# Calculating Altitude from Sonic Boom and Angle of Sight

• rlc
In summary, the problem involves calculating the speed and altitude of a high-speed jet plane based on the sonic boom heard and the angle at which the plane was seen. The equation used is v(plane)=velocity of sound/sin(alpha), and the altitude can be found using the formula (velocity * time)tan(alpha). By factoring in time and using a clear drawing of the sonic cone, the altitude was found to be 1521.46 m.
rlc

## Homework Statement

You hear the sonic boom of a high-speed jet plane exactly 4.50 s after it passes directly overhead in level flight. At the time you hear the boom, you see the plane at an angle of 16.0 o above the horizon. Assume that the speed of sound at the altitude of the plane is 325 m/s.
How fast is the plane traveling?
What is the altitude of the plane?

## Homework Equations

v(plane)=velocity of sound/sin(alpha)
But I don't know the equation to find altitude.

## The Attempt at a Solution

I know how to get the first question:
325/sin(16)=1179.1 m/s -->which LONCAPA says is right.

What I don't know is how to get the second part. How do you find the altitude based off of the information given?

Well, if LONCAPA (who's that?) says it's right, it must be right...

Did you make a drawing ?

In fact, part b) is fairly simple: If you hear a bang 4.5 s after a flash, how far away was the lightning ?

Or am I dreaming ?

 shooting at a rapid rate, eh? three-barrel ! Some catching up to do, or an exam coming up ?

LONCAPA is an online college homework site where you can plug your answers in and it tells you if that the answer it has as right.

325 m/s *4.5 s=1462.4 m
But the website says that this is incorrect. I'm assuming it is because of the angle. Do you know what equation to use or how to factor this information in?

Make a drawing of the sonic cone... And you'll see everything very clearly. It's a nice and easy problem.

I made a picture, but I think I did something wrong.
Does this make a triangle? I thought using 1179.1*tan(16 degrees) will give the altitude based off of calculus, but the homework website I am using says that this is the wrong answer. What am I missing?
(Also thank you for helping!)

rlc said:
LONCAPA is an online college homework site where you can plug your answers in and it tells you if that the answer it has as right.

325 m/s *4.5 s=1462.4 m
But the website says that this is incorrect. I'm assuming it is because of the angle. Do you know what equation to use or how to factor this information in?

It is incorrect because, by the time the sound reached your ears, the plane had moved away from the point where that sound originated.
Again: make a clear drawing and you'll see the solution... I remind you that alpha is the semi-angle between the axis of the cone (the trajectory of the plane) and any generatrix of the cone.

BvU
Ah! I got it!
I forgot to factor in time!
(1179.1m/s*4.50s)tan(16 degrees)=1521.46 m (which the website is right)

Well, sorry, can't think of anything better than what you came up with...

NTW: thanks for stepping in..

Last edited:
rlc said:
Ah! I got it!
I forgot to factor in time!
(1179.1m/s*4.50s)tan(16 degrees)=1521.46 m (which the website is right)

The answer may be right, but it appears to me that you reached it by manipulating the variables almost blindly. With a simple drawing of the sonic cone, the trajectory of the plane and the observer on the ground, everything is perfectly transparent...

It wasn't done blindly. I looked in my textbook, and it showed very clearly (like you said) how the cone created a triangle, where velocity times time was one side of the triangle, the angle was incorporated, and the altitude was another side of the triangle. Simple calculus allowed me to move on from there. Thank you for all of your help for this problem.

## 1. What is a Sonic Boom?

A sonic boom is a loud noise created by an object moving through the air faster than the speed of sound. It is caused by a sudden change in air pressure and can be heard as a loud bang or a series of booms.

## 2. How does a Sonic Boom affect altitude?

A Sonic Boom does not directly affect altitude as it is a result of an object's speed, not its height. However, the altitude at which the boom is heard can provide information about the altitude of the object creating it.

## 3. How is altitude measured in relation to Sonic Booms?

Altitude in relation to Sonic Booms is typically measured in feet above sea level. This is because the speed of sound is affected by air density, which is influenced by altitude. Therefore, altitude can affect the intensity and distance at which a Sonic Boom can be heard.

## 4. Can Sonic Booms occur at any altitude?

Yes, Sonic Booms can occur at any altitude. However, they are most commonly heard at higher altitudes where the air is thinner and the speed of sound is faster. The intensity and distance of the boom may also vary depending on the altitude at which it occurs.

## 5. How can scientists use Sonic Booms to find altitude?

Scientists can use the time delay between the initial boom and the arrival of the shockwave to determine the distance of the object creating the boom. This, combined with the altitude at which the boom is heard, can provide an estimate of the object's altitude. Additionally, sonic booms can also be measured using specialized equipment such as radar or microphones to accurately determine altitude.

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