A wave has dispersion ω(k)=7k + 6k³ with SI-compatible constants. Find group velocity at k=12 m⁻¹. Round the final result to 4 decimal places if needed. Answer in m/s.
Answer and explanation
2599 m/s
Differentiate before substituting: vg=7+18k².
Subjects
Waves dispersion
Choose questions individually, practise online, or create a worksheet with matching answers. Counts include generated variants, not only authored originals.
Make a worksheet355 question instances
Sample exercises
A wave has dispersion ω(k)=12k + 6k³ with SI-compatible constants. Find group velocity at k=5 m⁻¹. Round the final result to 4 decimal places if needed. Answer in m/s.
Answer and explanation
462 m/s
Differentiate before substituting: vg=12+18k².
A wave has dispersion ω(k)=6k + 7k³ with SI-compatible constants. Find group velocity at k=11 m⁻¹. Round the final result to 4 decimal places if needed. Answer in m/s.
Answer and explanation
2547 m/s
Differentiate before substituting: vg=6+21k².
Study notes
Group velocity from a dispersion relation
The group velocity generally differs from phase velocity ω/k; the dispersion constants carry compatible SI units.
Advanced universityGroup velocity from a dispersion relation · formula reference
The group velocity generally differs from phase velocity ω/k; the dispersion constants carry compatible SI units.
Advanced universityRelated courses
Physics4 lessons
University mechanics and waves
Connect rotation, oscillations, central forces and continuous wave models.
32 quiz questions · University
Physics4 lessons
Fields, circuits and thermal physics
Work with Gauss laws, electrical field models, thermodynamic laws and electromagnetic waves.
32 quiz questions · University
Physics4 lessons
Introduction to quantum physics and relativity
Compare relativistic measurement with quantum states, the Schrödinger equation and uncertainty.
32 quiz questions · University
Physics3 lessons
Analytical and statistical mechanics
Use Lagrangian and Hamiltonian methods, then interpret canonical ensembles.
24 quiz questions · Advanced university
Physics4 lessons
Advanced physics methods and spacetime
Explore perturbation theory, scattering, variational quantum estimates and a conceptual bridge to general relativity.
32 quiz questions · Advanced university