Problem 4 (20 points)

A 1750 Newton irregular beam is hanging horizontally by the ends from the ceiling by two vertical wires (A and B). Each wire is 1.25 meter long and weighing 0.290 Newton. The center of gravity of the beam is 1/3 the distance along the beam from the end where wire A is attached.

Wire B is attached to the other end of the beam. At the beam, the wires are plucked at the same time to create waves along the wires.

(4 points) A detail sketch of the problem

4a) (8 points) The wave speeds on the wires are to takes on a new condition such that vA=2vB by moving wire A.

Where should wire A be placed from the center of gravity of the beam such that its wave speed is twice that of the wave speed in wire B?

That is, what is the new distance from the center of gravity of beam to where wire A is to be attached such that

vA=2vB?

4b) (8 points) What is the time difference between the arrival of the two wave pulses at the ceiling for part a above with the condition that vA=2vB?

That is, what is t=tBtA?