estimate the dipolar sound power emitted and the distance out to which the note can be heard (when its intensity is a few decibels). Do your answers seem reasonable? What factors, omitted from this calculation, might change your answers?