160:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000 Aplicaciones de la derivada:@0.073089:0.043661:0.316384:0.043661:0.316384:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Simplificando:@0.323781:0.136836:0.423180:0.136836:0.423180:0.120402:0.323781:0.120402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.591207:0.162571:0.595901:0.162571:0.595901:0.146164:0.591207:0.146164:0.000000 L:@0.589742:0.178960:0.597363:0.178960:0.597363:0.162554:0.589742:0.162554:0.000000 = :@0.599120:0.169409:0.618006:0.169409:0.618006:0.152975:0.599120:0.152975:0.000000:0.000000:0.000000 1:@0.652891:0.160155:0.661874:0.160155:0.661874:0.143721:0.652891:0.143721:0.000000 4:@0.632220:0.180125:0.641202:0.180125:0.641202:0.163691:0.632220:0.163691:0.000000 L Tρ:@0.641129:0.180125:0.682490:0.180125:0.682490:0.163719:0.641129:0.163719:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.696848:0.169419:0.700879:0.169419:0.700879:0.152985:0.696848:0.152985:0.000000 Conclusión: :@0.323781:0.210789:0.416127:0.210789:0.416127:0.194119:0.323781:0.194119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la derivada es positiva, lo que indica que, si se :@0.416093:0.210789:0.749857:0.210789:0.749857:0.194355:0.416093:0.194355:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 aumenta la tensión:@0.749614:0.210789:0.895593:0.210789:0.895593:0.194119:0.749614:0.194119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , la :@0.895455:0.210789:0.930944:0.210789:0.930944:0.194355:0.895455:0.194355:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 T:@0.899505:0.210789:0.907622:0.210789:0.907622:0.194383:0.899505:0.194383:0.000000 frecuencia aumenta.:@0.323763:0.227431:0.480390:0.227431:0.480390:0.210997:0.323763:0.210997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.403080:0.227431:0.407773:0.227431:0.407773:0.211025:0.403080:0.211025:0.000000 3. Derivada de respecto a la densidad lineal (con y constante).:@0.293660:0.254794:0.818354:0.254794:0.818354:0.238124:0.293660:0.238124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.419189:0.254794:0.424398:0.254794:0.424398:0.238111:0.419189:0.238111:0.000000 ρ:@0.646390:0.254794:0.656275:0.254794:0.656275:0.238111:0.646390:0.238111:0.000000 L T:@0.697231:0.254794:0.730253:0.254794:0.730253:0.238111:0.697231:0.238111:0.000000:0.000000:0.000000 f:@0.568767:0.284819:0.573460:0.284819:0.573460:0.268413:0.568767:0.268413:0.000000 = :@0.573387:0.284819:0.626110:0.284812:0.626110:0.268379:0.573387:0.268385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.596751:0.277975:0.605733:0.277975:0.605733:0.261542:0.596751:0.261542:0.000000 2:@0.592977:0.294368:0.601960:0.294368:0.601960:0.277934:0.592977:0.277934:0.000000 L:@0.601886:0.294368:0.609507:0.294368:0.609507:0.277961:0.601886:0.277961:0.000000 T:@0.630173:0.277975:0.638291:0.277975:0.638291:0.261569:0.630173:0.261569:0.000000 ρ:@0.629455:0.294368:0.639027:0.294368:0.639027:0.277961:0.629455:0.277961:0.000000 Tomamos la derivada parcial respecto a ::@0.323781:0.325761:0.625789:0.325761:0.625789:0.309328:0.323781:0.309328:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ρ:@0.613088:0.325761:0.622660:0.325761:0.622660:0.309355:0.613088:0.309355:0.000000 :@0.528132:0.350145:0.532734:0.350145:0.532734:0.333157:0.528132:0.333157:0.000000 f:@0.530341:0.350561:0.535034:0.350561:0.535034:0.334155:0.530341:0.334155:0.000000 :@0.526669:0.366787:0.531271:0.366787:0.531271:0.349799:0.526669:0.349799:0.000000 L:@0.528878:0.367203:0.536499:0.367203:0.536499:0.350797:0.528878:0.350797:0.000000 = :@0.537143:0.357399:0.556029:0.357399:0.556029:0.340965:0.537143:0.340965:0.000000:0.000000:0.000000 1:@0.564612:0.349932:0.573594:0.349932:0.573594:0.333499:0.564612:0.333499:0.000000 2:@0.560838:0.366325:0.569821:0.366325:0.569821:0.349891:0.560838:0.349891:0.000000 L:@0.569747:0.366325:0.577368:0.366325:0.577368:0.349919:0.569747:0.349919:0.000000 – :@0.582190:0.357407:0.703628:0.357400:0.703628:0.340966:0.582190:0.340974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.586148:0.356991:0.590750:0.356991:0.590750:0.340003:0.586148:0.340003:0.000000 1:@0.599147:0.350561:0.608130:0.350561:0.608130:0.334128:0.599147:0.334128:0.000000 2:@0.599147:0.366954:0.608130:0.366954:0.608130:0.350520:0.599147:0.350520:0.000000 T:@0.628620:0.350561:0.636738:0.350561:0.636738:0.334155:0.628620:0.334155:0.000000 ρ:@0.627902:0.366954:0.637474:0.366954:0.637474:0.350548:0.627902:0.350548:0.000000 . :@0.672428:0.356984:0.690559:0.356984:0.690559:0.339995:0.672428:0.339995:0.000000:0.000000:0.000000:0.000000 T:@0.708526:0.350561:0.716644:0.350561:0.716644:0.334155:0.708526:0.334155:0.000000 ρ:@0.705213:0.366954:0.714785:0.366954:0.714785:0.350548:0.705213:0.350548:0.000000 2:@0.714719:0.360887:0.719956:0.360887:0.719956:0.351306:0.714719:0.351306:0.000000 –1/2:@0.650774:0.344889:0.672035:0.344889:0.672035:0.334432:0.650774:0.334432:0.000000:0.000000:0.000000:0.000000 Simplificando::@0.323781:0.398426:0.426309:0.398426:0.426309:0.381992:0.323781:0.381992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.565296:0.424739:0.569990:0.424739:0.569990:0.408333:0.565296:0.408333:0.000000 L:@0.563832:0.441128:0.571452:0.441128:0.571452:0.424722:0.563832:0.424722:0.000000 = – :@0.573209:0.431577:0.605183:0.431577:0.605183:0.415143:0.573209:0.415143:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.640053:0.422322:0.649036:0.422322:0.649036:0.405888:0.640053:0.405888:0.000000 4:@0.612497:0.442292:0.621480:0.442292:0.621480:0.425858:0.612497:0.425858:0.000000 Lp T:@0.621406:0.442292:0.676558:0.442286:0.676558:0.425880:0.621406:0.425886:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3/2:@0.638144:0.436222:0.652298:0.436222:0.652298:0.426641:0.638144:0.426641:0.000000:0.000000:0.000000 :@0.684013:0.431579:0.688044:0.431579:0.688044:0.415146:0.684013:0.415146:0.000000 f:@0.563636:0.471771:0.568330:0.471771:0.568330:0.455365:0.563636:0.455365:0.000000 L:@0.562172:0.488160:0.569792:0.488160:0.569792:0.471754:0.562172:0.471754:0.000000 = – :@0.571549:0.478609:0.603523:0.478609:0.603523:0.462175:0.571549:0.462175:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.638393:0.469354:0.647376:0.469354:0.647376:0.452920:0.638393:0.452920:0.000000 4:@0.605812:0.489324:0.614795:0.489324:0.614795:0.472890:0.605812:0.472890:0.000000 L T ρ:@0.614721:0.489324:0.665801:0.489324:0.665801:0.472918:0.614721:0.472918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3/2:@0.665805:0.483254:0.679959:0.483254:0.679959:0.473673:0.665805:0.473673:0.000000:0.000000:0.000000 :@0.682356:0.478609:0.686387:0.478609:0.686387:0.462175:0.682356:0.462175:0.000000 Conclusión: :@0.323781:0.521424:0.415521:0.521424:0.415521:0.504754:0.323781:0.504754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la derivada es negativa, lo que indica que si :@0.414989:0.521424:0.726158:0.521424:0.726158:0.504990:0.414989:0.504990:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 aumenta la densidad lineal:@0.725372:0.521424:0.926967:0.521424:0.926967:0.504754:0.725372:0.504754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.926913:0.521424:0.930944:0.521424:0.930944:0.504990:0.926913:0.504990:0.000000 ρ:@0.323781:0.538066:0.333353:0.538066:0.333353:0.521660:0.323781:0.521660:0.000000 , la frencuencia :@0.333279:0.538066:0.454141:0.538066:0.454141:0.521632:0.333279:0.521632:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.445490:0.538066:0.450184:0.538066:0.450184:0.521660:0.445490:0.521660:0.000000 disminuye:@0.454068:0.538066:0.533176:0.538066:0.533176:0.521396:0.454068:0.521396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.533072:0.538066:0.536274:0.538066:0.536274:0.521632:0.533072:0.521632:0.000000 4. Impacto en el tono de las