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Yes. In this case, the speed of sound in the ##\theta=\pi## (negative x-)direction is ##v_{-}' = \frac{4}{9}c##, and that in the opposite direction ##v_{+}' = 4c##.Dale said:By changing the electromagnetic interaction the produces sound waves in a material. Suppose that you have a material whose speed of sound is ##0.8 c## under the isotropic convention. Then if you use the convention that ##c(0)=\infty## and ##c(\pi)=0.5 c## then clearly the speed of sound in the ##\theta=\pi## direction can no longer be ##0.8 c##.
Proof: I use the following transformation, with ##k = 1##:
Source:Mathpages said:##x' = x \ \ \ \ \ \ \ \ \ \ y' = y \ \ \ \ \ \ \ \ \ \ z' = z \ \ \ \ \ \ \ \ \ \ t' = t+ \frac{kx}{c}##
...
##\frac{c'}{c} = \frac{1}{1-k \cos(\theta)}##
https://www.mathpages.com/home/kmath229/kmath229.htm
From the transformation for ##t'## follows: ##\frac{-x'}{0.8 c} = \frac{-x}{v_{-}'} + \frac{x}{c}##
and with ##x' = x## follows:
$$v_{-}' = \frac{4}{9} c$$
From the transformation for ##t'## follows: ##\frac{x'}{0.8 c} = \frac{x}{v_{+}'} + \frac{x}{c}##
and with ##x' = x## follows:
$$v_{+}' = 4 c$$