Physics HL
Physics HL
5
Chapters
329
Notes
Theme A - Space, Time & Motion
Theme A - Space, Time & Motion
Theme B - The Particulate Nature Of Matter
Theme B - The Particulate Nature Of Matter
Theme C - Wave Behaviour
Theme C - Wave Behaviour
Theme D - Fields
Theme D - Fields
Theme E - Nuclear & Quantum Physics
Theme E - Nuclear & Quantum Physics
IB Resources
Theme C - Wave Behaviour
Physics HL
Physics HL

Theme C - Wave Behaviour

Understanding Standing Waves: Origins & Key Principles

Word Count Emoji
611 words
Reading Time Emoji
4 mins read
Updated at Emoji
Last edited on 5th Nov 2024

Table of content

What is a standing wave? 🎸

Standing waves form when two or more traveling waves interact, especially when they're identical and moving in opposite directions. Imagine two waves: one red, one blue. When they meet, they produce a black wave.

 

Real World Example: Think about a guitar string. When you pluck it, standing waves are formed, and that’s why you hear a sound!

Key points ✨

  • Superposition: When two waves meet, they can either add up (constructive interference) or cancel out (destructive interference).
  • Nodes (N)
    • Points where the amplitude of the wave is zero (red and blue waves cancel out).
    • The medium (like a string or air in a flute) always has zero displacement at these points.
  • Antinodes (A)
    • Points of maximum amplitude on a standing wave.
    • Places where the red and blue waves are exactly in phase, resulting in the black wave having the largest possible displacement.
  • Phase & Frequency
    • Standing waves oscillate at the same frequency as the traveling waves.
    • Between two adjacent nodes (e.g., N to N'), all particles move in sync (in phase). But in adjacent nodal regions, they’re out of phase by 180° (or π rad).
  • Wavelength & Amplitude
    • Distance between two adjacent nodes (or antinodes) is equal to half the original wave's wavelength.
    • The amplitude varies along the standing wave. It's zero at the node and maximum at the antinode.

🌍 Real World Analogy: Imagine a busy walkway where people from two entrances meet in the middle. Some people are perfectly synchronized and walk together (like antinodes), while others clash and stop (like nodes).

 

🖥 To See It in Action: Search online for “applet for standing wave formation”. Animations can help visualize and understand the formation of standing waves.

Worked example 📝

  • Problem: Two waves with 80cm wavelength move in opposite directions on a rope. Label nodes and compare amplitudes and phases of two points P and Q.
  • Solution: a. Nodes are 40cm apart. So, nodes are at x=0, 40cm, and 80cm. b. P & Q are 180° out of phase. Q, being between two nodes, has a greater amplitude than P. c. At time t = T/4, P is at maximum positive displacement and Q is at maximum negative displacement.

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IB Resources
Theme C - Wave Behaviour
Physics HL
Physics HL

Theme C - Wave Behaviour

Understanding Standing Waves: Origins & Key Principles

Word Count Emoji
611 words
Reading Time Emoji
4 mins read
Updated at Emoji
Last edited on 5th Nov 2024

Table of content

What is a standing wave? 🎸

Standing waves form when two or more traveling waves interact, especially when they're identical and moving in opposite directions. Imagine two waves: one red, one blue. When they meet, they produce a black wave.

 

Real World Example: Think about a guitar string. When you pluck it, standing waves are formed, and that’s why you hear a sound!

Key points ✨

  • Superposition: When two waves meet, they can either add up (constructive interference) or cancel out (destructive interference).
  • Nodes (N)
    • Points where the amplitude of the wave is zero (red and blue waves cancel out).
    • The medium (like a string or air in a flute) always has zero displacement at these points.
  • Antinodes (A)
    • Points of maximum amplitude on a standing wave.
    • Places where the red and blue waves are exactly in phase, resulting in the black wave having the largest possible displacement.
  • Phase & Frequency
    • Standing waves oscillate at the same frequency as the traveling waves.
    • Between two adjacent nodes (e.g., N to N'), all particles move in sync (in phase). But in adjacent nodal regions, they’re out of phase by 180° (or π rad).
  • Wavelength & Amplitude
    • Distance between two adjacent nodes (or antinodes) is equal to half the original wave's wavelength.
    • The amplitude varies along the standing wave. It's zero at the node and maximum at the antinode.

🌍 Real World Analogy: Imagine a busy walkway where people from two entrances meet in the middle. Some people are perfectly synchronized and walk together (like antinodes), while others clash and stop (like nodes).

 

🖥 To See It in Action: Search online for “applet for standing wave formation”. Animations can help visualize and understand the formation of standing waves.

Worked example 📝

  • Problem: Two waves with 80cm wavelength move in opposite directions on a rope. Label nodes and compare amplitudes and phases of two points P and Q.
  • Solution: a. Nodes are 40cm apart. So, nodes are at x=0, 40cm, and 80cm. b. P & Q are 180° out of phase. Q, being between two nodes, has a greater amplitude than P. c. At time t = T/4, P is at maximum positive displacement and Q is at maximum negative displacement.

Unlock the Full Content! File Is Locked Emoji

Dive deeper and gain exclusive access to premium files of Physics HL. Subscribe now and get closer to that 45 🌟

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