A piano wire has length L and mass M. If its fundamental frequency is f, its tension is:
Correct answer: C. 4LMf2
- A. 2Lf/m
- B. 2Mf2/L
- C. 4LMf2
- D. 4f2L3/M
Explanation
The fundamental frequency of a vibrating string is given by the formula f = (1/2L)√(T/μ), where f is the frequency, L is the length of the string, T is the tension, and μ = M/L is the mass per unit length of the string. Solving for tension T, we rearrange the formula to get T = 4LMf2. Option C correctly represents this expression.Option A does not account for the square of the frequency or the mass, leading to an incorrect result. Option B incorrectly divides by length and does not properly incorporate the square of the frequency. Option D incorrectly includes a cubed length term and misplaces the variables in the formula, leading to an incorrect expression for tension.
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Progressive waves transfer energy through oscillations, with wavelength, frequency, amplitude and wave speed related by v = fλ; sound speed depends on the medium. Superposition produces interference and stationary waves in strings and organ pipes, while simple harmonic motion describes the oscillation itself and must be distinguished from wave propagation.
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