the lower end of a uniform bar of mass 45kg is attached to a wall by a frictionl

Question

the lower end of a uniform bar of mass 45kg 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 with the wall. what is the frequency of the fundamental standing wave for transverse waves on the wire

15.59 CP 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 hori- zontal 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?

Explanation / Answer

mass of the bar is 45 kg and length of the wire is 0.33 m and mass of 0.0920 kg

Tension in the string T = (1/2) mg*tan 30 = 22.5*9.81*tan 30 = 127.44 N

Mass per unit length of the wire = 0.0920/ 0.33 = 0.2788 kg/m

Frequency f = (1/2L)* ( T / m)

                   = [1/ (2*0.33)]* ( 127.44 / 0.2788) = 33.2 Hz

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