Use the adjective intelligible to describe speech that is loud and clear, like the intelligible words of your principal which, thanks to a microphone, you were able to hear.
When your goal is to make your writing intelligible to anyone who reads it, you choose clear, precise words and give details that tell more about what you mean. You might also include examples. Intelligible comes from the Latin word intelligibilis, "that can understand or that which can be understood." The earlier meaning of intelligible was "able to understand," which today is closer to the meaning of intelligent.