Example: If I had a vacuum cleaner and I turned it on and got another vacuum cleaner and turned it on; both vacuum cleaners are the same. Will the noise stay the same or be louder?I can see it being louder, but I think it will stay the same because it is the same noise which wouldn't really contribute to the loudness of the noise.
Say you have Signal 1 S1(t) and signal 2 S2(t), both functions of time. Obviously Sum= s1(t) + s2(t), and sound is additive, so yes, it is possible for the sum to be louder (but it can also be no change, or depending on the signs of the signals, they could cancel out) But Put 20 vacuum cleaners in one room and it will be REALLY loud. (Another example, imagine a race with one car and a race with 30 cars)
It depends. A vacuum cleaner is probably a bad example. A vacuum generates more of a white noise than a tone or particular 'sound' that could be easily tested or studied. Practically speaking and actually taking measurements, you'll probably find it louder, but not twice as loud. Pressure waves (sound) can be additive, or they can cancel each other out depending on their phase. If two identical pressure waves are exactly in phase, the result is a doubling of their amplitude. If they are exactly out of phase, they cancel each other out and you won't hear anything.
