Our perception of sound involves a complex process that goes beyond a simple mathematical relationship like I=kA² (where I represents intensity and A represents amplitude). While it is true that the intensity of a square wave may not change significantly compared to a sine wave of the same amplitude, our ears are capable of detecting and analyzing various aspects of sound beyond just intensity.
When we listen to a square wave, our ears can perceive its unique characteristics such as the distinct onset and offset of the sound, the rapid changes in amplitude, and the presence of harmonics (multiple frequencies) that are generated by the square wave. These characteristics contribute to our perception of the sound as a square wave.
The human auditory system is highly sophisticated and can process different aspects of sound, including frequency, amplitude, duration, and temporal patterns. Our ears have tiny hair cells in the inner ear that are responsible for converting sound vibrations into electrical signals that can be interpreted by the brain. These hair cells are sensitive to the various components of sound, and they respond differently to different frequencies and temporal patterns.
While the simple equation I=kA² may not fully capture the intricacies of our auditory perception, it provides a starting point for understanding the relationship between sound intensity and amplitude. However, our perception of sound involves a combination of factors, and our ears are capable of discerning and recognizing a wide range of sound waveforms, including square waves, through the complex processing done by the auditory system.