# Minimum velocity for a sonic boom?

• Chris L
In summary, the student showed that there is no answer to a question asking for the minimum velocity of a jet in order for it to produce a sonic boom, as the speed of sound in the situation is known. However, the teacher did not like this answer and refused to give him any marks, or discuss the question with him.
Chris L
On our grade 11 physics exam, there was a question asking for the minimum velocity of a jet in order for it to produce a sonic boom (the temperature of the air was given, so the speed of sound in the situation was known). According to our textbook, a sonic boom is produced only after the jet's velocity exceeds the speed of sound, so using some set theory I showed that there was no solution, as there is no smallest number greater than a given constant.

However, the teacher didn't like this answer and refused to give me any marks, or discuss the question with me. Out of curiosity (I don't intend to continue arguing with her), is there anything wrong with my argument in classical mechanics?

P.S. This is my first post, so I apologize in advance if this is in the wrong sub-forum. This was a question arising from school, but it's a perfectly valid classical mechanics question and I'm not asking for help on homework etc.

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Mixing math and physics can be dangerous in the presence of a physics teacher. Obviously the teacher was looking for Mach 1 as the answer, without looking at the mathematical niceties, i.e. the difference between > and ≥.

You're just arguing semantics at that point.

Technically you are correct assuming you think space is a continuum but based on how the question is phrased I believe you knew what your teacher really wanted and it would have been very easy to write it down.

A sonic boom is created at mach 1. The velocity has to be equal to or greater than the speed of sound (so I slightly disagree with your textbook), so the answer is the speed of sound. Besides, I think it was fairly clear what the teacher wanted the answer to be, so I don't think there's really any point in attempting a semantic "gotcha" on a question like that.

I guess I just have to keep in mind that math doesn't govern physics; it's sometimes hard to remember that though when the math you're doing in physics is more advanced than the math you're doing in math.

A sonic boom occurring right at Mach 1 makes a lot more sense...I double checked and the textbook says "greater than" in its glossary, but it's being discontinued so that could be one of the reasons why.

Teacher should have acknowledged your response as valid instead of throwing up a wall.

And I don't agree with everyone that just because this is what the teacher wanted to hear, then that is the short answer you should have given. What if she asked "what is the fastest speed an object with mass can achieve?"

In real life, you must consider the intended audience. http://www.phy.ilstu.edu/~rfm/107f07/epmjokes.html

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## 1. What is the minimum velocity required for a sonic boom?

The minimum velocity required for a sonic boom depends on several factors such as the altitude, atmospheric conditions, and the shape and size of the object. Generally, it is believed that an object needs to travel at a speed of at least 767 miles per hour (1,235 kilometers per hour) to produce a sonic boom.

## 2. Can any object produce a sonic boom if it reaches the minimum velocity?

No, not all objects are capable of producing a sonic boom even if they reach the minimum velocity. The object needs to be moving through a medium at a speed faster than the speed of sound and must also have a certain shape and size to produce a sonic boom. For example, a bullet fired from a gun can reach the minimum velocity for a sonic boom, but its small size and shape do not produce a detectable sonic boom.

## 3. How does altitude affect the minimum velocity for a sonic boom?

The higher the altitude, the lower the minimum velocity needed for a sonic boom to occur. This is because the air density decreases with increasing altitude, making it easier for an object to travel faster than the speed of sound. At higher altitudes, the minimum velocity for a sonic boom can be as low as 660 miles per hour (1,062 kilometers per hour).

## 4. What are the dangers of a sonic boom?

Sonic booms can be quite loud and can cause damage to buildings and other structures. They can also startle or frighten people and animals, potentially causing them to act unpredictably. In addition, sonic booms can disrupt sensitive equipment and have been known to break windows and damage aircraft in the past.

## 5. Are there any regulations regarding the minimum velocity for a sonic boom?

Yes, there are regulations in place to limit the occurrence of sonic booms over populated areas. In the United States, the Federal Aviation Administration (FAA) has set a maximum speed of Mach 1 (767 miles per hour) for commercial aircraft over land. Military aircraft are exempt from this regulation and can produce sonic booms at higher speeds, but they must still follow certain guidelines to minimize their impact on the ground.

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