Velocity of a plane when you hear a sonic boom?

In summary, a sonic boom is a loud noise caused by an object moving faster than the speed of sound. The speed of sound varies based on factors such as altitude and temperature, but is approximately 343 meters per second at sea level and room temperature. To create a sonic boom, a plane must be flying faster than the speed of sound (Mach 1), but the exact speed depends on the size and shape of the aircraft. The velocity of the plane is not constant while creating a sonic boom, as it must accelerate to reach the speed of sound and then decelerate as it passes through the sound barrier. It is possible for a plane to fly faster than the speed of sound without creating a sonic boom by using specialized designs and
  • #1
KoontzyN
3
0

Homework Statement


A plane flies directly over your head. When the plane is 45° above the horizon from your perspective, you hear a sonic boom. How fast is the plane flying?

Homework Equations


Doppler effect for a receding source
f- = fo / (1+Vsource/c)

The Attempt at a Solution


Any help would be appreciated, I'm not sure where to start!
 
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  • #2
The doppler shift of the frequency is not relevant. You need to make a triangle diagram of the speeds and do a little trigonometry.
 

What is a sonic boom?

A sonic boom is a loud noise created by the shock wave generated when an object moves faster than the speed of sound.

What is the speed of sound?

The speed of sound varies depending on factors such as altitude, temperature, and humidity. However, at sea level and room temperature, the speed of sound is approximately 343 meters per second (767 miles per hour).

How fast does a plane have to be going to create a sonic boom?

The speed required to create a sonic boom depends on various factors such as the size and shape of the aircraft. Generally, a plane must be flying faster than the speed of sound (Mach 1) to create a sonic boom.

Is the velocity of a plane constant while it creates a sonic boom?

No, the velocity of a plane is not constant while it creates a sonic boom. The plane must be accelerating to reach the speed of sound, and then decelerating as it passes through the sound barrier.

Can a plane fly faster than the speed of sound without creating a sonic boom?

Yes, it is possible for a plane to fly faster than the speed of sound without creating a sonic boom. This is achieved by using specialized designs and techniques to minimize the shock wave. However, a sonic boom will still occur when the plane decelerates below the speed of sound.

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