HKDSE Physics: Longitudinal Wave and Displacement-Distance Graph

t = 0.00 s

Wave Motion Direction:

Simulation Speed:

Compression (C) Rarefaction (R) Particle Velocity (v)

Sign Convention: Positive s = Motion in wave direction | Negative s = Motion opposite wave direction

PANEL 1: Particle Oscillations (Longitudinal Motion in Medium)

Aligned Distance x Axis Hover or click on graph/particles to inspect values

PANEL 2: Displacement-Distance Graph s(x, t)

Wave Physical Parameters

Wavelength (lambda) 4.0 m

Distance between consecutive C or R points.

Frequency (f) 0.50 Hz

Period T = 2.00 s.

Amplitude (A) 1.20 cm

Max particle displacement from equilibrium.

Wave Speed v = f * lambda = 2.00 m/s

Wave Number k = 2 * pi / lambda = 1.57 rad/m

Angular Freq omega = 2 * pi * f = 3.14 rad/s

Visual Analysis Overlays

Highlight Compressions (C) and Rarefactions (R) Show Instantaneous Velocity Vectors (v) Show Equilibrium Alignment Lines Show Shifted Profile Overlay (Wave Shift Method) Track and Label Key Test Particles (P1, P2, P3, P4)

HKDSE Physics Revision Guide: Longitudinal Waves and s-x Graphs

Questions on longitudinal waves and displacement-distance (s-x) graphs are standard HKDSE exam items. Below is a structured summary of core concepts, sign conventions, and analytical techniques.

1 HKDSE Sign Convention Definition

Positive Displacement (+s): Particle is displaced from equilibrium in the SAME direction as wave motion.
Negative Displacement (-s): Particle is displaced from equilibrium in the OPPOSITE direction to wave motion.
Zero Displacement (s = 0): Particle is currently passing through its equilibrium position. Note that particle speed is MAXIMUM at s = 0!

2 Locating C and R on the s-x Graph

Compressions (C) and Rarefactions (R) always occur at zero-crossing points (s = 0):

Compression (C) Particles gather together (Max density)

For a wave travelling rightward (+x), C corresponds to a negative slope (ds/dx < 0). Particles to the left moved right (+s) and particles to the right moved left (-s).

Rarefaction (R) Particles pull apart (Min density)

For a wave travelling rightward (+x), R corresponds to a positive slope (ds/dx > 0). Particles to the left moved left (-s) and particles to the right moved right (+s).

3 Determining Particle Velocity Direction: "Wave Shift Method"

Step 1: Shift Profile

Draw a dashed curve shifted slightly in the direction of wave travel (Right if wave travels right; Left if wave travels left).

Step 2: Compare Value

At position x, observe whether the new shifted profile goes UP towards +s or DOWN towards -s.

Step 3: Conclude Direction

If shift is UP (+s) -> particle moves in wave direction.
If shift is DOWN (-s) -> particle moves opposite wave direction.

Feature / Point	Graph Slope (ds/dx)	Particle Motion (Wave Travelling RIGHT ->)	Particle Motion (Wave Travelling LEFT <-)
Compression (C)	ds/dx < 0 (Rightward wave)	Moving RIGHT (Max speed)	Moving LEFT (Max speed)
Rarefaction (R)	ds/dx > 0 (Rightward wave)	Moving LEFT (Max speed)	Moving RIGHT (Max speed)
Peak Displacement (s = +A or -A)	ds/dx = 0	Instantaneously AT REST (v = 0)	Instantaneously AT REST (v = 0)

HKDSE Physics Topic III: Waves