Practice Dispersion And Wave Groups (6) - Non-Dispersive Transverse and Longitudinal Waves in 1D & Introduction to Dispersion

Practice: Dispersion and Wave Groups

Lesson 6Non-Dispersive Transverse and Longitudinal Waves in 1D & Introduction to Dispersion

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10 questions

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4 questions · about 3 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define dispersion in the context of waves.
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Think about how different colors of light spread in a prism.
Question 2.
What is the superposition principle?
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Consider how sound waves combine.
3Question 3.
What is dispersion in wave phenomena?
- Wave speed is constant
- Wave speed varies with frequency
- Wave motion is limited
- None of the above
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Think about how different colors in light travel at different speeds.
4Question 4.
Phase velocity is defined as:
- True
- False
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What do we mean by a specific phase?
Question 5.
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?
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Consider the implications of varying frequencies and their speeds on wave shape.
Question 6.
Derive an expression for group velocity given a nonlinear dispersion relation where ω(k) = ak^2 + bk + c. Determine vg.
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Differentiate the dispersion relation with respect to k.

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