# Finding the Directionality of a Sound

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! :)

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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.

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...