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21 December, 22:29

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

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Answers (1)
  1. 21 December, 22:49
    0
    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.
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