Finding distance from sonic boom

  • Thread starter leinad0213
  • Start date
In summary, the problem involves a supersonic plane flying due west at an altitude of 11.6 km and a speed of Mach 1.60 passing over an observer at point P. The question is to determine the horizontal distance from point P when the sonic boom is heard. The given information includes a temperature of 20C, which allows for the calculation of the speed of sound (Vs = 343 m/s). The equations Mach = V/Vs and Sinθ = V/Vs can be used to solve the problem, but a diagram may also be helpful in visualizing the solution.
  • #1
leinad0213
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Homework Statement



A supersonic plane passes directly over an observer at point P, flying due west at an altitude of 11.6 km and a speed of Mach 1.60. What is the plane's horizontal distance from point P when the sonic boom is heard?

I can assume T = 20C therefore Vs = 343 m/s

Homework Equations



Mach = V/Vs

Sinθ = V/Vs

The Attempt at a Solution



I have no idea. I do know however a right triangle is involved, but I don't know where to go from there.
 
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  • #2
Why don't you draw a diagram of the problem and see if that helps?
 
  • #3
Yep. SK's right. It should make the problem clearer.
 

1. How is distance from a sonic boom calculated?

The distance from a sonic boom can be calculated using the formula D = V*T, where D is the distance, V is the speed of sound, and T is the time it takes for the sound to reach the observer.

2. What is the speed of sound used in the calculation?

The speed of sound used in the calculation is typically the speed of sound at sea level, which is approximately 761 miles per hour or 1,225 kilometers per hour.

3. How do you measure the time it takes for the sonic boom to reach the observer?

The time it takes for the sonic boom to reach the observer can be measured using a stopwatch or a timer. The observer starts the timer when they hear the boom and stops it when they see the source of the boom, such as a passing airplane.

4. Can the distance from a sonic boom be affected by environmental factors?

Yes, the distance from a sonic boom can be affected by environmental factors such as air temperature, humidity, and wind speed. These factors can alter the speed of sound, thus affecting the calculation of the distance.

5. Is there a maximum distance that a sonic boom can travel?

The maximum distance that a sonic boom can travel depends on various factors such as the aircraft's speed, altitude, and atmospheric conditions. Generally, sonic booms can travel up to 100 miles before dissipating, but they can be heard at much greater distances under certain conditions.

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