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Can someone tell me what does the symbol mean in the formula for energy compared to amplitude? Looks like a partial infinity sign, almost like a fish symbol.

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As stated in the comment, the "fish" is the mathematical symbol for "proportional to". In the case of the amplitude and energy, $$ E\propto A^2 $$ means that $$ E=CA^2 $$ for some constant $C$.

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It seems that "fish" refers to $\propto$. It is means "proportional to". Since @Kyle Kanos has provided useful links about this, I won't repeat them.

But I want to add a useful tool for checking unfamilar symbols: http://detexify.kirelabs.org/classify.html

You can draw the symbol and get its latex code, and then it's easy to find its meaning (usually the latex command name itself is enough).

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