Wave Displacement and Phase

Definition

Displacement describes how far a particle is from its equilibrium position at a given instant. Phase describes the stage of oscillation of that particle within its cycle.

Phase allows comparison between different particles or points on a wave.

This concept supports oscillations, waves, and wave superposition.

---

Why It Matters

Understanding displacement and phase is essential for:

• interpreting wave graphs
• comparing motion of different points
• predicting constructive and destructive interference

Confusion between displacement, amplitude, and phase leads to incorrect reasoning in wave problems.

---

Key Representations

Displacement

• Measured from equilibrium
• Can be positive or negative
• Varies with time and position

---

Phase

Phase is measured in:

• fractions of a cycle
• degrees
• radians

For a wave:

$$\text{phase}=\omega t-kx$$

where:

• $\omega$ = angular frequency
• $k$ = wave number

---

Phase Difference

The phase difference between two points is:

$$\Delta \varphi ={\varphi }_1-{\varphi }_2$$

---

Interpretation of Phase Difference

• $\Delta \varphi =0$ → in phase
• $\Delta \varphi =\pi$ → completely out of phase
• $\Delta \varphi =2\pi$ → one full cycle difference

---

Graphical Representation

• Displacement–time graph: shows oscillation of a single point
• Wave profile (snapshot): shows displacement across space at an instant

---

Key Distinction

• Amplitude: maximum displacement
• Displacement: instantaneous position
• Phase: position within the cycle

---

Key Insight

Displacement tells you where the particle is, while phase tells you where it is in the cycle.

Links

• Related: superposition
• Related: oscillations
• Related: waves