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View Full Version : Speed of sound question, part 2

aubries
11-25-2002, 03:01 PM
This is a followup to a question I posted last week, and is a nuance which I forgot to include.

If I have an object traveling through a tube, in a vacuum, at 300m/s, and I vent the tube in front of it to let air in, I have been told that the pressure wave will travel towards my object at the speed of sound. When this wave collides with my object, it will be at a relative velocity of about 640 m/s, well over mach 1. I have assumed that this will be a sufficient condition to produce a sonic boom.

My question is this: since the absolute velocity of the object is still only 300 m/s (and now declerating from wind resistance), would that make it possible for someone riding in the object hear the sonic boom? Moreover, if the pressure wave is already moving at the speed of sound, would a sonic boom even be possible?

11-25-2002, 03:21 PM
The rules of physics sometimes break down at extremes. Sonic boom at extremely low density is one of them. Your experiment is similar to a spacecraft reentering the atmosphere. In low earth orbit it will collode with the occasional stray molecule. The molecules don't have enough random collisions with each other to form a measureable pressure wave. Lower in the atmophere the behave more nicely. The transition is a blurry one.

Ethilrist
11-25-2002, 03:22 PM
Sonic booms are the sound of an object which is travelling greater than the speed of sound relative to the medium. When the object impacts the air that just got let into the tube, the relative speed creates a sonic boom, which occupants of the object should be able to hear. If the object were standing still, and the air was forced past the object at greater than the speed of sound, there would also be a sonic boom.

micco
11-25-2002, 04:57 PM
A sonic boom is the sound caused by the pressure change associated with a shock wave. If a moving body creates a shock wave in the surrounding medium, the occupants of the body aren't going to hear it unless there is some external body (like your tube) to reflect that shock wave back so it impacts the body. In addition, since you're in a tube, it's unlikely you'd even get an oblique shock which would be swept back past the body and could possibly be reflected. Depending on the ratio between the tube and vehicle diameters, it's much more likely you'd get a normal shock standing off in front of the vehicle rather than an oblique shock.

Your scenario is very similar to a shock tube setup. A shock tube is an experimental apparatus used to study shocks and high speed flows. They are typically constructed as a long tube with a diaphram separating two sections. One side of the diaphram is evacuated (low pressure) and the other side is pumped to very high pressure. Calibrated diaphrams are used which will break as a specific point, causing a flow from the high-pressure side to the low pressure side. This causes a normal shock and multiple reflected shocks. Looking into some of the basic physics of shock tubes might answer a lot of your questions.

Do a search online for "shock tube" and you'll find descriptions of lots of lab setups. Any decent compressible flow fluid dynamics textbook will contain a description and the basic physics. Look in the aerospace engineering section of your library for a fluid dynamics textbook with "compressible flow" in the title.