Calculating the Diffraction Speed of a Cadillac

[600burger]

I'm slightlly confused on what to "assume" about this problem here:

A Cadillac with a mass of 2000 kg approaches a freeway underpass that is 10 m across. At what speed must the car be moving in order for it to have a wavelength such that it might diffract after passing through this "single slit"? Copmare to normal freeway speeds of ~30 m/s.


What I am not sure about is what should i assume its wavelength should be? Or how i find about what it should be. Since I am using l=h/m*v (where l is lambda/wavelength, h is planks, m is mass, and v is velocity) i solve for v, but to do that i must assume a wavelength. Anyone know what I am talking about?

Thanks,
Burg

 

[DrChinese]

People have tried to experimentally diffract Cadillacs through various types of underpasses previously. All have resulted in a great amount of debris and very few breakthoughs in physics. Even doing as a thought experiment is very likely to hurt your brain. Unless you know of a new model of Cadillac...

 

[jtbell]

Actually, with a velocity in the range that you're supposed to come up with in a problem like this one, it would be awfully hard to do any damage to your Cadillac unless you have a really old one that's about to fall apart on its own anyway!

Burg, if you scour your textbook really closely, you'll probably find a statement somewhere to the effect that in order to get significant diffraction effects, the wavelength of the wave should be roughly equal to the width of the aperture. This is kind of a hokey statement (I'd personally put it at 0.1 times the width of the aperture, or even smaller), but it's a common assumption for crude back-of-the-envelope type calculations involving diffraction in general (not just quantum-mechanical diffraction).

When you see the answer, and compare it to typical automobile speeds, I think you'll agree that a few powers of ten one way or the other isn't going to make a significant difference in practice!

 

[600burger]

the wavelength of the wave should be roughly equal to the width of the aperture.

This is what i thought i was supposed to do. From the experiment where they shot electorn through the gold sheet and it undergoes interferance. I thought it might be diffrent since that was the slit separation was the one that was close to the wavelength.

I came out with something like 10^-30 ish, can't remeber now since i already tunred it in. Slightlly strange to think about, but they did it with buckyballs! Not quite a cadillac...

-Burg