Turbine engine having acoustically tuned fuel nozzle

A fuel nozzle for a turbine engine having a combustion chamber is disclosed. The fuel nozzle has a common axis, a body member, and a barrel member. The fuel nozzle also has a mixing duct and an air inlet duct, each with predetermined lengths. The fuel nozzle additionally has a main fuel injection device located between the air inlet duct and the mixing duct. The main fuel injection device is configured to introduce a flow of fuel into the barrel member at a predetermine axial fuel introduction location. The predetermined axial fuel introduction location and the predetermined length of at least one of the mixing duct and the air inlet duct are such that a time-varying fuel to air equivalence ratio at a flame front downstream of an exit of the mixing duct is less than a time-averaged fuel to air equivalence ratio when a naturally-occurring time-varying pressure at the flame front is at a maximum.