  An analytical model is developed to study the sound produced by the
interaction between shock and instability waves in two-dimensional supersonic
jet flows. The jet is considered to be of vortex-sheet type and 2D Euler
equations are linearised to determine the governing equations for shock,
instability waves, and their interaction. Pack's model is used to describe
shock waves, while instability waves are calculated using spatial stability
analysis. The interaction between shock and instability waves can be solved
analytically by performing Fourier transform and subsequently using the method
of steepest descent. Sound produced by the interaction between the instability
wave and a single shock cell is studied first, after which that due to a number
of cells follows. We find that the model developed in this study can correctly
predict the frequencies of the fundamental screech tone and its first and
second harmonics. We show that the predicted sound directivity, even from a
single shock cell, is in good agreement with experimental data. In particular,
this model shows the strongest noise emission close to the upstream direction
but the emitted noise starts to rapidly decay as the observer angle approaches
180 degrees, which is in accordance with experimental results; this suggests
that the effective noise from a single shock cell is far from of the monopole
type as assumed in the classical Powell's model. We find that the noise
directivity is very sensitive to the local growth rate of the instability waves
and the noise is generated primarily through the Mach wave mechanism.
