1 00:00:01,375 --> 00:00:03,951 -Imagine, you are at the gym. 2 00:00:03,951 --> 00:00:05,802 But, you got there at a really bad time. 3 00:00:05,802 --> 00:00:08,203 Because there's this big, beefy bodybuilder. 4 00:00:09,449 --> 00:00:13,156 He just got told his membership is revoked. 5 00:00:13,156 --> 00:00:15,870 Because he's never wiping down his sweat 6 00:00:15,870 --> 00:00:16,283 off all the equipment. 7 00:00:16,283 --> 00:00:17,363 And he's mad. 8 00:00:17,538 --> 00:00:22,240 He's so mad, he takes the door, he rips the door off. 9 00:00:22,515 --> 00:00:24,716 Here's the door, and he throws it. 10 00:00:24,716 --> 00:00:25,742 He doesn't know where he's throwing it, 11 00:00:25,742 --> 00:00:27,719 but he ends up throwing it straight at you. 12 00:00:27,744 --> 00:00:30,272 At a speed, we'll call it Vd. 13 00:00:30,448 --> 00:00:31,752 You're looking at this door coming towards you. 14 00:00:31,752 --> 00:00:32,950 What do you do? 15 00:00:33,000 --> 00:00:35,503 I'm not ashamed to say, I might start screaming. 16 00:00:35,954 --> 00:00:37,154 I'm like, "Oh, no!" 17 00:00:37,279 --> 00:00:39,780 I start screaming at a certain frequency. 18 00:00:39,980 --> 00:00:43,609 And I'm going to call that frequency of the scream. 19 00:00:43,809 --> 00:00:47,436 So, my question is, here's the thing. 20 00:00:47,511 --> 00:00:50,139 This sound is gonna come over to here, 21 00:00:50,139 --> 00:00:51,939 it's gonna reflect off the door. 22 00:00:52,417 --> 00:00:54,742 Then it's gonna come back towards you. 23 00:00:55,368 --> 00:00:59,145 What sound would you hear, after this sound wave 24 00:00:59,145 --> 00:01:01,321 reflected off the door and got back to you? 25 00:01:01,321 --> 00:01:02,723 Would you hear the same frequency 26 00:01:02,723 --> 00:01:03,673 that you're screaming at? 27 00:01:03,673 --> 00:01:05,149 Would you hear a higher frequency? 28 00:01:05,149 --> 00:01:06,500 Would you hear a lower frequency? 29 00:01:06,500 --> 00:01:08,152 Exactly what frequency would you hear? 30 00:01:08,177 --> 00:01:10,778 Let's figure it out, it's a good problem. It's tricky. 31 00:01:11,864 --> 00:01:14,705 I wanna know, what frequency would I hear? 32 00:01:14,705 --> 00:01:16,708 So I'm gonna have to use the Doppler Effect formula. 33 00:01:16,708 --> 00:01:19,840 This could be best in moving stuff going on here. 34 00:01:19,840 --> 00:01:22,436 So the frequency that I hear-- 35 00:01:22,436 --> 00:01:24,694 I'm gonna have to do this in two steps actually. 36 00:01:24,694 --> 00:01:27,945 First of all, the sound gets over here to the door. 37 00:01:28,996 --> 00:01:30,999 I'm gonna think of the door as an observer first. 38 00:01:30,999 --> 00:01:33,625 This door is gonna act as a moving observer. 39 00:01:34,275 --> 00:01:34,827 It's gonna hear. 40 00:01:34,827 --> 00:01:36,530 I wanna know what sound 41 00:01:36,530 --> 00:01:39,604 this door would hear if it was moving this way. 42 00:01:39,604 --> 00:01:41,500 Now, doors can't hear anything, 43 00:01:41,500 --> 00:01:42,581 but if this door was a person, 44 00:01:43,565 --> 00:01:44,657 what frequency would it hear? 45 00:01:44,657 --> 00:01:46,457 It wouldn't be f-scream. 46 00:01:46,457 --> 00:01:47,808 It'd be something else. 47 00:01:47,808 --> 00:01:50,984 So I'm gonna call this f-door. 48 00:01:50,984 --> 00:01:52,785 Because I wanna know what the door hears. 49 00:01:52,785 --> 00:01:54,786 And if we use the Doppler Effect formula. 