Introduction:
The phrase "at last a sympathetic audience" is a statement made by an unidentified person. The intention behind this statement and the tone, whether sarcastic or serious, can be analyzed based on the context and surrounding information.

Identification of the Speaker:
The specific identity of the speaker is not mentioned in the given prompt. Therefore, it is crucial to examine the context or any additional information provided to determine the potential speaker of this statement. Without further details, it is challenging to pinpoint the exact person uttering these words.

Explanation of the Phrase:
1. Expression of Relief: The phrase "at last" indicates a sense of relief or satisfaction. It suggests that the speaker has been longing for or seeking a particular type of audience, and finally, they have found it.
2. Sympathetic Audience: The speaker refers to the audience as "sympathetic." A sympathetic audience typically implies a group of individuals who are understanding, supportive, or compassionate towards the speaker's perspective, ideas, or experiences.

Tone Analysis:
1. Serious: If the speaker is serious when saying "at last a sympathetic audience," it suggests that they have been looking for understanding or support for a long time, and they genuinely feel relieved and grateful to have finally found it.
2. Sarcastic: On the other hand, if the speaker is being sarcastic, the phrase may imply that they have encountered numerous unsympathetic audiences in the past. By saying "at last a sympathetic audience," they may be expressing their frustration with previous interactions and ironically highlighting the rarity of finding understanding listeners.

Conclusion:
Without additional context or information about the speaker, it is difficult to definitively determine whether the statement "at last a sympathetic audience" is meant to be serious or sarcastic. The intention and tone behind the phrase can vary based on the speaker's experiences, emotions, and the overall context in which it is uttered.