Final answer:
The pitch produced by metal pipes is influenced by their resonant frequencies and boundary conditions. Factors such as the length, radius, and whether the ends are open or closed affect the pitch. The observed difference in pitch is not solely due to size but also the specific properties and conditions of each pipe.
Step-by-step explanation:
The behavior you've observed in the metal pipes at the science exhibit can be explained by the physics of sound waves and the properties of musical instruments, which can be modeled as pipes. In a musical instrument such as a pipe, the pitch of the sound produced is determined by the resonant frequencies of the air column inside the pipe. Generally, a larger instrument like a tuba will produce a lower pitch due to a longer wavelength, and a smaller instrument like a piccolo will produce a higher pitch due to a shorter wavelength.
However, the pitch of a sound also depends on the boundary conditions of the pipe. Some instruments are modeled with symmetrical boundary conditions, having both ends open or closed, while others have anti-symmetrical boundary conditions, with one end closed and the other open. These differences affect the resonant frequencies and thus the pitch of the sounds produced by the instrument. The pitch can also be changed by altering the effective length of the air column, such as by opening and closing holes along the pipe, as with a flute, or employing a sliding bar, as with a trombone.
In your case, the difference in pitch with identical lengths but varying radii could be due to how the geometry affects the resonant frequencies of the air columns within the pipes. Without additional information about the pipes' boundary conditions or how they were played, it is difficult to provide a precise explanation for the observed pitches. Nonetheless, the idea that bigger pipes produce lower pitches is not always correct and depends on various factors, including boundary conditions and methods of sound production.