Concept:The fundamental frequency of a stretched string depends on its length, tension, and linear mass density.
Formula:$$ v = \sqrt{\frac{T}{m}} $$
$$ f_1 = \frac{v}{2L} $$
Solution:- Note: The unit 'kg/s' in the question is a historical typo for mass per unit length, which should be kg/m.
- First, find the wave speed: \( v = \sqrt{\frac{10}{0.004}} = \sqrt{\frac{10000}{4}} = \sqrt{2500} = 50 \text{ m/s} \).
- Now, apply the fundamental frequency formula with length \( L = 2 \text{ m} \):
- \( f_1 = \frac{50}{2 \times 2} = \frac{50}{4} = 12.5 \text{ Hz} \).
Why other options are incorrect:Option D occurs if the student forgets the '2' in the denominator. Option C occurs if one mistakenly uses \( L \) in the numerator instead of denominator.
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