Consider a stretched string under tension and fixed at both ends. If the tension is doubled and the cross-sectional area halved, then the frequency becomes:
Correct answer: A. Twice
- A. Twice
- B. Half
- C. Four times
- D. Eight times
Explanation
In a stretched string, the frequency of the fundamental mode is given by the formula: f = (1/2L) * √(T/μ), where T is the tension, L is the length, and μ is the mass per unit length. If the tension is doubled (T becomes 2T) and the cross-sectional area is halved, then the mass per unit length (μ) is also halved. Since frequency f is proportional to the square root of T/μ, doubling T and halving μ results in the frequency being multiplied by √(2/0.5) = √(4) = 2. Therefore, the frequency becomes twice its original value. The options 'Half', 'Four times', and 'Eight times' are incorrect as they do not correctly reflect the mathematical relationship between tension, mass per unit length, and frequency.
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