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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 I triple the mass per unit length of guitar string, its natural frequency changes by what factor? | |
Answer 0.58 | |
Notes
| User | Added | Note | e | d |
|---|---|---|---|---|
| KillGorack | 2023-07-20 19:48:53 | The natural frequency (f) of a vibrating string can be expressed by the formula: f = (1/2L) * sqrt(T/μ) where: L is the length of the string, T is the tension in the string, and μ is the linear mass density (mass per unit length) of the string. In this case, the mass per unit length (μ) is tripled, and the length and tension are kept constant. Thus, the new frequency (f') when the mass per unit length is tripled will be: f' = (1/2L) * sqrt(T/(3μ)) The new frequency f' is the old frequency f divided by sqrt(3). Therefore, the frequency changes by a factor of 1/sqrt(3), which is approximately 0.577. Thus, if the mass per unit length of a guitar string is tripled, its natural frequency will decrease by a factor of approximately 0.577. |
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