Asperity is the harsh tone or behavior people exhibit when they’re angry, impatient, or just miserable. Did your supervisor snap “Late again!” when you showed up 20 minutes after your shift was supposed to start? She's speaking with asperity.
The harshness that asperity implies can also apply to conditions, like "the asperities of life in a bomb shelter." The word can be used even more literally to refer to surfaces, as in "the asperity of an unfinished edge." But, most often, you will see asperity used in reference to grumpy voices or irritable behavior.