While riding a bicycle towards a vertical wall at 12 km h^ -1 , a...

Speed of the boy, $v_{b} = 12 \text{ km h}^{-1} = 12 \times \dfrac{5}{18} \text{ m s}^{-1} = \dfrac{10}{3} \text{ m s}^{-1}$

The boy acts as a source moving towards the stationary wall. The frequency of the sound reaching the wall is:

$f_{1} = f_{0} \left( \dfrac{v}{v - v_{b}} \right)<br><br>The wall reflects the sound with the same frequency$f_{1}$. Now, the boy acts as an observer moving towards the stationary wall. The frequency of the reflected sound received by the boy is:<br><br>$f_{2} = f_{1} \left( \dfrac{v + v_{b}}{v} \right) = f_{0} \left( \dfrac{v + v_{b}}{v - v_{b}} \right)$<br><br>Substituting the given values:<br><br>$f_{2} = 1600 \left( \dfrac{330 + \dfrac{10}{3}}{330 - \dfrac{10}{3}} \right)

$f_{2} = 1600 \left( \dfrac{990 + 10}{990 - 10} \right) = 1600 \left( \dfrac{1000}{980} \right)$

$f_{2} = 1600 \times \dfrac{50}{49} = \dfrac{80000}{49} \approx 1632.65 \text{ Hz}$

The closest value among the options is $1632 \text{ Hz}$.