Two trains are moving towards each other, each with a speed of 90...

Speed of each train, $v_s = v_o = 90 \text{ km h}^{-1} = 90 \times \dfrac{5}{18} \text{ m s}^{-1} = 25 \text{ m s}^{-1}$

Speed of sound, $v = 350 \text{ m s}^{-1}$

Actual frequency, $f = 500 \text{ Hz}$

Using the formula for Doppler effect when both source and observer are moving towards each other:

$f' = f \left( \dfrac{v + v_o}{v - v_s} \right)<br><br>Substituting the given values:<br><br>$f' = 500 \left( \dfrac{350 + 25}{350 - 25} \right)$<br><br>$f' = 500 \left( \dfrac{375}{325} \right)<br><br>f' = 500 \left( \dfrac{15}{13} \right)

$f' = \dfrac{7500}{13} \approx576.92$\text{ Hz}

Rounding off to the nearest integer, the apparent frequency is $577$\text{ Hz}.