What is the cause of a whisitling noise with bronchitis?

Tight airway. In children with bronchitis the whistling may be wheezing or it may be for mucous in the upper airway and the air moving by is making a whistling noise because the airway is tighter.
Wheezing. Many patients who have bronchitis will experience "wheezing", which is caused by bronchospasm. Bronchospasms are spasms of the airways that can cause a whistling sound, particularly heard when someone is breathing out. Oftentimes, a medication called "albuterol" is prescribed to alleviate the wheezing caused by the bronchospasms so as to make breathing easier.