Update: This has been resolved in Rebex Tiny Web Server v1.0.3!
Thank you for letting us know. The beeping sound is triggered when a message is written to the logging textbox. It does not happen an all PCs and not always. We are not able to reproduce it reliably, but sometimes it beeps even in our environment.
We will focus on this issue. In the meantime, please set "Log level" to Off
(dropdown above the "Start" button).