The choice between "in" and "with" in expressions like "to shriek with laughter," "to scream in anger," and "to shriek in fright" can indeed be confusing. Here's a breakdown of the usage and the nuance each preposition brings:
"With"
To shriek with laughter: Here, "with" is used to indicate the cause or accompaniment of the action. Laughter is the reason or the manner in which the shrieking is done. "With" suggests that the laughter is an accompaniment to the shrieking, essentially happening together.
Other examples: "to tremble with fear," "to jump with joy."
"In"
To scream in anger: In this case, "in" is used to denote the emotional state or condition causing the action. Anger is the state of mind during which the screaming happens. "In" often conveys being in a certain state or condition.
To shriek in fright: Similarly, "in" here indicates that fright is the emotional state causing the shrieking.
Other examples: "to cry in pain," "to speak in surprise."
General Rule of Thumb
Use "with" to indicate something that accompanies the action or is a characteristic of how the action is performed.
Use "in" to denote the emotional or mental state that prompts the action.