Lesson Plan

• Describe how the superposition of two opposite‑traveling waves creates a stationary wave.
• Apply the graphical method to construct the resultant wave at successive instants.
• Identify and label nodes and antinodes on a string using the spatial condition sin(kx)=0 or ±1.
• Calculate the allowed wavelengths and frequencies for a string fixed at both ends.

• Projector or interactive whiteboard
• Graph paper and rulers
• Calculator
• Worksheet with wave‑drawing tasks
• String with fixed supports for a short demo
• Prepared slides showing the trigonometric identity

Begin with the question, “What happens to a guitar string when it vibrates?” Students recall wave superposition and sine functions. Explain that today they will see why certain points stay still while others move maximally, and they will know how to prove it graphically. Success criteria: students will draw the stationary‑wave pattern and correctly label all nodes and antinodes.

1. Do‑now (5 min): short quiz on wave superposition and phase.
2. Mini‑lecture (10 min): introduce stationary waves and the graphical method.
3. Guided practice (15 min): students draw two opposite travelling sine waves at t=0, T/4, T/2 on graph paper and add them to obtain the resultant pattern.
4. Pair activity (10 min): using the worksheet, identify nodes and antinodes and record their positions.
5. Whole‑class check (5 min): discuss answers, clarify the sin(kx) conditions.
6. Application (5 min): calculate allowed wavelengths for a string of length L fixed at both ends.

Summarise that stationary waves arise from the superposition of two identical opposite‑travelling waves and that nodes and antinodes follow simple spatial conditions. For the exit ticket, each student writes one mathematical condition for a node and one for an antinode. Homework: complete the worksheet problems on standing waves on strings and prepare a short explanation of why only half‑wave multiples fit a fixed string.