Shock Waves Traveling to the Ground from a Jet

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SUMMARY

A jet flying at an altitude of 3300 m generates a shock wave at an angle of 43 degrees. To calculate the time until the sonic boom reaches the observer, one must first determine the distance the sound travels to the ground using the formula 3300/sin(43). This distance is then divided by the speed of sound, approximately 343 m/s, yielding a time of approximately 14 seconds. However, the calculation must account for the conical nature of the shock wave, which affects the perceived timing of the sonic boom.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine.
  • Knowledge of the speed of sound in air (343 m/s).
  • Familiarity with the concept of shock waves and their propagation.
  • Basic principles of physics related to sound and motion.
NEXT STEPS
  • Study the effects of altitude on sound propagation in different atmospheric conditions.
  • Learn about the mathematics of shock wave angles and their relationship to aircraft speed.
  • Explore the physics of sonic booms and their impact on the environment.
  • Investigate the relationship between jet speed and shock wave formation.
USEFUL FOR

Aerospace engineers, physics students, and anyone interested in the dynamics of sound waves and their interaction with high-speed aircraft.

Barry Melby
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A jet flying directly over you at an altitude of 3300 m produces a shock wave. The angle of the shock wave is 43 degrees. How long will it be until the sonic boom reaches you? How far does the jet travel during this time interval?

I know that I can figure out the second part of this problem if I get the first part, but I am not getting the correct answer for the first part.

For the first part I took 3300/sin(43) to get the total distance for the sound to travel to the ground. I then took this number and divided it by 343 m/s (speed of sound) to get approximately 14 seconds, but this appears to be wrong. Where did I go wrong?
 
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The shock wave is a cone traveling with and trailing behind the airplane.
 
Please don't delete the HW template when posting a HW thread.

What's the relationship between the speed of the plane and the angle of the shock wave?
 

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