The correct word is "during", as it refers to something happening within a specified time period, such as during the speech. Here's the breakdown of the options:
- For: Refers to purpose or reason, not suitable for time-related expressions.
- During: Correctly used to indicate something that occurs within a time frame, such as "during the speech."
- While: Can be used, but "during" is more fitting when referring to events that occur in a period of time.
- At: Refers to a specific point in time, but we need to express the ongoing nature of the interruptions, making "during" the better choice.
Therefore, the correct answer is "during".