Question

A particularly beautiful note reaching your ear from a rare Stradivarius violin has a wavelength of 39.1 cm. The room is slightly warm, so the speed of sound is 344 m/s.

If the string's linear density is 0.740 g/m and the tension is 160 N , how long is the vibrating section of the violin string? Express your answer with the appropriate units.

Answer 1

The frequency of the wave is given by

$f = \frac{nv}{2l}= \frac{v_s}{\lambda}\\ l = \frac{v\lambda}{2v_s} = \frac{\lambda}{2v_s}*\sqrt{\frac{T}{\mu}}= \frac{0.391}{2*344}\sqrt{\frac{160}{0.00074}}= 0.2643m = 26.43cm$