1 Attachment(s)

Find distances from angles

Hi,

I have come across a problem I cannot seem to solve by myself, so I was hoping anyone on here could help me with this.

I'm sure it's pretty easy to do what I want, I just can't think of any way...

I'm studying physics at a university (first year) so you may assume that my math level is beyond highschool, but I'll tell you if I don't understand :P

Please consider the attached image.

The point *P* can move along the circle with radius *R* as shown.

Points 1 and 2 are fixed, seperated by a distance *d*. They are also centered around the origin so the x-coordinate of point 1 will be -1/2*d* and the x-coordinate of point 2 will be +1/2*d*. You get the point.

I'll try to explain in detail what I need, but if you don't need that, I'll ask the question first:

How can I express the lengths *r1* and *r2* in the angle *a0*?

Explanation:

I need to find the distances *r1* and *r2*, based on the angle between the line OP and the x-axis (*a0*).

I need this for a physics project, where points 1 and 2 are two sound sources. I need to find the phase difference between source 1 and 2 at point *P*. Both sound sources are in phase, but because *r2* < *r1*, there will be a phase difference at point *P*.

To find the phase difference, I need to know the lengths of *r1* and *r2*.

I know, I could simply apply pythagoras or something, but I need to express these lengths in the angle that *r0* makes with the x-axis (*a0*).

The reason behind this is that the two sound sources form a kind of directional speaker. They are placed at exactly the right distance apart (1/2 * wavelength) so their waves cancel out at the sides and add up right infront. Now I want to create a graph of the soundpressure (which depends on the phase difference) of both speakers combined at point *P*, which will vary with the angle *a0*.

So I need to express both lengths *r1* and *r2* in the angle *a0* alone.

Does anyone know any way how to do this?

Thanks!!