No, having the same amplitudes is not a requirement for beat to occur. Beat is a phenomenon that arises when two waves with slightly different frequencies interfere with each other. The essential requirement for beat to occur is that the two waves have frequencies that are close to each other but not exactly the same.
When two waves with slightly different frequencies combine, they produce a pattern of constructive and destructive interference. If the frequencies are very close, the resulting interference pattern creates a perception of a beat—a periodic variation in the intensity or loudness of the combined wave.
The amplitudes of the two waves involved in beat can be different. The amplitudes determine the strength or magnitude of the waves, while the frequencies determine how quickly the waves oscillate. The key factor for beat is the frequency difference between the waves, which creates the pattern of constructive and destructive interference leading to the perception of beats.
For example, consider two musical tones played on different instruments. The amplitudes of the sound waves produced by each instrument may differ due to factors such as the intensity at which the musicians play. However, if the frequencies of the two tones are close enough, beat phenomena can still occur, resulting in a periodic variation in the loudness or intensity of the combined sound.
In summary, beat is primarily determined by the frequency difference between two waves, not their amplitudes. The amplitudes of the waves can be different, but as long as the frequencies are sufficiently close, beat phenomena can arise.