50 00:01:55,478 --> 00:01:58,390 f-door is gonna equal the frequency 51 00:01:58,390 --> 00:02:00,690 that the wave actually has. 52 00:02:00,841 --> 00:02:03,118 So, frequency of the scream. 53 00:02:05,495 --> 00:02:10,495 Times, the factor of speed of sound up top, 54 00:02:12,675 --> 00:02:16,351 plus or minus for a moving observer. 55 00:02:16,702 --> 00:02:21,154 The formula was plus or minus, speed of the observer. 56 00:02:21,154 --> 00:02:23,104 And my door, is the observer here. 57 00:02:23,104 --> 00:02:24,582 Pretending that my door can observe. 58 00:02:24,582 --> 00:02:26,590 I wanna know what frequency it receives, that it receives. 59 00:02:26,790 --> 00:02:28,660 That it hears. 60 00:02:28,660 --> 00:02:30,267 Divided by the speed of sound. 61 00:02:30,267 --> 00:02:33,180 Then I have to decide whether I want the plus or the minus. 62 00:02:33,180 --> 00:02:34,430 So I ask myself this-- 63 00:02:34,430 --> 00:02:35,394 I could never remember this as a student. 64 00:02:35,394 --> 00:02:37,570 I always forget, there's too many plus and minuses here. 65 00:02:37,870 --> 00:02:40,321 And I have to say to myself. 66 00:02:40,321 --> 00:02:43,548 If I'm moving toward the source, 67 00:02:43,548 --> 00:02:45,324 or if the source is moving toward me. 68 00:02:45,324 --> 00:02:48,750 I know that means frequency that I hear goes up. 69 00:02:48,950 --> 00:02:50,978 So the frequency this door experiences 70 00:02:50,978 --> 00:02:53,154 should be bigger than the frequency 71 00:02:53,154 --> 00:02:56,455 that's actually emitted by the person over here, by me. 72 00:02:56,580 --> 00:02:57,681 So if I want it to be bigger. 73 00:02:57,681 --> 00:02:59,632 I wanna have plus on top. 74 00:02:59,632 --> 00:03:01,508 I want a big numerator. 75 00:03:03,100 --> 00:03:04,936 I want the plus sign, because a big numerator 76 00:03:05,582 --> 00:03:07,890 gives me a larger frequency. 77 00:03:08,169 --> 00:03:09,217 That's the way I remember 78 00:03:09,217 --> 00:03:11,221 whether I should add or subtract it here. 79 00:03:11,523 --> 00:03:14,740 Alright, so I'm not done yet. 80 00:03:14,740 --> 00:03:15,475 You might think we're done. 81 00:03:15,475 --> 00:03:17,476 If that's the frequency the door hears. 82 00:03:17,476 --> 00:03:19,200 Well, that just reflects off the door. 83 00:03:19,200 --> 00:03:21,252 And then I should hear that frequency too. 84 00:03:21,655 --> 00:03:25,600 But no, because this is the frequency the door hears. 85 00:03:25,600 --> 00:03:30,233 But now the door re-radiates that sound back at you. 86 00:03:30,509 --> 00:03:33,635 This door is acting like a speaker, 87 00:03:33,635 --> 00:03:35,936 and it's acting a like moving speaker, 88 00:03:35,936 --> 00:03:37,712 because the door's moving. 89 00:03:37,712 --> 00:03:39,288 We know what happens with moving speakers. 90 00:03:39,288 --> 00:03:41,630 There's another Doppler Shift. 91 00:03:41,630 --> 00:03:43,389 So there's two Doppler Shifts that go on here. 92 00:03:43,389 --> 00:03:46,716 One, by the fact that this door is observing, 93 00:03:46,716 --> 00:03:48,642 experiencing a higher frequency. 94 00:03:48,817 --> 00:03:51,468 Then, when it re-radiates that sound outward. 95 00:03:51,468 --> 00:03:53,269 When it reflects that sound outward. 96 00:03:53,648 --> 00:03:55,774 It acts as a moving speaker. 97 00:03:55,774 --> 00:03:57,726 So I wanna know the frequency 98 00:03:57,726 --> 00:03:59,927 that I will actually hear. 99 00:04:01,203 --> 00:04:03,954 So, what frequency when it gets back to me. 100 00:04:04,281 --> 00:04:07,457 What frequency will I actually hear? 101 00:04:07,983 --> 00:04:10,590 Alright, we gotta do another Doppler Shift. 