The lower end of a uniform bar of mass 45.0 kg is attached to a wall by a frictionless hinge. The bar is held by a horizontal wire attached at its upper end so that the bar makes an angle of 30.0° with the wall. The wire has length 0.330 m and mass 0.0920 kg. What is the frequency of the fundamental standing wave for transverse waves on the wire?

Solution 59P The frequency of a fundamental standing wave in a wire is given by, 1 F f = 2L m …..(1) Here, F is the force on the wire, L is the length and m is the mass per unit length of the wire. Now, to understand the situation given in the question, let us have a look at the figure given below. 0 From the figure above, sin 30 = (Wire length)/(Bar length) 2 = 0.330 m/Bar length Bar length = 2 × 0.330 m = 0.660 m The distance between the lowest point of the bar to the wire (x) is calculated as follows, cos 30 = x/0.660 x = 0.660 m × cos 30 0 x = 0.571...