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

Speed of the source (boy on the bicycle), $v_s = 12 \text{ km h}^{-1} = 12 \times \dfrac{5}{18} \text{ m s}^{-1} = \dfrac{10}{3} \text{ m s}^{-1}$

Frequency of the source, $f = 1600 \text{ Hz}$

Speed of sound in air, $v = 330 \text{ m s}^{-1}$

The wall acts as a stationary observer while the source is moving towards it. Using the Doppler effect formula for a moving source and a stationary observer, the apparent frequency $f'$ received by the wall is given by:

$f' = f \left( \dfrac{v}{v - v_s} \right)<br><br>Substituting the given values:<br><br>$f' = 1600 \left( \dfrac{330}{330 - \dfrac{10}{3}} \right)$<br><br>$f' = 1600 \left( \dfrac{330}{\dfrac{990 - 10}{3}} \right)<br><br>f' = 1600 \left( \dfrac{990}{980} \right)

$f' = 1600$\times $\dfrac{99}{98}$

$f' \approx1616.32$\text{ Hz}

The closest frequency is $1616$\text{ Hz}.