Concept:A string fixed at both ends forms stationary waves. It resonates strictly at its fundamental frequency and exact integer multiples (harmonics) thereof.
Formula:$$ f_n = n \left( \frac{v}{2L} \right) $$
Solution:- First, calculate the fundamental frequency (first harmonic, \( n = 1 \)).
- Given: Velocity \( v = 24 \text{ m/s} \), Length \( L = 6.0 \text{ m} \).
- \( f_1 = \frac{24}{2 \times 6} = \frac{24}{12} = 2 \text{ Hz} \).
- The string will only resonate at whole integer multiples of this fundamental base frequency (\( n=1, 2, 3... \)).
- Harmonics: \( 1 \times 2 = 2 \text{ Hz} \), \( 2 \times 2 = 4 \text{ Hz} \), \( 3 \times 2 = 6 \text{ Hz} \), and so on.
- The set 2 Hz, 4 Hz, 6 Hz perfectly matches this sequence.
Why other options are incorrect:Option A describes harmonics of a 1 Hz fundamental. Option C describes harmonics of a 3 Hz fundamental. Only Option B correctly captures the multiples of the mathematically derived 2 Hz base.
Quality & Fidelity Assurance:
Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.