MHB Solve for frequency & angle in dispersion equation

[NiToNi]

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

 

[Mathick]

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 $x = \frac{\sin[ \frac{\pi \cdot f \cdot W}{c}\ \cdot \;\sin(\theta) ] }{ \frac{\pi \cdot f \cdot W}{c}\ \cdot \;\sin(\theta)}$ ?

 

[NiToNi]

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?