Concept:A full longitudinal wave cycle consists of one compression and one rarefaction. Therefore, the distance between the center of a compression and the center of the very next rarefaction is exactly half a wavelength (\( \lambda/2 \)).
Formula:$$ v = f\lambda \implies \lambda = \frac{v}{f} $$
Solution:- Note: The question says "angular frequency" but provides the unit Hz, which signifies standard linear frequency (\( f \)). We will proceed using \( f = 440 \text{ Hz} \).
- First, find the full wavelength: \( \lambda = \frac{340 \text{ m/s}}{440 \text{ Hz}} = \frac{34}{44} \approx 0.7727 \text{ m} \).
- The question asks for the separation between a compression and an adjacent rarefaction, which is \( \frac{\lambda}{2} \).
- \( \frac{\lambda}{2} = \frac{0.7727}{2} \approx 0.386 \text{ m} \).
Why other options are incorrect:Mathematical errors in division yield the other decimal numbers. The accepted answer is fundamentally derived from the full wavelength calculation.
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