Wave Model
Introduction & Overview
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Quick Overview
Standard
In the Wave Model, we analyze how a disturbance moves through a system. Transverse waves (like light or a string) oscillate at right angles to the direction of travel, whereas longitudinal waves (like sound) oscillate back and forth in the same direction. All waves are defined by mathematical properties such as frequency, wavelength, and speed, which are governed by the fundamental wave equation.
Detailed
The wave model provides a mathematical and physical framework to understand how energy propagates.
1. Types of Waves
- Mechanical Waves: Require a medium (solid, liquid, or gas) to travel. Energy is passed from particle to particle. (Example: Ocean waves, sound).
- Electromagnetic Waves: Disturbances in electric and magnetic fields. They do not require a medium and can travel through the vacuum of space. (Example: X-rays, Radio waves).
2. Wave Geometry
- Transverse Waves: The displacement of the medium is perpendicular to the direction of energy transfer. It consists of crests (high points) and troughs (low points).
- Longitudinal Waves: The displacement is parallel to the direction of energy transfer. These waves move via compressions (high pressure) and rarefactions (low pressure).
3. Fundamental Parameters
To describe a wave, we use specific measurements:
- Amplitude (): The maximum displacement from the rest position. Relates to the wave's energy.
- Wavelength (): The distance between two consecutive identical points (e.g., crest to crest).
- Frequency (): The number of cycles per second (Measured in Hertz).
- Period (): The time it takes for one complete cycle ().
- Wave Speed (): How fast the wave travels. Calculated as:
- Angular Frequency (): The rate of change of the phase angle ().
- Wave Number (): The spatial frequency of a wave ().
4. The One-Dimensional Wave Equation
The behavior of a wave in a medium is described by a second-order partial differential equation. This equation links how the wave changes in space to how it changes in time:
Essentially, this equation ensures that the "shape" of the wave remains consistent as it moves at a constant velocity .
Audio Book
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The Medium and the Message * **Chunk Text:** Mechanical waves require a medium (solid, liquid, or gas) to travel. Energy is passed from particle to particle. * **Detailed Explanation:** This explains why we can't hear sound in space. Sound needs atoms to bump into each other to pass the energy along. Without a medium, the energy has no "vehicle" to move. * **Real-Life Example or Analogy:** Think of a game of telephone. The message (energy) moves down the line, but the people (medium) stay in their seats.
Chapter 1 of 2
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Chapter Content
Mechanical waves require a medium (solid, liquid, or gas) to travel. Energy is passed from particle to particle.
* Detailed Explanation: This explains why we can't hear sound in space. Sound needs atoms to bump into each other to pass the energy along. Without a medium, the energy has no "vehicle" to move.
* Real-Life Example or Analogy: Think of a game of telephone. The message (energy) moves down the line, but the people (medium) stay in their seats.
Detailed Explanation
This explains why we can't hear sound in space. Sound needs atoms to bump into each other to pass the energy along. Without a medium, the energy has no "vehicle" to move.
* Real-Life Example or Analogy: Think of a game of telephone. The message (energy) moves down the line, but the people (medium) stay in their seats.
Examples & Analogies
Think of a game of telephone. The message (energy) moves down the line, but the people (medium) stay in their seats.
Transverse vs. Longitudinal * **Chunk Text:** Transverse waves oscillate perpendicular to travel; longitudinal oscillate parallel. * **Detailed Explanation:** This distinguishes the physical "shape" of the energy flow. In transverse waves, the motion is up-and-down while the wave moves forward. In longitudinal waves, it's a push-and-pull motion in the direction of travel. * **Real-Life Example or Analogy:** Shaking a rug is a transverse wave. Pushing a line of people from the back so they bump into each other is a longitudinal wave.
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Chapter Content
Transverse waves oscillate perpendicular to travel; longitudinal oscillate parallel.
* Detailed Explanation: This distinguishes the physical "shape" of the energy flow. In transverse waves, the motion is up-and-down while the wave moves forward. In longitudinal waves, it's a push-and-pull motion in the direction of travel.
* Real-Life Example or Analogy: Shaking a rug is a transverse wave. Pushing a line of people from the back so they bump into each other is a longitudinal wave.
Detailed Explanation
This distinguishes the physical "shape" of the energy flow. In transverse waves, the motion is up-and-down while the wave moves forward. In longitudinal waves, it's a push-and-pull motion in the direction of travel.
* Real-Life Example or Analogy: Shaking a rug is a transverse wave. Pushing a line of people from the back so they bump into each other is a longitudinal wave.
Examples & Analogies
Shaking a rug is a transverse wave. Pushing a line of people from the back so they bump into each other is a longitudinal wave.
Key Concepts
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Energy Transport: Waves move energy, not mass.
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The Wave Equation: The mathematical link between spatial and temporal changes in a wave.
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Phase: The position of a point in time on a cycle of a waveform.
Examples & Applications
Transverse: Light waves, radio waves, ripples on a pond.
Longitudinal: Sound waves, ultrasound, p-type earthquake waves.
Memory Aids
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Memory Tools
Analogy
Memory Tools
Transverse = Perpendicular; Longitudinal = Parallel.
Flash Cards
Glossary
- Trough
The lowest point of a transverse wave.
Reference links
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