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On a string instrument, the length of a string "l"

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varies inversely as the frequency.

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So, l = k*1/f.

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An 11-inch string has a frequency of 400 cycles per second

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So, f = 400 cycles / second

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Find the constant of proportionality and

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then find the frequency of a 10 inch string

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So 11 = k *1/400. So to solve for the constant of proportionality

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we will mutiply both sides by 400 cycles / second

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so the left hand side becomes 400 * 11 = 4400 cycles*inches/second

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4400 cycles*inches/second = k

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We can say the length = 4400cycles*inches/second * 1/f

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Now we are taking of a situation where l= 10 inches

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10 inches = 4400 cycles*inches/second * 1/f

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We could mutiply both sides by "f" & we can also divide

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both sides by 10 inches.

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Left hand side we are left with "f" = frequency

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Right hand side we have 4400/10 = 440cycles/second

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So when our string is 10 inches long

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our frequency has increased to 440 cycles/second

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So when our string was 11 inches long f= 400cycles/second

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when our string is shorter at 10 inches our

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f has increased to 440 cycles/second