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# Dispersion Relation for Waves on a String

**Keywords:**Waves, Middle Division, Dispersion Relation, Frequency, Wave Number, Interactive Demo

### Highlights of the activity

- This integrated lab activity is designed to help upper-division undergraduate students observe different resonances and explore the dispersion relation for waves on a string.
- Students used an experimental set-up to find the angular frequency of the wave.
- The compare and contrast wrap-up discussion compiles each group's result to determine the dispersion relation for waves by plotting the angular frequency of the waves as a function of wave vector.

### Reasons to spend class time on the activity

Students generally do not consider the dispersion relations in lower division course. We find that middle division students know that speed of a wave is the product of the wavelength and frequency, but they don't think of angular frequency as a function of wave number, nor are they aware of the different types of speed relevant in the study of waves: phase velocity, group velocity and material velocity. This activity is used to introduce these important ideas.