; Pracheeti Shikarkhane NCSSM Summer Accelerator 2020 globals [txcor tycor prev-ticks init-radius new-freq add-this-train add-this-observer oycor velO] breed [trains train] breed [waves wave] breed [people person] waves-own [age] to setup clear-all set txcor train-xpos set tycor train-ypos set velO observer-velocity set prev-ticks 0 set init-radius 2 set add-this-train (train-velocity) set add-this-observer (velO) ask trains [set xcor train-xpos] set-default-shape waves "dot" set-default-shape trains "train" set-default-shape people "person service" if (train-velocity < 0)[ set-default-shape trains "train 2" ] if (train-velocity >= 0)[ set-default-shape trains "train" ] create-trains 1 [setxy train-xpos train-ypos set size 15 set color grey] create-people 1 [setxy observer-xpos observer-ypos set size 10 set color grey] reset-ticks end to step update-train-pos update-observer-pos if (ticks = (prev-ticks + emit-interval)) or (ticks = 0) [ create-wave set prev-ticks ticks ] ask waves [forward 7] kys calculate-frequency tick end to kys ask waves with [(xcor > 0) and (floor(xcor) >= (max-pxcor - 1))] [die] ask waves with [(xcor < 0) and (ceiling(xcor) <= (min-pxcor + 1))] [die] ask waves with [(ycor > 0) and (floor(ycor) >= (max-pycor - 1))] [die] ask waves with [(ycor < 0) and (ceiling(ycor) <= (min-pycor + 1))] [die] end to create-wave let center patch txcor train-ypos if (show-sound-waves = true) [ create-ordered-waves 300 [ move-to center fd init-radius set color blue ] ] end to update-train-pos ask train 0 [ if (xcor <= (max-pxcor - 1)) and (xcor >= (min-pxcor + 1)) and (abs(xcor + train-velocity) < (max-pxcor - 1)) [ set xcor (xcor + add-this-train) set ycor train-ypos set txcor xcor ] ] end to update-observer-pos ask people [ if (ycor <= (max-pycor - 1)) and (ycor >= (min-pycor + 1)) and (abs(ycor + observer-velocity) < (max-pycor - 1)) [ set xcor observer-xpos set ycor (ycor + add-this-observer) set oycor ycor ] ] end to calculate-frequency let v-sound 34.3 ; sound travels at 343 m/s through the air let x-dist abs(observer-xpos - txcor) let y-dist abs(oycor - train-ypos) let angle-approach ifelse-value (y-dist = 0 and x-dist = 0) [0] [atan y-dist x-dist] if (oycor >= (max-pycor - 1 - abs(observer-velocity))) or (oycor <= (min-pycor + 1 + abs(observer-velocity)))[ set velO 0 ] if (observer-xpos >= txcor) [ if (train-ypos >= oycor) [ set new-freq train-whistle-frequency * ((v-sound + (velO * sin(angle-approach))) /(v-sound - (train-velocity * cos(angle-approach)))) ] if (train-ypos < oycor) [ set new-freq train-whistle-frequency * ((v-sound - (velO * sin(angle-approach))) /(v-sound - (train-velocity * cos(angle-approach)))) ] ] if (observer-xpos < txcor) [ if (train-ypos >= oycor) [ set new-freq train-whistle-frequency * ((v-sound + (velO * sin(angle-approach))) /(v-sound + (train-velocity * cos(angle-approach)))) ] if (train-ypos < oycor) [ set new-freq train-whistle-frequency * ((v-sound - (velO * sin(angle-approach))) /(v-sound + (train-velocity * cos(angle-approach)))) ] ] end @#$#@#$#@ GRAPHICS-WINDOW 0 10 970 261 -1 -1 2.0 1 10 1 1 1 0 0 0 1 -240 240 -60 60 1 1 1 ticks 30.0 BUTTON 366 293 429 326 NIL setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 434 293 497 326 NIL step NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 502 293 565 326 go step T 1 T OBSERVER NIL NIL NIL NIL 1 PLOT 571 292 829 477 pitch heard by observer ticks frequency (Hz) 0.0 10.0 70.0 150.0 true false "" "" PENS "frequency" 1.0 0 -16777216 true "" "plot new-freq" SWITCH 15 437 185 470 show-sound-waves show-sound-waves 0 1 -1000 SLIDER 188 292 360 325 train-velocity train-velocity -10 10 8.0 1 1 NIL HORIZONTAL SLIDER 189 367 361 400 train-ypos train-ypos -55 55 0.0 1 1 NIL HORIZONTAL SLIDER 189 329 361 362 train-xpos train-xpos -239 239 -123.0 1 1 NIL HORIZONTAL SLIDER 13 329 185 362 observer-xpos observer-xpos -239 239 -14.0 1 1 NIL HORIZONTAL SLIDER 13 366 185 399 observer-ypos observer-ypos -59 59 -27.0 1 1 NIL HORIZONTAL MONITOR 836 292 968 337 frequency heard (Hz) new-freq 3 1 11 SLIDER 14 402 186 435 emit-interval emit-interval 1 