No, it is not necessary for two waves with the same amplitude to form standing waves. The formation of standing waves depends on several factors, including the properties of the waves and their interaction.
Standing waves are formed when two waves of the same frequency and amplitude traveling in opposite directions superpose (combine) in such a way that they interfere constructively and destructively. The interference pattern results in stationary points called nodes and points of maximum displacement called antinodes.
For standing waves to form, the waves must have the same frequency and travel in opposite directions. The amplitude of the waves does not directly determine the formation of standing waves. However, the amplitude can affect the intensity or magnitude of the resulting standing wave pattern.
Even if two waves have different amplitudes, they can still form standing waves if their frequencies and directions of travel meet the conditions for constructive and destructive interference. Conversely, if the waves have the same amplitude but differ in frequency or direction, they will not form standing waves.
In summary, the formation of standing waves depends on the frequency and direction of the waves, while the amplitude does not play a direct role in determining whether standing waves will form.