You are walking along a small country road one foggy morning and come to an intersection. While you are crossing, you hear an ambulance siren. As a paramedic, you know that the siren sounds at a frequency of 7.87 kHz. But, as an amateur musician with perfect pitch, you can tell that the frequency you are hearing is actually 8.61 kHz. Is the ambulance moving toward or away from you? The ambulance is moving toward you! At what speed is the ambulance traveling? mph?

64.945 miles per hour

Explanation:

Since the frequency of sound heard is higher than actual frequency, the ambulance is moving towards you!

The frequency of sound waves as heard from a distance for a sound wave coming towards one at v₀ m/s and whose real frequency is f₀ is given by

+f = f₀/[1 - (v₀/v)]

+f = frequency of sound as heard from the distance away = 8.61 KHz

f₀ = real frequency of sound = 7.87 KHz

v₀ = velocity at which the sound source is moving towards the reference point = ?

v = velocity of sound waves = 343 m/s

8.61 = 7.87/(1 - (v₀/v))

1 - (v₀/343) = 0.9141

v₀/343 = 1 - 0.9141 = 0.0859

v₀ = 343 × 0.0859 = 29.48 m/s = 64.945 miles per hour

hypothesising or postulating

prndulum needs thread, weight clock to time swings