I have a peacock mantis and although I hear him all the time, I can't recall if there is any kind of pattern and I don't think there is a definitive pattern. It seems more dependent on what he's doing at the time. Usually its him clubbing the tank in an attempt dig deeper and sometimes its him swinging at the clownfish and missing against the rock. I know this doesn't help you resolve your issue but it's my experience.
Like tuan says it depends on what they're doing. I have 2 peacocks and I'll hear them click against the bottom of the tank when digging, they'll try to bash a giant rock to move it or if I walk by and startle them. Other than that they're quiet