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A rightward-traveling wave is expressed as $f(x,t)=f(x-vt,0)$ because the wave maintains its shape while shifting horizontally. After time $t$, the wave has moved a distance $vt$ to the right.

Conditions: The wave propagates in the positive x-direction.; The propagation speed is constant $v$.; The waveform remains unchanged during propagation.

A rightward-traveling wave is expressed as $f(x,t)=f(x-vt,0)$ because the wave maintains its shape while shifting horizontally. After time $t$, the wave has moved a distance $vt$ to the right.

Conditions: The wave propagates in the positive x-direction.; The propagation speed is constant $v$.; The waveform remains unchanged during propagation.