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The following physics responses are provided by a student and, as such, should be considered in that context. While every effort is made for accuracy, absolute correctness cannot be fully guaranteed.
| Question | |
C | 14 |
I | |
Question If the tension on a guitar string is increased by a factor of 3, the fundamental frequency at which it vibrates is changed by what factor? | |
Answer sqrt(3) | |
Notes
| User | Added | Note | e | d |
|---|---|---|---|---|
| KillGorack | 2023-07-20 20:27:20 | The fundamental frequency of a vibrating string is given by the formula: f = (1/2L) * sqrt(T/μ) where: f is the frequency, L is the length of the string, T is the tension in the string, μ is the linear density (mass per unit length) of the string. From this formula, you can see that the frequency is proportional to the square root of the tension. Therefore, if the tension T is increased by a factor of 3 (to become 3T), the frequency f' becomes: f' = (1/2L) * sqrt(3T/μ) = sqrt(3) * (1/2L) * sqrt(T/μ) = sqrt(3) * f Hence, the fundamental frequency at which the string vibrates is changed by a factor of sqrt(3), which is approximately 1.732. |
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