For a longitudinal wave in air, the excess pressure and displacement are related such that
A{'text': 'They are exactly out of phase by π/2 rad apart', 'label': 'A'}
B{'text': 'They vary exactly in phase with one another everywhere', 'label': 'B'}
C{'text': 'They vary independently with no consistent relation', 'label': 'C'}
D{'text': 'They are always equal in magnitude at every space point', 'label': 'D'}
Answer & Solution
Correct answer: A. {'text': 'They are exactly out of phase by π/2 rad apart', 'label': 'A'}
1. In a sound wave, pressure variation δp and particle displacement y are related.
2. δp is proportional to the negative of the space derivative of y (from Newton's second law + elastic behaviour).
3. That derivative introduces a π/2 phase shift.
4. So pressure and displacement waves are out of phase by π/2 — pressure nodes are displacement antinodes.
_Source: NCERT Class 11 Physics, Ch 14 "Waves", §14.4_
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