Smiles and humour depend on the context
Laughter can ease tension, but it may not be the right response
A smile or shared humour can create a more pleasant atmosphere if everyone is comfortable with it. But humour isn’t a universal way to handle tension. Someone might laugh out of habit, embarrassment or because they don’t know what to say. So don’t automatically treat laughter as agreement, satisfaction or proof that a problem has gone away.
If you’ve made a mistake, self-deprecating humour can lighten the conversation only if it doesn’t minimise the impact on others. First say what needs to be put right. For example: “I got the date wrong, which caused a problem for you. I’ll fix it today. If it helps, we can have a laugh about my chaotic calendar afterwards.”
If the other person doesn’t smile or respond to a joke, you don’t have to persuade them to relax. Return to the matter at hand or ask what they need now. Don’t use humour to change the subject, make fun of someone or avoid responsibility.
When discussing a sensitive topic, attentive listening and a clear question are usually a better first sign of respect than trying to make someone laugh.