6 - Dispersion and Wave Groups
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Practice Questions
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Define dispersion in the context of waves.
💡 Hint: Think about how different colors of light spread in a prism.
What is the superposition principle?
💡 Hint: Consider how sound waves combine.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is dispersion in wave phenomena?
💡 Hint: Think about how different colors in light travel at different speeds.
Phase velocity is defined as:
💡 Hint: What do we mean by a specific phase?
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Challenge Problems
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A string is vibrating, creating waves at different frequencies. If the phase velocity is 150 m/s and you have two frequencies, 50 Hz and 75 Hz, how does the wave shape evolve over time?
💡 Hint: Consider the implications of varying frequencies and their speeds on wave shape.
Derive an expression for group velocity given a nonlinear dispersion relation where ω(k) = ak^2 + bk + c. Determine vg.
💡 Hint: Differentiate the dispersion relation with respect to k.
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