Understanding air particle velocity as cross product freq x disp

AI Thread Summary
The discussion focuses on the relationship between air particle velocity and particle displacement in the context of microphone technology. The equation presented, u(t) = jω × x(t), raises confusion regarding the use of the cross product, as participants note that the terms appear to be scalars. Clarification is sought on whether the equation should be interpreted as a dot product instead. The conversation reveals that the equation resembles the standard form for velocity in simple harmonic motion, leading to the conclusion that the maximum particle displacement can be considered the amplitude. Overall, the notation used in the book is critiqued for causing misunderstanding.
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I'm reading a book on microphones and came across the following:

The relation between air particle velocity (u) and particle displacement (x) is given by:
u(t) = j\omega \times x(t)

where \omega = 2\pi f and x(t) is the maximum particle displacement value.

and then it goes off talking about something else...

I feel stupid for asking this, but I don't get how the above equation works? For one, I thought cross products could only be be involving vectors? Aren't all the terms above scalars? Should I treat it as a dot product?

Any help in understanding the above, so I can see how the terms affect each other is greatly appreciated!
 
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I don't think it is a cross product. It looks like the standard equation for velocity of a particle moving in simple harmonic motion.

I don't know why the book used ##\times## as a multiplication sign here.
 
Thanks, AlephZero! Typical of me getting thrown off by poor notation...
 
AlephZero: Are you saying that that equation is pretty much: v = - A\omega \sin \omega t? Does that mean I can consider the "maximum particle displacement" in the first equation, as the amplitude, A?
 
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