The three forms of noise (internal, external and cultural) are a part of the overall environment and context of the speech. They impact and are impacted by both.
Context is the situation in which a speech is given. This includes the actual space or physical setting, the occasion of the speech and the reasons the speech is being given.
Environment refers to all external surrounding a that influence a public speaking event. This involves thing that happen around the the time of the speech that may cause the speaker, audience or content to change in some way in context to what has occurred or is occurring. Audiences interpret the context based on what is going on in their own minds or lives.
Scholarly articles for Context and environment