Sound radiation by a sphere with variable temperature

The model problem of sound emission by temperature inhomogeneities in a compressible heat-conducting gas at rest has been solved. A harmonic law of temperature oscillation is specified on the surface of the sphere. Exact expressions for temperature and pressure disturbances in a linear formulation are obtained under the condition that the sphere as a sound source is compact. It is shown that pressure disturbances near the sphere are small and can be considered constant, which makes it possible to use the classical heat equation near the sphere and alternatively obtain an expression for pressure disturbances far from the sphere based on estimating the rate of change in the volume of the near-wall spherical layer.