Displacement profile in a longitudinal wave Steps:

• Recognize the wave as longitudinal, where air particle displacement is parallel to propagation direction.
• At an instant, displacement varies sinusoidally with distance along the wave, forming compressions and rarefactions.
• From point P to Q (distance x), plot displacement y versus position along the wave axis.
• Select the graph matching this sinusoidal pattern, as it represents the wave's spatial variation.

Why C is correct:

• C depicts sinusoidal displacement versus distance, aligning with the harmonic nature of progressive sound waves per the wave equation y = A sin(kx - ωt).

Why the others are wrong:

• A shows a transverse-like wiggle, incorrect for longitudinal particle motion.
• B indicates constant displacement, ignoring wave oscillation.
• D displays irregular or damped variation, not matching uniform progressive wave.

Final answer: C