Question: If any time-dependent sinusoidal harmonic function, (f(x, t)=) (A sin (k x-omega t)), satisfies the wave equation, what determines the values of the wave number

If any time-dependent sinusoidal harmonic function, $f(x, t)=$ $A \sin (k x-\omega t)$, satisfies the wave equation, what determines the values of the wave number $k$ and the angular frequency $\omega$ for, say, a wave on a string?

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