Plane Speed: Calculating Mach with Shockwave Delay

In summary, Mach number is a unitless measure of an object's speed compared to the speed of sound, commonly used to measure the speed of aircraft. The shockwave delay is the time it takes for a shockwave to travel from the front of the plane to the tail, calculated by dividing the length of the plane by the speed of sound and taking into account the Mach number. The main factors affecting the calculation of shockwave delay are the length of the plane, speed of sound, altitude, air density, and plane design. Shockwave delay can impact the performance of a plane by causing drag and turbulence, but accurate calculations can help improve aerodynamics and overall performance. It is important to accurately calculate Mach number and shockwave delay in aircraft
  • #1
DmX0rZ
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Homework Statement



A plane passes from 900 meters over my head. I hear the shockwave after 2.2 seconds. At what speed in Mach is the plane flying ? Speed of sound = 331. 4 m/s

Homework Equations



Machs = speed of plane / speed of sound

The Attempt at a Solution



I don't have any clue where to go with this, maybe find the angle of the cone ? it gave me an angle of like .14 degrees and an impossible answer of the plane speed... dah

Thanks in advance
 
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  • #2
Don't double post.
 
  • #3
for any help. I would approach this problem by first identifying the variables and their values. In this case, we have the distance of the plane from the observer (900 meters), the time delay for the shockwave to reach the observer (2.2 seconds), and the speed of sound (331.4 m/s).

Next, I would use the given information to calculate the speed of the plane. We can use the formula speed = distance/time to calculate the speed of the plane, which in this case would be 900 meters/2.2 seconds = 409.09 m/s.

Now, to calculate the speed of the plane in Mach, we can use the formula Machs = speed of plane / speed of sound. Plugging in the values we calculated, we get Machs = 409.09 m/s / 331.4 m/s = 1.23 Mach. This means that the plane is flying at 1.23 times the speed of sound.

In order to find the angle of the cone, we would need more information such as the size of the plane or the distance between the observer and the plane. Without this information, it is not possible to calculate the angle of the cone.

Overall, we can use the given information to calculate the speed of the plane in Mach, but we would need more information to calculate the angle of the cone.
 

1. What is Mach number and how is it related to the speed of a plane?

Mach number is a unitless measure of an object's speed compared to the speed of sound in the surrounding medium. It is commonly used to measure the speed of aircraft, with Mach 1 being the speed of sound. For example, if a plane is traveling at Mach 2, it is traveling twice the speed of sound in the air.

2. How is shockwave delay calculated in relation to a plane's Mach number?

The shockwave delay is the time it takes for a shockwave to travel from the front of the plane to the tail. It is calculated by dividing the length of the plane by the speed of sound in the air. This calculation can be adjusted by taking into account the plane's Mach number, as the speed of sound changes with air temperature and pressure at high speeds.

3. What factors affect the calculation of shockwave delay?

The main factors that affect the calculation of shockwave delay are the length of the plane and the speed of sound in the air. Other factors that can also affect the calculation include the altitude and air density, as well as the shape and design of the plane's nose and tail.

4. How does shockwave delay impact the performance of a plane?

Shockwave delay can have a significant impact on the aerodynamics and performance of a plane. When a plane reaches supersonic speeds, shockwaves form around the nose and tail, causing drag and turbulence. By calculating the shockwave delay, engineers can design planes with streamlined shapes and adjust the speed of sound to reduce these effects and improve performance.

5. Why is it important to accurately calculate Mach number and shockwave delay in aircraft design?

Accurate calculations of Mach number and shockwave delay are crucial in aircraft design to ensure the safety and efficiency of the plane. If these calculations are not taken into account, it can lead to aerodynamic instabilities and potentially dangerous situations. By accurately calculating these factors, engineers can design planes that can safely reach high speeds and perform optimally in different flight conditions.

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