IB Physics: Waves Practice - Wyatt's Notes
IB Physics — Waves Practice
16 MCQ practice problems covering core IB Physics wave behaviour content, from basic wave properties to interference, standing waves, and the Doppler effect.
Practice Questions
Intuition
For wave problems, always identify whether you’re dealing with a travelling wave (moving through space) or a standing wave (stationary pattern). For interference, draw a path difference diagram: if the path difference from two sources to a point is a whole number of wavelengths, you get constructive interference; if it’s a half-wavelength (or odd multiple), you get destructive. For the Doppler effect, remember that the source moving toward you increases frequency (blue shift), while moving away decreases it (red shift).
Why it matters: Wave problems test your understanding of superposition, interference, and resonance — concepts that apply to sound, light, radio, and many other phenomena. These skills are essential for telecommunications, medical imaging, and understanding the nature of light. These practice questions range from basic wave equation applications to complex interference patterns.
Worked Example
Question: A diffraction grating has 500 lines per mm. What is the angle of the first-order maximum for light of wavelength 600 nm?
Solution: d = 1/500 mm = 2 × 10⁻⁶ m = 2000 nm. Using d sinθ = nλ: sinθ = nλ/d = (1 × 600) / 2000 = 0.3. θ = sin⁻¹(0.3) = 17.5°. For the second order (n = 2): sinθ = 1200/2000 = 0.6, θ = 36.9°. For the third order (n = 3): sinθ = 1800/2000 = 0.9, θ = 64.2°.
Common Mistakes
- Forgetting that frequency does not change when a wave enters a new medium. Only wavelength and speed change. This is a very common MCQ trap — always remember that frequency is determined by the source.
- Confusing the conditions for constructive and destructive interference in diffraction gratings. For a grating with slit separation d, constructive interference occurs when d sinθ = nλ, where n is an integer. Destructive interference occurs between the maxima.
- Misidentifying the fundamental frequency of a standing wave. For a string fixed at both ends, the fundamental has nodes at both ends and one antinode in the middle, giving λ = 2L. The second harmonic has two antinodes, giving λ = L.
- Forgetting that the speed of sound in air increases with temperature (approximately 0.6 m/s per °C). This affects calculations involving sound waves at different temperatures.
Cross-References
- Kinematics: Kinematics describes particle motion, and oscillating particles in waves follow kinematic principles.
- Mechanics: Mechanics covers energy transfer, and waves are a mechanism for transferring energy without transferring matter.
- Nuclear and Quantum: Wave-particle duality connects wave phenomena with particle properties — the photoelectric effect and de Broglie wavelength bridge these concepts.
- Electricity: Electromagnetic waves are oscillating electric and magnetic fields, and AC circuits involve wave phenomena.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.