 Hello, I'm BDS Tevens. This is a video that I've wanted to record for some time now. I'm going to show you how to use a GNU radio companion without any software defined radio device. Just a software, show you how you can still do some simple things like generate signals and listen to those signals, for example, combine them. And we are going to start with just a simple sound wave that is generated and we are going to listen to it. And then later I'm going to combine two sound waves to have an acoustic beat. And as you can see here on Wikipedia, a beat is an interference pattern between two sounds of slightly different frequencies. And that's what I'm going to do here. So let me go over to GNU radio companion. So I have a new schema here. I'm going to change some settings like I prefer the WX GUI and the sample rate. Since we are going to work with audio, I'm going to put a sample rate at 48 kilohertz like this. And now so we need a signal source. And in the waveform generators here, you have a signal source double click this and it appears here. So 48 kilohertz for the sample rate goes sign. The frequency of the source is 1 kilohertz and the amplitude is 1. And it's a complex output. The blue says that the output is a complex number. So I'm going to change some things. First of all, I'm going to go to floating point real numbers because we're going to work with audio. And I'm going to put the frequency at 400 hertz. Because if you're still familiar with the old phone sets, the 400 hertz is the tone that you hear when you lift the phone set. So this is going to generate a source like this. And then we need also a speaker to listen to this. And in audio, you can go to audio sync. The audio sync here is at 48 kilohertz. We can just connect the two like this. And then I can run this program. Now I need to save it first. So let's say video beat and save this. And now what you hear is that 400 hertz tone. Let me stop that. I also want to visualize that signal. And for that, I'm going to go to instrumentation, WX, and I'm going to take the scope like this. The scope here. 48 kilohertz, that's okay. Not complex. I want float. And I am also just going to connect this output to here. So in GNU radio, that's really simple, just connect it. And then when I run this here, so we hear the sound. You can also see the signal. And if I go to manual and increase the number of seconds per division, you can see here the cosine wave. So the amplitude is one. As you can see, let me stop this. And now what I'm going to do is add another source. So let me first delete these connectors like this. And I'm going to copy this block like this, have two sources. And I'm going to combine them. And here also in GNU radio, this is easy. We just need a mathematical operator to add two numbers, this one here. And as you can see, it is blue. That's complex, but I don't want complex. I want floating point. And then I can add the two inputs together. And then go to my speaker and to my scope. So both cosine 400 amplitude one. Run this like this. And let me raise this a bit like this. So now you can see that the amplitude is two. From top two to bottom minus two. And that is because here we are adding two signals together of amplitude one. So at the top, when you add both together, one plus one gives two. And at the bottom, minus one, minus one is minus two. So that's why the amplitude is larger here. Let me stop this. And now we are going to make an acoustic beat. So I'm going to change the frequency very slightly. I'm going to put it at 401 hertz like this. And let me run this. Okay. And now what you hear, this signal becoming louder and then less loud and becoming silent and then loud again. That is an acoustic beat effect. So two signal sources, two sine waves here of a very slightly different frequency are combined, they are added together. And so since they are not in phase, you have moments where they will cancel each other out and you have moments where they will amplify each other. And on the Wikipedia page, this is nicely illustrated here with this diagram and here with this movie where you can see this. So if I come back to this and I go to auto range, I disable this. And let's increase the count here that we have two. Okay. So you see now that it is variating between zero and two. And if I increase the number of seconds per division, here you see something like a pulsating sine wave. But if I continue to increase this, you can now see that the amplitude of the pulsation also changes. Let me increase this further like this one more. Okay. And now we can see a nice beat pattern. You see that the sine wave, when they are combined, they increase, increase until maximum and then they go down until the minimum. Well, no, zero. Sorry. And the minimum is here and so on. So what you can also see is that the distance between those two zeros is one second. And that also is illustrated here on the Wikipedia page, the beat frequency. So the increasing and decreasing of the sound that you hear, the beat frequency is just the difference between the two frequencies that you are combining. So we are combining 400 and 401. So the difference is one hertz. And one hertz is indeed a frequency that has a difference here of one second. One hertz corresponds to a period of one second.