A train traveling at 82.8 kilometers per hour is blowing its horn as it approaches you. The horn has a frequency of 312 Hz. Assume the speed of the sound is 331 m/s. What is the observed frequency of the horn?

335 Hz

312 Hz

292 Hz

412 Hz

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.