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A steel wire of length 1 m, mass 0.1 kg and uniform cross-sectional area 107m2 is rigidly fixed at both ends. The temperature of the wire is decreased by 80/3C. If transverse waves are set up in the wire, the frequency (in Hz) is ___ .

The Young’s modulus of steel = 2×1011Nm2 and coefficient of linear expansion of steel = 1.2×105perC.


Solution

Contraction ΔL=αLΔθ

Young's modulus Y=TLAΔL;T = tension

 T=YAΔLL=YAαΔθ

=2×1011×107×1.2×105×803

=6.4 N

Frequency of fundamental mode is 

V=22LTμ;μ = mass per unit length of wire = 12×16.40.1=4 Hz
 

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