102 00:04:10,611 --> 00:04:11,636 Here we go. 103 00:04:11,636 --> 00:04:13,512 The frequency I hear will be 104 00:04:13,512 --> 00:04:17,641 the frequency the speaker was trying to radiate, 105 00:04:17,641 --> 00:04:18,966 which was this. 106 00:04:19,410 --> 00:04:21,968 Remember, this was the frequency, 107 00:04:21,968 --> 00:04:24,194 the door was receiving. 108 00:04:24,194 --> 00:04:26,870 This was the frequency right here, f-door. 109 00:04:26,870 --> 00:04:30,221 So, it's gonna be that times another shift. 110 00:04:30,221 --> 00:04:32,220 So, let me just rewrite this over here. 111 00:04:32,220 --> 00:04:35,549 But times--I need to multiply this by another factor. 112 00:04:35,749 --> 00:04:37,775 I need to multiply this by another factor 113 00:04:37,775 --> 00:04:39,301 that takes into account, 114 00:04:39,301 --> 00:04:41,760 the fact that the speaker-- 115 00:04:41,760 --> 00:04:42,377 this door's not a speaker, 116 00:04:42,377 --> 00:04:44,605 but it's acting as a moving speaker, because it's moving. 117 00:04:44,605 --> 00:04:46,606 The fact that this door is moving. 118 00:04:46,933 --> 00:04:48,633 And that looks like this. 119 00:04:48,633 --> 00:04:50,709 That factor, if you remember, 120 00:04:50,709 --> 00:04:52,160 speed of sound on top. 121 00:04:52,160 --> 00:04:54,236 And on the bottom it's speed of sound 122 00:04:55,066 --> 00:04:59,288 plus or minus the speed of the actual speaker. 123 00:04:59,338 --> 00:05:02,240 Which is the door here, so I'm gonna put Vd. 124 00:05:02,240 --> 00:05:04,191 Now again, we're gonna have to pick plus or minus. 125 00:05:04,191 --> 00:05:07,417 Well, same thing. I go through the same thought process. 126 00:05:07,417 --> 00:05:08,944 The only thing I like memorizing is the fact 127 00:05:08,944 --> 00:05:10,645 that if things come toward each other, 128 00:05:10,645 --> 00:05:12,421 the frequency should be increasing. 129 00:05:12,871 --> 00:05:16,223 So again, speaker, this door moving toward me. 130 00:05:16,473 --> 00:05:18,524 The Doppler Shift should increase 131 00:05:18,524 --> 00:05:20,500 the frequency that I hear. 132 00:05:20,500 --> 00:05:22,426 So, to increase the frequency. 133 00:05:22,426 --> 00:05:24,852 Let's see, this is the denominator here. 134 00:05:24,977 --> 00:05:27,753 I want to increase the total amount of frequency. 135 00:05:28,155 --> 00:05:30,181 I need to make the denominator smaller. 136 00:05:30,281 --> 00:05:30,808 So it seems weird, 137 00:05:30,808 --> 00:05:33,234 but I need to have a negative sign down here. 138 00:05:33,284 --> 00:05:34,435 I wanna subtract. 139 00:05:34,535 --> 00:05:36,986 I wanna subtract because subtracting 140 00:05:36,986 --> 00:05:38,586 gives me a smaller denominator. 141 00:05:38,662 --> 00:05:40,587 Dividing by a smaller denominator 142 00:05:40,587 --> 00:05:42,888 gives me a larger total amount. 143 00:05:42,989 --> 00:05:44,341 And I know that I should be getting 144 00:05:44,341 --> 00:05:47,192 a larger total amount for the frequency I hear. 145 00:05:47,217 --> 00:05:48,993 Because the frequency should get increased 146 00:05:48,993 --> 00:05:50,644 by this Doppler Shift. 147 00:05:50,969 --> 00:05:52,169 So, this is it. 148 00:05:52,320 --> 00:05:54,372 The frequency that I would hear. 149 00:05:54,372 --> 00:05:57,849 I would hear a frequency of the amount I scream 150 00:05:57,849 --> 00:05:59,575 times, these two factors. 