An ambulance traveling eastbound at 154.0 km/h with sirens blaring at a frequenc

Question

An ambulance traveling eastbound at 154.0 km/h with sirens blaring at a frequency of 6.50 102 Hz passes cars traveling in both the eastbound and westbound directions at 49.0 km/h. (Assume the speed of sound is 343 m/s.)

(a) What is the frequency observed by the eastbound drivers as the ambulance approaches from behind?

(b) What is the frequency observed by the eastbound drivers after the ambulance passes them?

(c) What is the frequency observed by the westbound drivers as the ambulance approaches them?

(d) What is the frequency observed by the westbound drivers after the ambulance passes them?

Explanation / Answer

a)

VL = speed of listener = speed of eastbound drivers = 49 km/h = 49 (5/18) m/s = 13.61 m/s

Vs = speed of source = speed of eastbound ambulance = 154 km/h = 154 (5/18) = 42.78 m/s

frequncy observed by the eastbound drivers is given as

f' = (V - VL) f / (V - Vs)

f' = (343 - 13.61) (650) / (343 - 42.78) = 713.2 Hz

b)

VL = speed of listener = speed of eastbound drivers = 49 km/h = 49 (5/18) m/s = 13.61 m/s

Vs = speed of source = speed of eastbound ambulance = 154 km/h = 154 (5/18) = 42.78 m/s

frequncy observed by the eastbound drivers after ambulance pass is given as

f' = (V - VL) f / (V + Vs)

f' = (343 - 13.61) (650) / (343 + 42.78) = 554.98 Hz

c)

VL = speed of listener = speed of eastbound drivers = 49 km/h = 49 (5/18) m/s = 13.61 m/s

Vs = speed of source = speed of eastbound ambulance = 154 km/h = 154 (5/18) = 42.78 m/s

frequncy observed by the westbound drivers before ambulance pass is given as

f' = (V + VL) f / (V - Vs)

f' = (343 + 13.61) (650) / (343 - 42.78) = 772.1 Hz

d)

VL = speed of listener = speed of eastbound drivers = 49 km/h = 49 (5/18) m/s = 13.61 m/s

Vs = speed of source = speed of eastbound ambulance = 154 km/h = 154 (5/18) = 42.78 m/s

frequncy observed by the westbound drivers after ambulance pass is given as

f' = (V - VL) f / (V + Vs)

f' = (343 - 13.61) (650) / (343 + 42.78) = 554.98 Hz

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