Question 1100491: the frequency of vibration of a given string is directly proportion to the square root of the tension T and inversely proportional to the length L and the diameter D ,if T is increased by 50% and L is halved, calculate the percentage change in the frequency
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! y = k * x is direct variation formula.
y = k / x is inverse variation formula.
z = k * x / y is direct and inverse variation formula combined.
k is the constant of proportionality.
the frequency of vibration of a string is directly proportional to the square root of the tension T and inversely proportional to the length L and the diameter D.
i believe that, when they say inversely proportional to the length L and the diameter D, that they mean inversely proportional to L * D.
assuming that interpretation is correct, your formula will become V = (K * T) / (L * D).
if T is increased by 50% and L is halved, the formula would become:
V = (1.5 * K * T) / (.5 * L * D)
this can be simplified to V = (3 * K * T) / (L * D).
the frequency would be equal to 3 times what it was.
3 times what it was is 300% of what it was.
the frequency would be equal to 2 times more than what it was.
that would be an increase of 200% more than what it was.
i think, by change, they mean what it became, and, in my mind, it became 300% of what it was, so i would go with 300%.
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