In a sound wave, a displacement node is a pressure antinode and vice versa, Why?

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter13: Mechanical Waves
Section: Chapter Questions
Problem 68P: A sound wave moves down a cylinder as in Active Figure 13.19. Show that the pressure variation of...
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In a sound wave, a displacement node is a pressure antinode and vice versa, Why?

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Node

Node is the point where amplitude of oscillation is minimum, i.e. displacement is minimum. We know that, pressure is inversely proportional to displacement. Thus, for minimum displacement, the pressure will be maximum. Hence, a displacement node is pressure antinode.  

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