The frequency of the fundamental mode of a string stretched by a tension / and having mass m and length l is given by:
Correct answer: B. f = 1/2l √T/m
- A. f = ½ √T/ml
- B. f = 1/2l √T/m
- C. f = 1/2l√T/m
- D. f = 1/2√T/m
Explanation
The fundamental frequency of a string stretched by tension T, with mass m and length l, is given by the formula f = 1/2l √T/m. This formula considers the tension's impact on wave speed and the string's physical properties. Option B correctly represents this formula. Option A misplaces the square root and factors, leading to an incorrect expression. Option C closely resembles the correct formula but contains a typographical error, which makes it incorrect. Option D omits the factor of length, which is critical in determining the frequency.
This question appeared on the ETEA MDCAT 2006 paper, which you can sit online with every answer explained.
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About Stationary Waves
Stationary waves form when two waves of the same frequency and amplitude travel in opposite directions and interfere. The topic covers nodes, antinodes, wavelength, phase, resonance, and the allowed frequencies on strings and in air columns. Unlike progressive waves, stationary waves do not transfer energy from one point to another.
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