= Solution
For two equal-amplitude waves with the same frequency and <wavenumber>, choose their phases so that
$$
A\cos(kx-\omega t)+A\cos(kx+\omega t)=\boxed{2A\cos kx\cos\omega t.}
$$
The spatial amplitude and temporal oscillation separate. Positions with $\cos kx=0$ are fixed <nodes of a standing wave>, while positions with $|\cos kx|=1$ are <antinodes>. Different initial phases merely shift this pattern in space and time.
A <travelling wave> has a phase profile that moves at its <phase velocity>; a <standing wave> has stationary nodes and each point oscillates with its fixed local amplitude. The two counterpropagating waves carry equal opposite time-averaged energy flux, so their superposition has zero net time-averaged energy transport. Instantaneous energy can still move within the standing pattern.
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