00:02
Hi, this is a nice question about interference of waves and in this particular case of sound waves.
00:08
So we have two loudspeakers positioned at a and b.
00:12
So let's try and sketch that.
00:13
So this is one of the loudspeakers at the point i think this is a, yes.
00:20
And then we have another loudspeaker here at the point b.
00:24
And the distance between these two speakers is given by at a different point c we have a listener.
00:32
And this is the position of the listener at point c.
00:39
We know that the two speakers vibrate in phase.
00:41
So this means that the two speakers are coherent.
00:45
And we know the frequency.
00:46
So the frequency is given in the question is 77 hertz.
00:53
We also know the speed of sound.
00:55
So we know v.
00:56
Let's call v the speed of sound.
00:59
And we know that the listener who sits at point c here's the fourth constructive interference, not counting the point at infinity, and we know that this happens at the distance of 8 meters.
01:13
So let's call this distance d as being 8 meters, and i will use capital d for this distance.
01:25
Good.
01:26
So what does that matter? what does that mean that the listener hears the fourth constructive interference? well, we have sound coming from a that goes through this distance, so it goes a distance of 8 meters, and then we have sound coming from the second speaker from b that travels a slightly different distance.
01:52
So we can actually use this triangle here to find the distance that sound travels from the speaker b to the listener at c.
02:00
And by pythagoras theorem that distance is d squared, square root of, capital d squared, plus little d squared...