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Which of the following statements is true? The frequency of a vibrating string is

Physics
JAMB 1979

Which of the following statements is true? The frequency of a vibrating string is

  • A. proportional to its length
  • B. inversely proportional to the tension within it
  • C. proportional to the aptitude of vibration
  • D. inversely proportional to its cross-section
  • E. proportional to the square root of the tension within it
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Correct Answer: Option E
Explanation

The frequency (f) of a vibrating string is determined by the laws of transverse vibrations, summarized by the formula:

f = \(\frac{\text{n}}{2L}\)\(\sqrt{\frac{T}{\mu}}\)

Where T is the tension, L is the length, and \(\mu\) is the mass per unit length. According to the Law of Tension, the frequency is directly proportional to the square root of the tension. (f ∝ \(\sqrt{T}\))


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