SOLUTION: A pianos strings frequency (f) varies directly with the square root of the strings tension (t) and inversely with both the length (l) and diameter (d) The middle c note has a fr

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Question 612084: A pianos strings frequency (f) varies directly with the square root of the strings tension (t) and inversely with both the length (l) and diameter (d)
The middle c note has a frequency of 262 hz. the string producing this note has a tension of 670 and a length of 62 and a diameter of 0.1025 cm, write an equation that relates f,t,l, and d.
Also find the frequency of the note produced by a string with a tension of 1629 and a length of 201.g and a diameter of 0.49.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A pianos strings frequency (f) varies directly with the square root of the strings tension (t) and inversely with both the length (l) and diameter (d)
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f+=+k%2Asqrt%28t%29%2F%28l%2Ad%29
The middle C note has a frequency of 262 hz. the string producing this note has a tension of 670 and a length of 62 and a diameter of 0.1025 cm, write an equation that relates f,t,l, and d.
f+=+k%2Asqrt%28t%29%2F%28l%2Ad%29
262+=+k%2Asqrt%28670%29%2F%2862%2A0.1025%29
k = 64.324948
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Also find the frequency of the note produced by a string with a tension of 1629 and a length of 201.g and a diameter of 0.49.
f+=+k%2Asqrt%281629%29%2F%28201%2A0.49%29
f = 26.36 Hz
That's a note between G# and A, but out of tune.
G# or Ab = 25.96
A = 27.50
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A is exactly 27.5 Hz using International A-440 tuning.