The end of the runway at Princess Juliana International Airport on the Caribbean
ID: 2031232 • Letter: T
Question
The end of the runway at Princess Juliana International Airport on the Caribbean island of St Maarten is right next to a beach, and watching the planes land just overhead is a popular tourist attraction. In this video posted on Youtube, www.youtube.com/watch?v=zAfQwDizpRo a KLM Boeing 747, prepares to land. It approaches tourists on the beach who hear a high pitched sound from the engines of frequency 1900 Hz. After the jet has passed overhead, the frequency drops to 1020 Hz (I used a frequency analyzer to determine these values directly from the video). Assuming the air temperature that day was 86O F (which is 30.0O C), find the speed of the jet as it prepared to land.
Explanation / Answer
let f is the actual frequency of the engine produced.
f' = 1900 Hz
f'' = 1020 Hz
speed of sound, v_sound = 331 + 0.6*30
= 349 m/s
v_jet = ?
when jet approches,
f' = f*v_sound/(v_sound - v_jet)
1900 = f*349/(349 - v_jet) --------(1)
when jet moves away,
f'' = f*v_sound/(v_sound + v_jet)
1020 = f*349/(349 + v_jet) --------(2)
take equation(1)/equation(2)
1900/1020 = (349 + v_jet)/(349 - v_jet)
1900*(349 - v_jet) = 1020*(349 + v_jet)
1900*349 - 1900*v_jet = 1020*349 + 1020*v_jet
(1900*349 - 1020*349) = v_jet*(1020 + 1900)
v_jet = (1900*349 - 1020*349)/(1020 + 1900)
= 105 m/s
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