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

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

The frequency of the direct sound heard by the person in the car is the same as the original frequency, since there is no relative motion between the person and the horn:

$f_1 = 400 \text{ Hz}$

For the reflected sound, the car acts as a moving source approaching the stationary cliff, and the person in the car acts as a moving observer approaching the stationary cliff. The apparent frequency of the reflected sound heard by the person is:

f_2 = f \left(\dfrac{v + v_c}{v - v_c} \right)

Substituting the given values:

f_2 = 400 \left(\dfrac{335 + 15}{335 - 15} \right) =400 \left(\dfrac{350}{320} \right) =$437.5 \text{ Hz}$

The beat frequency is the difference between the two frequencies:

$f_b = f_2 - f_1 = 437.5 - 400 = 37.5 \text{ Hz}$

The number of beats heard in $10$ seconds is:

$n = f_b \times 10 = 37.5 \times 10 = 375$