Finding the Directionality of a Sound

[tesla93]

I recently performed a noise lab and I am required to write a program to find the room constant of the room where the data was collected. Basically I would be using the formula:

Lp = Lw + 10log(Q/[4*pi*r^2] + 4/R)

Where Lp is the sound pressure level which was collected during the experiment, Lw was given by the professor, Q is 1 and r is the distance from the sound source to the reciever. My problem is that the Lw given is in 4 different directions - it's hard to explain but the sound source is a rectangular box, and the source was emitted in a north, west, east, south way. But my receiver was always on an angle and I can't figure out how to calculate a resultant sound, because sound isn't a force so I can't just sum them together. There's a picture attached showing what I mean. The four arrows are the sounds being emitted. Is there some way I can calculate the directionality to get the sound that the receiver picked up?

I found this equation for a directionality index,

DI = Lp(theta) - Lp

Could this be used?

Thanks for looking! :)

 

[mfb]

because sound isn't a force so I can't just sum them together.

Sound (with a reasonable intensity) is linear, you can just add multiple sound sources as you would do it with forces.

Is there some way I can calculate the directionality to get the sound that the receiver picked up?

That looks problematic.

 

[tesla93]

But the sounds are going in different directions, my professor said you can't treat sounds like forces and take a resultant. He said that I had to use the directionality index but I don't know how to apply that. I used

Lp = Lw - 20log(r) - 11 - Ae with the only unknown being Lw, solved for Lw, and then multiplied that by the directionality I found, but it gave some huge number around 700 dB, and when I plugged that into the final equation to solve for the room constant, I got a negative value. I'm totally lost right now...