Yes, for a standing wave to be formed, the two waves involved need to have the same wavelength. A standing wave is created when two waves with the same frequency and amplitude traveling in opposite directions superpose and interfere with each other. The resulting wave pattern appears to be stationary, with certain points of constructive and destructive interference.
In a standing wave, there are specific locations called nodes and antinodes. Nodes are points where the displacement of the wave is always zero, while antinodes are points where the displacement reaches maximum amplitude. The nodes and antinodes remain fixed in space and do not move.
For two waves to form a standing wave, they must have the same wavelength, which is the distance between two consecutive points of the same phase. When waves with different wavelengths superpose, they do not maintain a stable interference pattern, and a standing wave cannot form. Instead, they create a complex pattern of varying interference that does not exhibit stationary nodes and antinodes.
Therefore, in order to form a stable standing wave, the two waves must have the same wavelength. This requirement ensures that the constructive and destructive interference occur consistently at the same positions, resulting in a stationary wave pattern with nodes and antinodes.