Doppler effect: reflection off a moving object

imagine you are at the gym but you got there at a really bad time because there's this big beefy bodybuilder and you know what he just got told his membership is revoked cuz he's never wiping down his sweat off all the equipment and he's mad he's so mad he takes the door and he rips the door off here's the door and he throws it he doesn't know where he's thrown it but he ends up throwing it straight at you at a speed we'll call it VD you're looking at this door coming towards you what do you do I'm not ashamed to say I might start screaming I'm like oh no I start screaming at a certain frequency I'm gonna call that frequency of the scream alright so my question is here's the thing this sound is gonna come over to here it's gonna reflect off the door then it's gonna come back towards you what sound would you hear after this sound wave reflected off the door and got back to you would you hear the same frequency - you're screaming at would you hear a higher frequency would you hear a lower frequency exactly what frequency would you hear let's figure it out it's a good problem it's tricky so I want to know what frequency would I hear so I'm have to use the Doppler effect formulas cuz we've got some moving stuff going on here so the frequency that I hear imma have to do this in two steps actually first of all the sound gets over here to the door I'm gonna think of the door as an observer first the store is gonna act as a moving observer it's gonna hear I want to know what sound this door would hear if it was moving this way now doors can't hear anything but if this door was a person what frequency would it hear it wouldn't be F scream and be something else so I'm gonna call this F door because I want to know what the door hears and if we use the Doppler effect formula F door is gonna equal the frequency that the wave actually has so frequency of the scream maybe it's a yell let's scream okay x over here I've got this factor of it's the speed of sound up top and then it's plus or minus for a moving observer the formula was plus or minus speed of the observer and my door is the observer here I'm pretending that my door can observe I want to know what frequency it receives that it hears divided by the speed of sound now I have to decide whether I want the plus or the minus so I ask myself this I can never remember this as a student always forget there's too many plus and minuses here and I just say to myself if I'm moving toward the source or if the source is moving toward me I know that means frequency that I hear goes up so the frequency this door experiences should be bigger than the frequency that's actually emitted by the person over here by me so if I wanted to be bigger I want to have Plus on top I want a big numerator so I'm gonna erase that I want the plus sign because a big numerator gives me a larger frequency that's the way I remember whether I should add or subtract up here alright so now I'm not done yet you might think we're done if that's the frequency of the door here's well that just reflects off the door and then I should hear that frequency too but no because this is the frequency of the door hears but now the door reradiates that sound back at you this door is acting like a speaker and it's acting like a moving speaker because the doors moving and we know what happens with moving speakers there's another Doppler shift so there's two Doppler shifts that go on here one by the fact that this door is observing experiencing a higher frequency then when it reread E eights that sound outward when it reflects that sound outward it acts as a moving speaker if I want to know the frequency that I will actually hear so what frequency when it gets back to me what frequency will I actually hear all right we've got to do another Doppler shift here we go the frequency I hear will be alright the frequency that the speaker was trying to radiate which was this remember this was the frequency the door was receiving this was the frequency right here F door so it's going to be that another shift so let me just rewrite this over here but times I need to multiply this by another factor you need to multiply this by the another factor that takes into account and the fact that the speaker this door is not a speaker but it's acting as a moving speaker because it's moving the fact that this door is moving and that looks like this that factor if you remember speed of sound on top and then on the bottom its speed of sound plus or minus the speed of the actual speaker which is the door here someone put VD now again we have to pick plus or minus well same thing I go through the same thought process the only thing I like memorizing is the fact that if things come toward each other the frequency should be increasing so again speaker this door moving toward me the Doppler shift should increase the frequency that I hear so to increase the frequency let's see this is on the this is the denominator here if I want to increase the total amount of frequency I need to make the denominator smaller so it seems weird but I need to have a negative sign down here I want to subtract and I want to subtract because subtracting gives me a smaller denominator dividing by a smaller denominator gives me a larger total amount and I know that I should be getting a larger total amount for the frequency I hear because the frequency should get increased by this Doppler shift so this is it the frequency that I would hear I would hear a frequency of the amount I scream times these two factors because there's two Doppler shifts happening here and you can clean things up if you want you can cancel off these V s's if you wanted to which is fine but the important thing is that there's two Doppler shifts and you might think well this is just stupid I mean this was a really stupid example what am I ever gonna find myself in a gym and some beefy bodybuilder throws the door at me well it is kind of stupid but here's a real-life example instead of a door imagine this is blood blood flowing and know that bodybuilder didn't like explode or something imagine instead of a gym instead of a gym this is a vein or the inside of your body somewhere and instead of me this is some sensitive piece of equipment that wants to image that wants to scan the blood flow and know how fast is the blood flowing well here's a way to do it you send sound waves in those sound waves reflect off of moving objects come back at you if you can tell how much the frequency changed you know this is looking this is dependent on the speed of the thing that was moving so this I called it speed of door but in this case it would be the speed of the blood you could figure out how fast that blood is flowing in there and that's useful or if you're not a doctor and you wanted to know if you're a police officer and there's a car chase there's a car heading toward you you want to know how fast it goes this car is coming towards you at some speed and you want to know how fast it's going you could be parked over here you could use radar shoot that radar it wouldn't be sailing this time it's electromagnetic waves this radar would hit the car it would bounce back at you that frequency would shift it would shift by a certain amount that depends on the speed of the car and this is how they can figure out how fast you're going and maybe give you a ticket so slow down out there make sure you don't get caught by the radar