151 00:05:59,575 --> 00:06:01,677 Because there's two Doppler Shifts happening here. 152 00:06:01,677 --> 00:06:03,753 And, you can clean things up if you want. 153 00:06:03,753 --> 00:06:08,753 You can cancel off these Vs's, if you wanted to. 154 00:06:08,981 --> 00:06:09,856 Which is fine. 155 00:06:09,856 --> 00:06:12,334 But, the important thing is that there's two Doppler Shifts. 156 00:06:12,334 --> 00:06:14,785 And, you might think well this is just stupid. 157 00:06:15,800 --> 00:06:17,787 I mean, this was a really stupid example. 158 00:06:17,787 --> 00:06:19,212 When am I ever gonna find myself in a gym, 159 00:06:19,212 --> 00:06:21,863 and some beefy, bodybuilder throws a door at me? 160 00:06:22,130 --> 00:06:23,890 Well, it is kinda stupid 161 00:06:23,890 --> 00:06:25,415 But, here's a real life example. 162 00:06:25,415 --> 00:06:30,415 Instead of a door, imagine this is blood, blood flowing. 163 00:06:30,744 --> 00:06:33,170 No, the bodybuilder didn't explode or something. 164 00:06:33,672 --> 00:06:36,204 Imagine, instead of a gym 165 00:06:37,039 --> 00:06:39,592 this is a vein inside of your body. 166 00:06:40,367 --> 00:06:41,668 And, instead of me. 167 00:06:41,668 --> 00:06:44,019 This is some sensitive piece of equipment 168 00:06:44,588 --> 00:06:46,395 that wants to image, that wants to scan 169 00:06:46,874 --> 00:06:50,277 the blood flow and know how fast is the blood flowing. 170 00:06:50,277 --> 00:06:51,578 Well, here's a way to do it. 171 00:06:51,578 --> 00:06:53,954 You send sound waves in. 172 00:06:53,954 --> 00:06:56,280 Those sound waves reflect off of moving objects, 173 00:06:56,280 --> 00:06:57,405 and come back at you. 174 00:06:57,405 --> 00:07:00,657 If you can tell how much the frequency changed. 175 00:07:01,487 --> 00:07:04,484 You know--this is dependent on the speed 176 00:07:04,914 --> 00:07:06,486 of the thing that was moving. 177 00:07:06,861 --> 00:07:08,543 So, I called it speed of door. 178 00:07:08,543 --> 00:07:10,193 But in this case it would be the speed of the blood. 179 00:07:10,193 --> 00:07:13,195 You can figure out how fast that blood's flowing in there. 180 00:07:13,220 --> 00:07:14,120 That's useful. 181 00:07:14,120 --> 00:07:15,796 Or, if you're not a doctor. 182 00:07:15,796 --> 00:07:17,672 And you wanted to know--if you're a police officer. 183 00:07:17,672 --> 00:07:19,473 There's a car chase, 184 00:07:19,473 --> 00:07:20,848 and there's a car heading toward you. 185 00:07:20,848 --> 00:07:22,501 You wanna know how fast it goes. 186 00:07:22,501 --> 00:07:24,952 This car's coming toward you at some speed. 187 00:07:24,952 --> 00:07:26,653 And you wanna know how fast it's going. 188 00:07:26,653 --> 00:07:27,807 You could be parked over here. 189 00:07:27,807 --> 00:07:30,385 You could use radar, shoot that radar. 190 00:07:30,385 --> 00:07:33,636 It wouldn't be sound, this time it's electromagnetic waves. 191 00:07:33,636 --> 00:07:34,887 This radar would hit the car. 192 00:07:34,887 --> 00:07:36,238 It would bounce back at you, 193 00:07:36,238 --> 00:07:37,863 that frequency would shift. 194 00:07:37,863 --> 00:07:39,139 It would shift by a certain amount 195 00:07:39,139 --> 00:07:41,540 that depends on the speed of the car. 196 00:07:41,540 --> 00:07:43,541 This is how they can figure how fast you're going. 197 00:07:43,541 --> 00:07:44,445 And maybe give you a ticket. 198 00:07:44,445 --> 00:07:46,121 So, slow down out there. 199 00:07:46,121 --> 00:00:00,000 Make sure you don't get caught by the radar.