Minimum velocity for a sonic boom?

[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.

 

[mathman]

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 ≥.

 

[Feldoh]

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.

 

[cjl]

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.

 

[Chris L]

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.

 

[Lsos]

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?"

 

[lewando]

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