how frequency and length are related with respect to proportionality
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Pitch is how these tones relate to each other. For a vibrating string, the frequency is inversely proportional to the length, directly proportional to the square root of its tension, and inversely proportional to the square root of its weight per unit length.
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The fundamental frequency of a vibrating string is inversely proportional to its length. ... The fundamental frequency of a vibrating string is inversely proportional to the square root of the mass per unit length.
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