Ok, I must be missing something very obvious here. After applying the boundary conditions, we can write:

$$ A_R e^{i \delta_R} = (\frac{v_2 - v_1}{v_1 + v_2}) A_I e^{i \delta_I} $$


$$ A_T e^{i \delta_T} = (\frac{2v_2}{v_1 + v_2}) A_I e^{i \delta_I} .$$

Then, my book says if the second string is lighter, we have $v_2 > v_1$, so $ \delta_T = \delta_R = \delta_I $. I am really not seeing how we can deduce $ \delta_T = \delta_R = \delta_I $ from $v_2 > v_1$.


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