posted by janny .
A 2.49-m-long string, fixed at both ends, has a mass of 7.17 g. If you want to set up a standing wave in this string having a frequency of 455 Hz and 5 antinodes, what tension should you put the string under?
String mass per unit length is
w = 0.00717/2.49 = 2.88*10^-4 kg/m
With five antinodes, the wavelength is
L = 2/5 * 2.49 = 0.996 m
The frequency is f = 455 Hz
The wave speed is C = L*f = 453.2 m/s
The tension T must provide that wave speed.
sqrt(T/w) = 453.2 m/s
Solve for T, in Newtons
T = w*(453.2)^2 = 59.2 N