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If f_A = 1/(2π)√(g/L_A) and f_B = 1/(2π)√(g/L_B), then f_A/f_B = ?

1. L_B/L_A
2. L_A/L_B
3. 4 = L_B/L_A
4. L_B/L_A regardless of mass

Correct answer: L_B/L_A

Solution

The frequencies f_A and f_B are inversely proportional to the square root of their respective lengths (L_A and L_B). Taking the ratio f_A/f_B, the square root terms invert, resulting in f_A/f_B = √(L_B/L_A), which simplifies to L_B/L_A.

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