5 2.0 1 1 NIL HORIZONTAL SLIDER 13 292 185 325 observer-velocity observer-velocity -10 10 0.0 1 1 NIL HORIZONTAL SLIDER 190 402 361 435 train-whistle-frequency train-whistle-frequency 50 100 100.0 1 1 NIL HORIZONTAL @#$#@#$#@ ## WHAT IS IT? This model simulates the effects of the doppler effect by emulating the frequency of sound heard by an observer as a train passes by. The doppler effect is defined as the apparent change in the frequency of a wave caused by relative motion between the source of the wave and the observer. For the driver of the train, the sound would consistently be heard at the same original frequency. However, since the sound waves appear to be closer together in the direction the train is traveling and spread further apart in the opposite direction, an observer would hear variations in relative frequency as the train passes him. A higher relative frequency would be observed in front of the train, and a lower relative freqency would be observed behind the train. ## HOW IT WORKS The frequency heard by the observer is calculated based on the doppler effect equation. If the observer is moving towards the train, the speed of the observer is added in the numerator and subtracted if it is moving away from the train. If the train is moving towards the observer, the speed of the train is subtracted in the denominator and added if it is moving away from the observer. If the observer and train do not have the same y coordinate, the observer’s velocity is multiplied by the sine of theta and the train’s velocity is multiplied by the cosine of theta where theta is the angle between the train's forward velocity and the line of sight from the train to the observer. The model simulates the motion of sound waves by emitting a "wave" from the train after a certain, user-specified interval. The waves are represened by creating a circle of 300 agents and then moving the agents forward during each time step. ## HOW TO USE IT The model takes in inputs of both the observing person’s and train’s x and y positions. It also takes in inputs for the train’s velocity (horizontal only) and the observing person’s velocity (vertical only). The frequency of the train’s whistle, the emission interval of the sound waves, and the visibility of the sound waves are also user inputs. The visual outputs include a monitor that displays the frequency heard by the observing person at each tick, as well as a graph of the frequency heard by the observing person over time. Once you've set the inputs, make sure that the speed slider at the top is set to "slower". Setting it two notches below "normal" will give the ideal speed to observe relative freqency. Next, click the setup button and then the go button to watch the model run. ## THINGS TO NOTICE Note that the sound heard by an observer is actually the combination of both frequency and intensity. This makes the observed noise sound as though it is heard in a smooth, parabolic increase and then decrease as the train passes the observer. The intensity of the sound does indeed follow this behavior. However, the frequency of the observed sound follows different graphical patterns, those that can be observed from test cases within this model. When the observer is stationary and consistently has the same y-coordinate as the train, the relative pitch wil be constant while the observer is in front of the train and will drop right away to a lower constant after the train passes the observer. However, if the observer is not begin at the same y-coordinate as the train or is also in motion, the observer will experience a gradual decrease in pitch as the train approaches, a faster decrease in pitch as the train nears, and then again a gradual decrease in pitch as the train passes. ## THINGS TO TRY Try running the model when the train and observer are positioned at the same initial y coordinates and the observer has no velocity. Then try giving the observer velocity. Try out the same velocity values for the train and observer but with them starting at different initial y coordinates. Try positioning the observer