The amplitude of a stationary wave is not necessarily equal to the amplitude of the individual waves creating it due to the phenomenon of interference. When two waves superpose, their amplitudes can either reinforce each other (constructive interference) or cancel each other out (destructive interference), depending on their relative phases.
In the case of a stationary wave, also known as a standing wave, it is formed by the superposition of two waves of the same frequency and amplitude traveling in opposite directions. As these waves pass through each other, they interfere constructively at certain points, resulting in regions of maximum displacement called antinodes, and interfere destructively at other points, resulting in regions of zero displacement called nodes.
At the antinodes, the two waves are in phase, meaning their crests and troughs align, resulting in constructive interference. As a result, the amplitudes of the two waves add up, leading to an increased amplitude at the antinodes.
At the nodes, the two waves are out of phase, meaning their crests and troughs are misaligned, resulting in destructive interference. The waves cancel each other out, leading to a complete reduction in amplitude at the nodes.
Therefore, the amplitude of a stationary wave is determined by the superposition and interference of the two component waves, resulting in a pattern with alternating regions of high and low amplitude. The amplitude of the stationary wave is typically not equal to the amplitude of the individual waves that create it, except at the antinodes.