Concept:The spatial structure of a standing wave directly dictates its wavelength. The distance between two consecutive antinodes represents exactly half a wavelength.
Formula:$$ \frac{\lambda}{2} = \text{Distance between antinodes} $$
$$ v = f \lambda $$
Solution:- We are given the distance between antinodes: \( \frac{\lambda}{2} = 25 \text{ cm} \).
- Solve for wavelength: \( \lambda = 50 \text{ cm} = 0.5 \text{ m} \).
- Using the wave equation \( f = \frac{v}{\lambda} \), substitute \( v = 300 \text{ m/s} \) and \( \lambda = 0.5 \text{ m} \).
- \( f = \frac{300}{0.5} = 600 \text{ Hz} \).
Why other options are incorrect:Option A assumes 25 cm is the full wavelength (\( 300/0.25 = 1200 \text{ Hz} \), ). If a student assumes 25 cm is \( \lambda/4 \), they get 1 meter, yielding 300 Hz (Option B). Thus, confusing the loop geometry is the primary trap.
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