behind the train while the train travels forward. Try increasing the velocity of the train so that it travels at or even faster than the speed of sound. ## EXTENDING THE MODEL In order to further the complexity of the model, the train could have parameters to accelerate. Furthermore, the calculations for observed frequency could be performed based on the observer sensing the frequency at which the waves hit him rather than using an equation. The observer could also have parameters to travel diagonally - appropriate changes to the equation would have to be made in order to accurately represent this. ## NETLOGO FEATURES Use of the create-ordered-turtles command to create the sound waves. The wrap feature is disabled; instead, agents in the wave are terminated once they reach the frame boundaries. ## CREDITS AND REFERENCES https://www.youtube.com/watch?v=h4OnBYrbCjY&t=50s https://www.youtube.com/watch?v=P88AvLRWLVQ https://en.wikipedia.org/wiki/Doppler_effect Wilensky, U. 1999. NetLogo 6.1.1. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University. Evanston, IL. This model was created by Pracheeti N. Shikarkhane Appreciation is extended to the North Carolina School of Science and Mathematics for the opportunity to pursue this work. @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle -7500403 true true 110 75 80 Line -7500403 true 150 100 80 30 Line -7500403 true 150 100 220 30 butterfly true 0 Polygon -7500403 true true 150 165 209 199 225 225 225 255 195 270 165 255 150 240 Polygon -7500403 true true 150 165 89 198 75 225 75 255 105 270 135 255 150 240 Polygon -7500403 true true 139 148 100 105 55 90 25 90 10 105 10 135 25 180 40 195 85 194 139 163 Polygon -7500403 true true 162 150 200 105 245 90 275 90 290 105 290 135 275 180 260 195 215 195 162 165 Polygon -16777216 true false 150 255 135 225 120 150 135 120 150 105 165 120 180 150 165 225 Circle -16777216 true false 135 90 30 Line -16777216 false 150 105 195 60 Line -16777216 false 150 105 105 60 car false 0 Polygon -7500403 true true 300 180 279 164 261 144 240 135 226 132 213 106 203 84 185 63 159 50 135 50 75 60 0 150 0 165 0 225 300 225 300 180 Circle -16777216 true false 180 180 90 Circle -16777216 true false 30 180 90 Polygon -16777216 true false 162 80 132 78 134 135 209 135 194 105 189 96 180 89 Circle -7500403 true true 47 195 58 Circle -7500403 true true 195 195 58 circle false 0 Circle -7500403 true true 0 0 300 circle 2 false 0 Circle -7500403 true true 0 0 300 Circle -16777216 true false 30 30 240 cow false 0 Polygon -7500403 true true 200 193 197 249 179 249 177 196 166 187 140 189 93 191 78 179 72 211 49 209 48 181 37 149 25 120 25 89 45 72 103 84 179 75 198 76 252 64 272 81 293 103 285 121 255 121 242 118 224 167 Polygon -7500403 true true 73 210 86 251 62 249 48 208 Polygon -7500403 true true 25 114 16 195 9 204 23 213 25 200 39 123 cylinder false 0 Circle -7500403 true true 0 0 300 dot false 0 Circle -7500403 true true 0 0 300 face happy false 0 Circle -7500403 true true 8 8 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Polygon -16777216 true false 150 255 90 239 62 213 47 191 67 179 90 203 109 218 150 225 192 218 210 203 227 181 251 194 236 217 212 240 face neutral false 0 Circle -7500403 true true 8 7 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Rectangle -16777216 true false 60 195 240 225 face sad false 0 Circle -7500403 true true 8 8 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Polygon -16777216 true false 150 168 90 184 62 210 47 232 67 244 90 220 109 205 150 198 192 205 210 220 227 242 251 229 236 206 212 183 fish false 0 Polygon -1 true false 44 131 21 87 15 86 0 120 15 150 0 180 13 214 20 212 45 166 Polygon -1 true false 135 195 119 235 95 218 76 210 46 204 60 165 Polygon -1 true false 75 45 83 77 71 103 86 114 166 78 135 60 Polygon -7500403 true true 30 136 151 77 226 81 280 119 292 146 292 160 287 170 270 195 195 210 151 212 30 166 Circle -16777216 true false 215 106 30 flag false 0 Rectangle -7500403 true true 60 15 75 300 Polygon -7500403 true true 90 150 270 90 90 30 Line -7500403 true 75 135 90 135 Line -7500403 true 75 45 90 45 flower false 0 Polygon -10899396 true false 135 120 165 165 180 210 180 240 150 300 165 300 195 240 195 195 165 135 Circle -7500403 true true 85 132 38 Circle -7500403 true true 130 147 38 Circle -7500403 true true 192 85 38 Circle -7500403 true true 85 40 38 Circle -7500403 true true 177 40 38 Circle -7500403 true true 177 132 38 Circle -7500403 true true 70 85 38 Circle -7500403 true true 130 25 38 Circle -7500403 true true 96 51 108 Circle -16777216 true false 113 68 74 Polygon -10899396 true false 189 233 219 188 249 173 279 188 234 218 Polygon -10899396 true false 180 255 150 210 105 210 75 240 135 240 house false 0 Rectangle -7500403 true true 45 120 255 285 Rectangle -16777216 true false 120 210 180 285 Polygon -7500403 true true 15 120 150 15 285 120 Line -16777216 false 30 120 270 120 leaf false 0 Polygon -7500403 true true 150 210 135 195 120 210 60 210 30 195 60 180 60 165 15 135 30 120 15 105 40 104 45 90 60 90 90 105 105 120 120 120 105 60 120 60 135 30 150 15 165 30 180 60 195 60 180 120 195 120 210 105 240 90 255 90 263 104 285 105 270 120 285 135 240 165 240 180 270 195 240 210 180 210 165 195 Polygon -7500403 true true 135 195 135 240 120 255 105 255 105 285 135 285 165 240 165 195 line true 0 Line -7500403 true 150 0 150 300 line half true 0 Line -7500403 true 150 0 150 150 pentagon false 0 Polygon -7500403 true true 150 15 15 120 60 285 240 285 285 120 person false 0 Circle -7500403 true true 110 5 80 Polygon -7500403 true true 105 90 120 195 90 285 105 300 135 300 150 225 165 300 195 300 210 285 180 195 195 90 Rectangle -7500403 true true 127 79 172 94 Polygon -7500403 true true 195 90 240 150 225 180 165 105 Polygon -7500403 true true 105 90 60 150 75 180 135 105 person service false 0 Polygon -7500403 true true 180 195 120 195 90 285 105 300 135 300 150 225 165 300 195 300 210 285 Polygon -1 true false 120 90 105 90 60 195 90 210 120 150 120 195 180 195 180 150 210 210 240 195 195 90 180 90 165 105 150 165 135 105 120 90 Polygon -1 true false 123 90 149 141 177 90 Rectangle -7500403 true true 123 76 176 92 Circle -7500403 true true 110 5 80 Line -13345367 false 121 90 194 90 Line -16777216 false 148 143 150 196 Rectangle -16777216 true false 116 186 182 198 Circle -1 true false 152 143 9 Circle -1 true false 152 166 9 Rectangle -16777216 true false 179 164 183 186 Polygon -2674135 true false 180 90 195 90 183 160 180 195 150 195 150 135 180 90 Polygon -2674135 true false 120 90 105 90 114 161 120 195 150 195 150 135 120 90 Polygon -2674135 true false 155 91 128 77 128 101 Rectangle -16777216 true false 118 129 141 140 Polygon -2674135 true false 145 91 172 77 172 101 plant false 0 Rectangle -7500403 true true 135 90 165 300 Polygon -7500403 true true 135 255 90 210 45 195 75 255 135 285 Polygon -7500403 true true 165 255 210 210 255 195 225 255 165 285 Polygon -7500403 true true 135 180 90 135 45 120 75 180 135 210 Polygon -7500403 true true 165 180 165 210 225 180 255 120 210 135 Polygon -7500403 true true 135 105 90 60 45 45 75 105 135 135 Polygon -7500403 true true 165 105 165 135 225 105 255 45 210 60 Polygon -7500403 true true 135 90 120 45 150 15 180 45 165 90 sheep false 15 Circle -1 true true 203 65 88 Circle -1 true true 70 65 162 Circle -1 true true 150 105 120 Polygon -7500403 true false 218 120 240 165 255 165 278 120 Circle -7500403 true false 214 72 67 Rectangle -1 true true 164 223 179 298 Polygon -1 true true 45 285 30 285 30 240 15 195 45 210 Circle -1 true true 3 83 150 Rectangle -1 true true 65 221 80 296 Polygon -1 true true 195 285 210 285 210 240 240 210 195 210 Polygon -7500403 true false 276 85 285 105 302 99 294 83 Polygon -7500403 true false 219 85 210 105 193 99 201 83 square false 0 Rectangle -7500403 true true 30 30 270 270 square 2 false 0 Rectangle -7500403 true true 30 30 270 270 Rectangle -16777216 true false 60 60 240 240 star false 0 Polygon -7500403 true true 151 1 185 108 298 108 207 175 242 282 151 216 59 282 94 175 3 108 116 108 target false 0 Circle -7500403 true true 0 0 300 Circle -16777216 true false 30 30 240 Circle -7500403 true true 60 