When sound waves travel through a medium, such as air, they propagate as a series of compressions and rarefactions. These compressions and rarefactions create a pressure wave that travels through the air. When this pressure wave reaches our ears, it is detected by the ear's anatomy, which then converts the mechanical vibrations into electrical signals that can be interpreted by the brain.
The speed of sound in a particular medium depends on factors such as temperature, humidity, and the density of the medium. In dry air at sea level, for example, the speed of sound is approximately 343 meters per second (or about 1,125 feet per second). This means that sound waves can travel long distances relatively quickly.
The perception of sound reaching the brain with no noticeable delay is due to the fact that sound travels at a very high speed compared to the distances typically encountered in everyday situations. For example, if you are standing 10 meters away from a sound source, it would take approximately 0.03 seconds for the sound to reach your ears (assuming no other factors that could affect the speed of sound). This delay is generally imperceptible to humans.
Additionally, our brains are adept at processing and interpreting sound signals quickly. The auditory system is designed to analyze and make sense of sound information efficiently, allowing us to perceive and respond to sounds in real-time.
Therefore, while sound waves do travel over distances, the speed of sound and the efficient processing capabilities of the auditory system enable us to perceive sound as if it reaches the brain with no significant delay.