SOLUTION: The frequency of vibration (f) of a guitar string varies directly as the square root of the tension (T) and inversely as the length (L) of the string. If the frequency is 40 vibrat

Algebra ->  Equations -> SOLUTION: The frequency of vibration (f) of a guitar string varies directly as the square root of the tension (T) and inversely as the length (L) of the string. If the frequency is 40 vibrat      Log On


   

Question 1055120: The frequency of vibration (f) of a guitar string varies directly as the square root of the tension (T) and inversely as the length (L) of the string. If the frequency is 40 vibrations per second when the tension is 25 lb and the length of the string is 3 ft, find the frequency when the tension is 81 lb and the string is 4 ft long.
Answer by ikleyn(52756) About Me  (Show Source):
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The frequency of vibration (f) of a guitar string varies directly as the square root of the tension (T) and inversely as the length (L)
of the string. If the frequency is 40 vibrations per second when the tension is 25 lb and the length of the string is 3 ft,
find the frequency when the tension is 81 lb and the string is 4 ft long.
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The condition says that f = k%2A%28sqrt%28T%29%2FL%29, where "k" is the proportionality coefficient, which is constant.

At these circumstances, k = %28f%2AL%29%2Fsqrt%28T%29 is the constant.

Therefore,

%2840%2A3%29%2Fsqrt%2825%29 = %28x%2A4%29%2Fsqrt%2881%29,   (*)

where "x" is the frequency under the question.

Simplify (*)

%2840%2A3%29%2F5 = %28x%2A4%29%2F9.

Now solve for x and get the answer.