The tension along a wire reduced by 19 %.The percentage reduction in frequency will be
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The percentage decrease in frequency is 10%.
Since frequency is proportional to the square root of tension,
f ∝ √T
we can use the following equation to solve the problem.
(f1/f2) = √(T1 / T2)
T1=100%
T2=81% since tension decreased by 19%.
(f1 / f2) = √[(T1) / (0.81 T1)]
(f1 / f2) = √[(100) / 81] = (10 / 9)
(f2 / f1) = (9 / 10)
f1 – (f2 / f1) = 1 – (9 / 10)
[(f1 – f2) / f1] = (1 / 10)
% decrease in frequency = (1 / 10) × 100 = 10%
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