Problem 3

A taut string of length

L=0.80\,\mathrm m

is fixed at both ends and carries transverse waves at

v=120\,\mathrm{m/s}

. The endpoints are nodes; neglect bending stiffness and consider normal modes. (a) Find the first requested quantity. (b) Find the second quantity. (c) Determine the final result and check its units. (a) Find the funda (a) Find the fundamental wavelength and frequency. (b) Find the frequency of the mode with three half-wavelengths. (c) Count its antinodes.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

f_n=nv/(2L)

problems.proof.analysis

Rearranging the governing relation isolates the first requested result. Keeping the signs explicit also checks that its direction and magnitude are physically sensible.