Hey, guys, let's do an example. Two submarines approach one. Another underwater sub one emits a sonar pulse at one times 10 to the three. Hertz, which travels from sub one towards sub two, is then reflected off of sub to traveling back to sub one. If the speed of sound of water is 1500 m per second, sub one is approaching sub two at a speed of 18 m per second and sub two is approaching sub one at a speed of 15 m per second. What frequency to sub to detect the sonar polls at what frequency to sub one detector reflected sonar pulse app. Okay, so I'll break this up into questions A and questions be question A is what? Frequency to sub to detect the pulse emitted by sub one act. Okay, so here's one sub your second sub. My crappy subs. Sub one is moving towards sub two at 18 m per second sub twos, moving towards sub one at 15 m per second and sub one is emitting sound towards it sub to Okay, so we have the source. We have the detector, the sources sub one, the detectors sub to so the detected frequency is going to be V plus V D over V plus V s ffs. Okay, now the speed of sound is just gonna be 1500. Just like the problem says, 1500 m per second. The question is, what are the signs going to be? And it's emitted at 1000 hertz. What are the signs? And value is gonna be for our velocities for the detector and source. Okay, The sources sub one. So clearly the source should be 18. But is it plus or minus the detectors? Sub two. So includes should be 15 for the detective speed, but is it plus or minus? Don't forget the, uh, corden system. The detectors at the origin and you draw a line from the detector to the source, and that's the positive direction. So the detector is moving towards the source, so that's positive. The source is moving towards the detector, so that is negative. Okay. And all of this equals a detected frequency of 10 hurts. So this is the frequency that sub to detects the sonar pulse from sub one act. Okay, now, part B. Same problem. But now some to someone this one's moving at 18. Still, this one's moving at 15. Still, But now sub two is acting like the source because those sonar be sonar waves are bouncing off of south of sub two and heading back towards sub one. Remember that sound that any wave is reflected off of any circus at the same frequency? So this is exactly like the sub emitting a sound at 1000 at 10. 22 hurts. That's exactly the set up to the problem. So the detected sound is V plus V D the plus V s s. But our detector on our source have flipped. Now, Sub two is the source, Right? And sub one is the detector. So this is still gonna be 1500 plus some speed, some velocity. This is still gonna be 1500 plus some velocity, but now the source frequency is 10. 22 hurts, okay? And our coordinate system has sub two on the right sub one on the left. And remember that the corn systems from the detector to the source is positive. So the detectors velocity is positive. This is plus 15 right? Oh, sorry. The This is the source. I got these backwards. I had also gotten this one backwards, but it still worked because the mirror image looks the same. In this case, the detector is truly on the right and the source is on the left. If I were to flip this around, you would see sub two is the detector. Sub one is the source. This is positive. They're moving towards each other. The detector speed is still positive. The source speed is still negative. Okay, so work out the exact same way. The detectors moving towards the source source moving towards the detector. So you get that same thing, but now the detector sub one. So this is plus 18 the sources sub too. So this is minus 15 and plugging this all in. We get 10 45 hertz. This is how sonar works. Sub one admitted a pulse at 1000 hertz and the received the pulse back at 1000 45 Hertz. Because that sub knows its own speed, it can use this exact equation to find the speed of the other sub based on how large that Doppler shift is. Okay, So is this how sonar for submarines work? Alright, guys, that wraps up this problem. Thanks for watching