Hi Oleanda------ have been thinking about your complainant for most of the morning --- just a thought.
If you were to lose your tenant , through the man who has complained , and subsequent tenants were also complained about , until it becomes an almost impossible to let property-------would you need to sell?
I do not want to know your financial details , in this hypothetical case, but could the man who has complained see this as a way to buy a house on the cheap as it were.
Do not trust him ,until, as has been said , you have real evidence from him .
People can be extremely devious at times. And the noise issue, if indeed there is one ,is between him and your tenant, and Environmental Health.
All the best.