Let Ω be a domain in ℝ³ in which Ω^{τ}=Ω×[0,τ]⊂ℝ³⁺¹ is a spatio-tempral domain upon which a non trivial solution of a sound wave exists.

Let us consider the following cross sections of Ω^{τ}

Σ¹={(x,y,z,t₀):(x,y,z)∈Ω and t₀∈(0,τ)} - a temporal cross section of Ω^{τ}

Σ²={(x,y,z₀,t):(x,y,z₀,t)=(x,y,z₀,t)_{∣t=t₀}∈Ω^{τ} and t∈(0,τ)} - a spatial cross section of Ω^{τ}

On which cross section do sound waves exist to be heard? and therefore can flat landers communicate with voices as we see in cartoons?

This question emanates from an idea of the fact that worldly natural phenomena exist in 3+1 space-time and nature (the world) is 3-D. Thus any natural worldly phenomenon such as sound should exist in a 3-D space evolving in time.

References

[1]  A Simple Proof that the World is Three-Dimensional

     Tom Morley

      SIAM Review, Vol. 27, No. 1. (Mar., 1985), pp. 69-71. 

[2] Where are the hidden dimensions of space?  https://www.researchgate.net/post/Where_are_the_hidden_dimensions_of_space 

I appreciate your answers, insightful comments and discussions ?

Regards, 

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