Selected Solutions $$

• 1.We know from class that the period of a pendulum undergoing small angular displacement is T = 2p(L/g)^1/2. If we solve this equation for L, we get

  L = T² g/(4p²)

  Plugging in the values from the problem, we get:

  L = (88.4 s²)(9.8 m/s²)/(39.4) = 22.0 m

• 2. For waves travelling on a string, we know that the wave speed is given by

  v = (T/m)^1/2

  For a wave speed of 20.0 m/s and a tension of 6.0 N, we find that the mass per unit length of the string is

  m = T/v² = 6.0 N/400 m²/s² = .015 kg/m

  In order to get a waves speed of 30.0 m/s, we need the tension to be

  T = v²m = (900 m²/s²)(.015 kg/m) = 13.5 N.