Final answer:
Old buildings can fail during earthquakes due to resonance when the earthquake's frequency matches the building’s natural frequency, causing excessive vibrations. The large span of roofs on gymnasiums and churches makes them more vulnerable to collapse, and constructive interference can amplify damage in certain areas.
Step-by-step explanation:
One common cause of failure for old buildings during earthquakes is resonance, which occurs when the earthquake's frequency matches the building’s natural frequency, resulting in exaggerated vibrations and potential collapse. The failure of roofs in structures like gymnasiums and churches can often be attributed to their large surface areas and span, which are supported only at the edges. This design makes them more susceptible to these resonant effects compared to smaller, more rigid structures such as family homes. Additionally, the phenomenon of constructive interference can amplify the earthquake waves at certain points, causing more damage at locations further from the earthquake's epicenter.