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I understand conceptually why amplitude doesn't affect frequency (especially when relating to sound - singing louder shouldn't change the frequency of the note I sing). However, the equation for the maximum velocity of an object in simple harmonic motion is $$ v = A \cdot \omega $$ where $A$ is the amplitude and $\omega$ the angular speed.

But I also know that $\omega = 2\pi\cdot f$

So there is an equation $v = A\cdot2\pi f$ that relates amplitude and frequency but they don't have a relationship. How?

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  • $\begingroup$ Please, in the future use proper maths markup (see my edit to learn how this is done with TeX / MathJax). $\endgroup$
    – leftaroundabout
    Commented Feb 24, 2016 at 16:30

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You are presuming that the maximum velocity stays the same; it won't. If you have higher amplitude, but the same frequency, then things will move faster at the extremes to maintain the frequency. If you constrain yourself to maintain the max velocity, then your amplitude and frequency are dependent on each other.

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