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Check out this simulation I put together using Scratch that shows that changes to wave speed DO NOT affect frequency! scratch.mit.edu/projects/1904...
TABLE OF CONTENTS:
2:32 - What determines the frequency of a wave?
3:36 - Does "higher frequency" mean "faster waves"?
4:56 - What happens if a wave's speed changes? Does frequency change then?
5:50 - How are frequency and wavelength related?
6:54 - Mathematical relationships
8:15 - Practice problems