As the air passes through the pipe, it experiences a sudden expansion at the open end. This causes the flow to separate from the pipe wall and create a turbulent jet. The turbulent flow creates pressure fluctuations that propagate as sound waves. The intensity of the sound depends on the velocity and turbulence of the air jet.
For a given volume flow rate, the velocity of the air jet is inversely proportional to the cross-sectional area of the pipe. Therefore, the smaller the pipe diameter, the higher the air jet velocity and the greater the noise.
In contrast, for a larger diameter pipe, the air jet velocity is lower, and the turbulence is less pronounced. This results in a lower noise level.
Additionally, the frequency of the sound produced also plays a role in the perceived loudness. Smaller pipes tend to produce higher-pitched sounds, which are generally perceived as being more annoying than lower-pitched sounds.
In summary, the smaller diameter of a pipe leads to higher air jet velocity, increased turbulence, and higher-pitched sound, all of which contribute to the louder noise produced when air escapes from the open end of a small pipe.