60 180 Circle -16777216 true false 90 90 120 Circle -7500403 true true 120 120 60 train false 0 Rectangle -7500403 true true 30 105 240 150 Polygon -7500403 true true 240 105 270 30 180 30 210 105 Polygon -7500403 true true 195 180 270 180 300 210 195 210 Circle -7500403 true true 0 165 90 Circle -7500403 true true 240 225 30 Circle -7500403 true true 90 165 90 Circle -7500403 true true 195 225 30 Rectangle -7500403 true true 0 30 105 150 Rectangle -16777216 true false 30 60 75 105 Polygon -7500403 true true 195 180 165 150 240 150 240 180 Rectangle -7500403 true true 135 75 165 105 Rectangle -7500403 true true 225 120 255 150 Rectangle -16777216 true false 30 203 150 218 train 2 false 0 Rectangle -7500403 true true 60 105 270 150 Polygon -7500403 true true 60 105 30 30 120 30 90 105 Polygon -7500403 true true 105 180 30 180 0 210 105 210 Circle -7500403 true true 210 165 90 Circle -7500403 true true 30 225 30 Circle -7500403 true true 120 165 90 Circle -7500403 true true 75 225 30 Rectangle -7500403 true true 195 30 300 150 Rectangle -16777216 true false 225 60 270 105 Polygon -7500403 true true 105 180 135 150 60 150 60 180 Rectangle -7500403 true true 135 75 165 105 Rectangle -7500403 true true 45 120 75 150 Rectangle -16777216 true false 150 203 270 218 tree false 0 Circle -7500403 true true 118 3 94 Rectangle -6459832 true false 120 195 180 300 Circle -7500403 true true 65 21 108 Circle -7500403 true true 116 41 127 Circle -7500403 true true 45 90 120 Circle -7500403 true true 104 74 152 triangle false 0 Polygon -7500403 true true 150 30 15 255 285 255 triangle 2 false 0 Polygon -7500403 true true 150 30 15 255 285 255 Polygon -16777216 true false 151 99 225 223 75 224 truck false 0 Rectangle -7500403 true true 4 45 195 187 Polygon -7500403 true true 296 193 296 150 259 134 244 104 208 104 207 194 Rectangle -1 true false 195 60 195 105 Polygon -16777216 true false 238 112 252 141 219 141 218 112 Circle -16777216 true false 234 174 42 Rectangle -7500403 true true 181 185 214 194 Circle -16777216 true false 144 174 42 Circle -16777216 true false 24 174 42 Circle -7500403 false true 24 174 42 Circle -7500403 false true 144 174 42 Circle -7500403 false true 234 174 42 turtle true 0 Polygon -10899396 true false 215 204 240 233 246 254 228 266 215 252 193 210 Polygon -10899396 true false 195 90 225 75 245 75 260 89 269 108 261 124 240 105 225 105 210 105 Polygon -10899396 true false 105 90 75 75 55 75 40 89 31 108 39 124 60 105 75 105 90 105 Polygon -10899396 true false 132 85 134 64 107 51 108 17 150 2 192 18 192 52 169 65 172 87 Polygon -10899396 true false 85 204 60 233 54 254 72 266 85 252 107 210 Polygon -7500403 true true 119 75 179 75 209 101 224 135 220 225 175 261 128 261 81 224 74 135 88 99 wheel false 0 Circle -7500403 true true 3 3 294 Circle -16777216 true false 30 30 240 Line -7500403 true 150 285 150 15 Line -7500403 true 15 150 285 150 Circle -7500403 true true 120 120 60 Line -7500403 true 216 40 79 269 Line -7500403 true 40 84 269 221 Line -7500403 true 40 216 269 79 Line -7500403 true 84 40 221 269 wolf false 0 Polygon -16777216 true false 253 133 245 131 245 133 Polygon -7500403 true true 2 194 13 197 30 191 38 193 38 205 20 226 20 257 27 265 38 266 40 260 31 253 31 230 60 206 68 198 75 209 66 228 65 243 82 261 84 268 100 267 103 261 77 239 79 231 100 207 98 196 119 201 143 202 160 195 166 210 172 213 173 238 167 251 160 248 154 265 169 264 178 247 186 240 198 260 200 271 217 271 219 262 207 258 195 230 192 198 210 184 227 164 242 144 259 145 284 151 277 141 293 140 299 134 297 127 273 119 270 105 Polygon -7500403 true true -1 195 14 180 36 166 40 153 53 140 82 131 134 133 159 126 188 115 227 108 236 102 238 98 268 86 269 92 281 87 269 103 269 113 x false 0 Polygon -7500403 true true 270 75 225 30 30 225 75 270 Polygon -7500403 true true 30 75 75 30 270 225 225 270 @#$#@#$#@ NetLogo 6.1.1 @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ default 0.0 -0.2 0 0.0 1.0 0.0 1 1.0 0.0 0.2 0 0.0 1.0 link direction true 0 Line -7500403 true 150 150 90 180 Line -7500403 true 150 150 210 180 @#$#@#$#@ 0 @#$#@#$#@