MHB Solve for frequency & angle in dispersion equation

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The discussion focuses on solving for frequency (f) and angle (theta) in the equation x = sin[(pi*f*W)/c * sin(theta)] / [(pi*f*W)/c * sin(theta)]. The user seeks assistance due to confusion with the "arcsin of arcsin" concept. It is clarified that W and c are constants, while f and W are variables representing frequency and source width, respectively. The user aims to calculate f and theta based on known values of x, W, and theta, or x, f, and W. The conversation emphasizes the need for mathematical guidance in rearranging the equation for these variables.
NiToNi
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OK I'm about to grow (more) gray hairs...

Could some friendly soul smarter than myself kindly help me solve for both f and theta respectively in the following equation, please:

x = sin[ (pi*f*W)/c * sin(theta) ] / [ (pi*f*W)/c * sin(theta) ]

Getting stuck at "arcsin of arcsin" sort of thing...

Many thanks in advance (Nod)

Nick
 
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NiToNi said:
OK I'm about to grow (more) gray hairs...

Could some friendly soul smarter than myself kindly help me solve for both f and theta respectively in the following equation, please:

x = sin[ (pi*f*W)/c * sin(theta) ] / [ (pi*f*W)/c * sin(theta) ]

Getting stuck at "arcsin of arcsin" sort of thing...

Many thanks in advance (Nod)

Nick

W and c are constant, am I right?

And it should look like $x = \frac{\sin[ \frac{\pi \cdot f \cdot W}{c}\ \cdot \;\sin(\theta) ] }{ \frac{\pi \cdot f \cdot W}{c}\ \cdot \;\sin(\theta)}$ ?
 
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Hi Mathick,

Thanks for your reply :)

Your rearranging is correct - that's what it should look like.

However f and W are not constants per se. f is frequency (Hz) and W is source width (m), both of which are (positive) variables.

What I probably should have said though is that x is a ratio (power factor) so values are between 0 and 1:

0 < x < 1

As the equation is arranged now, I can calculate the power factor (x) knowing f, W and theta. What I am trying to do is solve also for f and W so I can calculate:

a. f knowing x, W and theta;

b.theta knowing x, f and W

Does thatn make sense?
 
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