What's the linear mass density of a string?

PLEASE HELP! A 10 kg mass hangs in equilibrium from a string of total length L = 5.0 m?

• A 10 kg mass hangs in equilibrium from a string of total length L = 5.0 m and linear mass density µ = 0.0036 kg/m. The string is wrapped around two light, frictionless pulleys that are separated by the distance d = 2.0 m (Fig. P14.32a). http://www.webassign.net/sf5/p14_32.gif Figure P14.32 (a) Determine the tension in the string. I got 65.74 N (which is right) (b) At what frequency must the string between the pulleys vibrate in order to form the standing wave pattern shown in Figure P14.32b? ________Hz (I got 405.401 but is wrong)

• Answer:

  The speed of a wave on a string is v = √[ T / μ ] and the speed of any wave is v = fλ so fλ = √[ T / μ ] Solve for the frequency f f = (1/λ) √[ T / μ ] From the picture, the wavelength λ is 2/3 the distance between the pulleys. f = [ 3 / (2∙2 m) ] √[ 65.74 N / 0.0036 kg/m ] = 101 Hz Note that your answer is exactly 4 times my answer (if you ignore significant figures). Perhaps you just forgot to divide by (2∙2 m) when performing the calculation.