The answer is 335 Hz.
To calculate this, we will use the following formula:
f₀ = f × v ÷ (v - v₁)
where:
f₀ - frequency heard
f - actual frequency
v - speed of sound
v₁ - speed of source
We know:
f = 312 Hz
v = 331 m/s
v₁ = 82.8 km/h = 23 m/s
We need:
f₀ = ?
f₀ = f × v ÷ (v - v₁)
⇒ f₀ = 312 Hz x 331 m/s ÷ (331 m/s - 23 m/s)
⇒ f₀ = 312 Hz × 331 m/s ÷ 308 m/s
⇒ f₀ = 335.3 Hz ≈ 335 Hz
Thus, the frequency of the horn is 335 Hz.