Compressions in longitudinal wave displacement graphs occur at zero-displacement points with negative slope

Steps:

• In a longitudinal wave, compressions are regions where particles are closest, corresponding to negative ∂ξ/∂x on the displacement vs. distance graph.
• ∂ξ/∂x is the slope of the graph; maximum compression is where this slope is most negative.
• For a sinusoidal wave, this occurs at points where displacement ξ = 0 and the curve crosses the axis downward (negative slope).
• Examine the graph points: select the zero-displacement point with negative slope.

Why B is correct:

• B is the zero-displacement point with negative slope, where ∂ξ/∂x is most negative, defining the compression center per wave strain definition.

Why the others are wrong:

• A: Positive displacement peak (ξ max, slope ≈0), a rarefaction center.
• C: Negative displacement trough (ξ min, slope ≈0), a rarefaction center.
• D: Zero displacement but positive slope, a rarefaction center.

Final answer: B