Propagation algorithm - MONICA-Project/sound-heat-map GitHub Wiki

The model used to calculate the sound heat map is a simplified physical model. The main elements are:

  • The loudspeakers on the venue are assumed point sources with an adjustable gain A. Each i-th loudspeaker produces the direct sound pressure at the j-th location

    f1

    where r_ij is the distance from the i-th loudspeaker to the j-th point to predict the sound and k=omega/c is the wavenumber. The speed of sound c is model linearly as a function of the temperature T in Celsius

    f2

  • The first order reflections of the walls surrounding the venue are included as image sources with a reflection coefficient of 1.

    reflection diagram

    The sound field produced by these reflections is

    f3

    where N_w is the number of walls.

The total sound field created by each loudspeaker to the receiver position is

f4

The gain A can adjusted by hand or fitted to the measured sound level L_p at the sound level meters locations such that

f5

where N_s is the number of loudspeakers and N_r is the number of sound level meters.

Once A is found, the sound level can be predicted at different locations r'.