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Why not? Not to be overly terse . . . because it's NOT inversely proportional to the mass per unit length. It's inversely proportional to the SQUARE ROOT of the MPUL. If the fundamental frequency of a string were inversely proportional to its MPUL, then doubling the MPUL of the string would cut the fundamental frequency in half (that is, reduce it 50 percent). But we know from observation and analysis that that is not the case. If we double the MPUL of the string, then the fundamental frequency is reduced by about 29 percent, not 50 percent. To reduce the fundamental frequency of the string by half, we would have to quadruple the MPUL of the string!

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Q: Mersenne's Law says the frequency of a vibrating string is inversely proportional to the square root of the mass per unit length but why not simply to the mass per unit length?
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