Wave speed is set by the medium, not the source
The mistake
Assuming shaking a rope faster makes the wave travel faster.
Why it feels right
More vigorous shaking feels like it should send the wave faster.
How to catch it
You changed v when only the frequency changed.
The first principle
v = √(T/μ) for a string — fixed by tension and density. Raising frequency shortens wavelength (v = fλ), not the speed.
worked mini-example
You shake a rope twice as fast. What happens to wave speed?
Common wrong move
It doubles.
Correct
Speed is unchanged; wavelength halves.
Test the repair SHM-02 · transfer
Make a fresh prediction before referring to the worked example.