Q$1.($a$)$ The continuous development of turbofan technology reveals that at the same rated thrust a turbofan engine with low$-$bypass$-$ratio radiates substantially less noise than by a turbojet. Sketch the magnitudes and patterns of noise radiation of various sources in a low$-$bypass$-$ratio turbofan engine schematically shown in Figure Q$1($a$).$

$(5$ marks$)$

Figure Q$1($a$)$

$($b$)$ Figure Q$1($b$)$ shows the configuration of a stator$-$rotor stage of the low$-$pressure turbine of a turbofan engine. Explain, with sketches, the noise generation mechanisms of broadband and tonal components of turbine noise.

$(11$ marks$)$