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Answer:
(a) 498.4 Hz
(b) 442 Hz
Solution:
As per the question:
Length of the wire, L = 1.80 m
Weight of the bar, W = 531 N
The position of the copper wire from the left to the right hand end, x = 0.40 m
Length of each wire, l = 0.600 m
Radius of the circular cross-section, R = 0.250 mm =
Now,
Applying the equilibrium condition at the left end for torque:
The weight of the wire balances the tension in both the wires collectively:
Now,
The fundamental frequency is given by:
where
(a) For the fundamental frequency of Aluminium:
where
(b) For the fundamental frequency of Copper:
where