Travelling towards a cliff, a car moves with a speed of 54 km h^ -1...

Speed of the car, $v_c = 54 \text{ km h}^{-1} = 54 \times \dfrac{5}{18} \text{ m s}^{-1} = 15 \text{ m s}^{-1}$

Frequency of the horn, $f_0 = 400 \text{ Hz}$

Speed of sound, $v = 335 \text{ m s}^{-1}$

The sound is reflected from the cliff. The cliff acts as a stationary observer for the incident sound and as a stationary source for the reflected sound.

The apparent frequency heard by the person in the car is given by the Doppler effect formula for a source and observer approaching each other:

f' = f_0 \left(\dfrac{v + v_c}{v - v_c} \right)

Substituting the given values:

$f' = 400 \left( \dfrac{335 + 15}{335 - 15} \right)$

f' = 400 \left(\dfrac{350}{320} \right)

$f' = 400 \times$\dfrac{35}{32}

$f' = 12.5 \times 35 = 437.5 \text{ Hz}$