SOLUTION: The frequency of vibration of a guitar string varies directly as the square root of the tension and inversely as the length of the string. If the frequency is 40 vibrations per sec

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Question 867557: The frequency of vibration of a guitar string varies directly as the square root of the tension and inversely as the length of the string. If the frequency is 40 vibrations per second when the tension is 25 pounds and the length of the string is 3 feet, find the frequency when the tension is 36 pounds and the string is 4 feet long?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The frequency of vibration of a guitar string varies directly as the square root of the tension and inversely as the length of the string. If the frequency is 40 vibrations per second when the tension is 25 pounds and the length of the string is 3 feet, find the frequency when the tension is 36 pounds and the string is 4 feet long?
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F+=+k%2Asqrt%28T%29%2FL
40+=+k%2Asqrt%2825%29%2F3
Solve for k
k = 120/5 = 24
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find the frequency when the tension is 36 pounds and the string is 4 feet long?
F+=+k%2Asqrt%28T%29%2FL
F+=+24%2Asqrt%2836%29%2F4
F = 36 Hz
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That's a low note.
The formula is good for all vibrating strings under tension.
36 Hz and 40 Hz are more likely to be on a piano than a guitar.
Maybe a bass guitar, I'm not familiar with those.
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google Tal Wilkenfield for bass players, I love her.