The two loud sounds happened within about two minutes of each other, as Giuliani spoke.
Footage of the moment has been shared on Twitter, where it has already been viewed more than 3.4 million times.
Internet users noticed Jenna Ellis' face, as the attorney assisting Giuliani sat next to him. Her side-glance immediately after the sound did not go unnoticed.
Michigan has already certified Biden as the official winner in the state, beating Trump by about 150,000 votes.
At the same hearing in the state this week, one of the Trump campaign's star witnesses alleging election fraud suddenly shot to viral fame.
The hearing lasted four hours and included testimony from several people who claimed to have witnessed misconduct on election night. One of them was Melissa Carone.
Carone said she was contracted by Dominion, the company behind the electronic voting systems used by some American counties, to do IT work at the TCF Centre in Detroit.
Dominion has confirmed this, and said Carone was indeed "one of several thousand technicians we hired for a day or two". Her job at the vote counting centre was to "troubleshoot level one problems for staff".
She faced questions from a number of Michigan state politicians, representing both major parties, but one testy exchange with Representative Steven Johnson, a Republican, is getting the most attention.
It concerned discrepancies in Detroit's poll book, in which the number of voters recorded as having cast ballots did not match up with the number of ballots actually counted.
This is not an unusual phenomenon. It has happened repeatedly in previous elections, including Trump's victory in 2016.
The discrepancy is usually just a handful of votes, and can be caused by human error, a jammed tabulator, or someone signing in to vote and then leaving without waiting around to cast their ballot.
Carone had another explanation. Her testimony was that she witnessed election workers counting the same ballots "nine to ten times", and that this happened with thousands of ballots.
If true, that would mean Detroit reported tens of thousands more votes for Joe Biden than had actually been cast.
Johnson queried how Carone's testimony could possibly be accurate, as it would have caused a much larger discrepancy between the poll book and the number of votes counted.
"Are we saying that the poll book is either wildly off, or that they are filling in names?" Johnson asked.
Carone replied: "Wildly off. It's wildly off, and dead people voted, and illegals voted. So that's my answer."
The Trump legal team has been making headlines for both getting cases thrown out and starring in embarrassing moments, including the bizarre press conference at the Four Seasons Landscaping parking lot and the press conference during which Giuliani's hair dye dripped down his face.
