The perception of loudness is not solely determined by the intensity of a sound wave but also by its spectral content and shape. While square waves and sine waves may have the same intensity (amplitude), they differ in their harmonic content and temporal characteristics, which can influence how we perceive them.
Square waves contain multiple harmonics and have a more complex spectral content compared to pure sine waves, which consist of a single frequency. The additional harmonics present in square waves contribute to a richer and more energetic sound, which can be perceived as louder, even at the same intensity level.
Furthermore, square waves have sharp transitions from high to low amplitude, resulting in rapid changes in air pressure. These rapid changes contain high-frequency components that can be more easily detected by our auditory system, making the sound appear louder.
Regarding the distance traveled, square waves and sine waves generally propagate through a medium, such as air, in a similar manner. The distance traveled by a sound wave depends on factors like the intensity of the source, atmospheric conditions, and any obstacles present in the environment. As long as the intensity (amplitude) of the wave remains the same, both square waves and sine waves will tend to attenuate over distance in a similar manner.
However, it's important to note that square waves contain more high-frequency content, which can be attenuated more quickly compared to lower-frequency components. This attenuation can result in a perception that square waves dissipate faster than sine waves over distance, but the underlying mechanism is related to frequency rather than the shape of the wave itself.
In summary, square waves are perceived as louder than sine waves with the same intensity due to their richer harmonic content and rapid transitions. However, the distance traveled by sound waves, regardless of their shape, depends on various factors and is not significantly influenced by the wave shape itself.