notas::@0.293660:0.565429:0.564739:0.565429:0.564739:0.548759:0.293660:0.548759:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • :@0.325203:0.590291:0.334223:0.590291:0.334223:0.573621:0.325203:0.573621:0.000000:0.000000 Cuando se reduce la longitud efectiva (poniendo un dedo sobre la cuerda): :@0.355403:0.590291:0.931097:0.590291:0.931097:0.573621:0.355403:0.573621:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 como la derivada respecto a es negativa, :@0.355329:0.606933:0.668234:0.606933:0.668234:0.590499:0.355329:0.590499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L:@0.566350:0.606933:0.573971:0.606933:0.573971:0.590527:0.566350:0.590527:0.000000 al reducir:@0.668639:0.606933:0.739662:0.606933:0.739662:0.590263:0.668639:0.590263:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la frecuencia aumenta :@0.739636:0.606933:0.930906:0.606933:0.930906:0.590499:0.739636:0.590499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 L:@0.743999:0.606933:0.751619:0.606933:0.751619:0.590527:0.743999:0.590527:0.000000 f:@0.852270:0.606933:0.856964:0.606933:0.856964:0.590527:0.852270:0.590527:0.000000 y, por tanto,:@0.355329:0.623575:0.440699:0.623575:0.440699:0.607141:0.355329:0.607141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el tono de la nota sube:@0.440555:0.623575:0.617482:0.623575:0.617482:0.606905:0.440555:0.606905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (más agudo).:@0.617301:0.623575:0.715688:0.623575:0.715688:0.607141:0.617301:0.607141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • :@0.325203:0.648436:0.334223:0.648436:0.334223:0.631767:0.325203:0.631767:0.000000:0.000000 Cuando se incrementa la tensión (girando la llave de ajuste)::@0.355403:0.648436:0.800098:0.648436:0.800098:0.631767:0.355403:0.631767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 como la derivada :@0.800196:0.648436:0.930924:0.648436:0.930924:0.632003:0.800196:0.632003:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 respecto a es positiva,:@0.355311:0.665078:0.529241:0.665078:0.529241:0.648644:0.355311:0.648644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 T:@0.436377:0.665078:0.444494:0.665078:0.444494:0.648672:0.436377:0.648672:0.000000 al aumentar:@0.529186:0.665078:0.625690:0.665078:0.625690:0.648409:0.529186:0.648409:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , la frecuencia aumenta y, por tanto, el :@0.625658:0.665078:0.931059:0.665078:0.931059:0.648644:0.625658:0.648644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 T:@0.630095:0.665078:0.638212:0.665078:0.638212:0.648672:0.630095:0.648672:0.000000 f:@0.743078:0.665078:0.747772:0.665078:0.747772:0.648672:0.743078:0.648672:0.000000 tono de la nota sube:@0.355329:0.681720:0.511180:0.681720:0.511180:0.665051:0.355329:0.665051:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (más agudo).:@0.511018:0.681720:0.609405:0.681720:0.609405:0.665286:0.511018:0.665286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • :@0.325203:0.706581:0.333708:0.706581:0.333708:0.690147:0.325203:0.690147:0.000000:0.000000 :@0.355405:0.706581:0.359436:0.706581:0.359436:0.690147:0.355405:0.690147:0.000000 Cuando aumenta la densidad lineal (cambiando a otra cuerda más densa): :@0.355405:0.706581:0.930381:0.706581:0.930381:0.689911:0.355405:0.689911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 como la derivada respecto a es negativa,:@0.355331:0.723223:0.690527:0.723223:0.690527:0.706789:0.355331:0.706789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ρ:@0.583323:0.723223:0.592895:0.723223:0.592895:0.706817:0.583323:0.706817:0.000000 :@0.690895:0.723223:0.694209:0.723223:0.694209:0.706817:0.690895:0.706817:0.000000 al aumentar:@0.695939:0.723223:0.792299:0.723223:0.792299:0.706553:0.695939:0.706553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , la frecuencia :@0.792559:0.723223:0.930963:0.723223:0.930963:0.706789:0.792559:0.706789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ρ:@0.798688:0.723223:0.808260:0.723223:0.808260:0.706817:0.798688:0.706817:0.000000 f:@0.922238:0.723223:0.926932:0.723223:0.926932:0.706817:0.922238:0.706817:0.000000 disminuye y, por tanto, o el:@0.355350:0.739864:0.550511:0.739864:0.550511:0.723431:0.355350:0.723431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tono de la nota baja:@0.550264:0.739864:0.705505:0.739864:0.705505:0.723195:0.550264:0.723195:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (más grave).:@0.705345:0.739864:0.796422:0.739864:0.796422:0.723431:0.705345:0.723431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Resumen de los efectos::@0.293685:0.764730:0.468701:0.764730:0.468701:0.748296:0.293685:0.748296:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • :@0.325203:0.792090:0.333708:0.792090:0.333708:0.775656:0.325203:0.775656:0.000000:0.000000 :@0.355405:0.792090:0.375266:0.792090:0.375266:0.775656:0.355405:0.775656:0.000000:0.000000:0.000000:0.000000:0.000000 Reducir la longitud:@0.371198:0.792090:0.514951:0.792090:0.514951:0.775420:0.371198:0.775420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 aumenta la frecuencia tono más alto.:@0.514793:0.792090:0.820245:0.792090:0.820245:0.775656:0.514793:0.775656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • :@0.325203:0.816951:0.333708:0.816951:0.333708:0.800518:0.325203:0.800518:0.000000:0.000000 :@0.355406:0.816951:0.375268:0.816951:0.375268:0.800518:0.355406:0.800518:0.000000:0.000000:0.000000:0.000000:0.000000 Aumentar la tensión:@0.371200:0.816951:0.525108:0.816951:0.525108:0.800282:0.371200:0.800282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 aumenta la frecuencia tono más alto.:@0.524956:0.816951:0.830405:0.816951:0.830405:0.800518:0.524956:0.800518:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • :@0.325203:0.841812:0.333708:0.841812:0.333708:0.825378:0.325203:0.825378:0.000000:0.000000 :@0.355405:0.841812:0.367351:0.841812:0.367351:0.825378:0.355405:0.825378:0.000000:0.000000:0.000000 Aumentar la densidad lineal:@0.367259:0.841812:0.583331:0.841812:0.583331:0.825142:0.367259:0.825142:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.371088:0.841812:0.374990:0.841812:0.374990:0.825142:0.371088:0.825142:0.000000 disminuye la frecuencia tono más bajo.:@0.583139:0.841812:0.903185:0.841812:0.903185:0.825378:0.583139:0.825378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Interdisciplinariedad :@0.078581:0.145861:0.244955:0.145861:0.244955:0.128914:0.078581:0.128914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Música y:@0.078581:0.162502:0.141637:0.162502:0.141637:0.146069:0.078581:0.146069:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 física:@0.078581:0.179144:0.114162:0.179144:0.114162:0.162710:0.078581:0.162710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La afinación de un violín :@0.079018:0.215389:0.242759:0.215389:0.242759:0.200450:0.079018:0.200450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 aplica principios de :@0.079018:0.230518:0.210489:0.230518:0.210489:0.215579:0.079018:0.215579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 física:@0.079018:0.245647:0.113590:0.245647:0.113590:0.230493:0.079018:0.230493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , especialmente en :@0.113507:0.245647:0.241146:0.245647:0.241146:0.230708:0.113507:0.230708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 acústica mecánica de :@0.079018:0.260776:0.240266:0.260776:0.240266:0.245622:0.079018:0.245622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.134876:0.260776:0.149434:0.260776:0.149434:0.245836:0.134876:0.245836:0.000000:0.000000:0.000000 ondas:@0.079018:0.275905:0.121355:0.275905:0.121355:0.260751:0.079018:0.260751:0.000000:0.000000:0.000000:0.000000:0.000000 . La frecuencia de :@0.121271:0.275905:0.239255:0.275905:0.239255:0.260965:0.121271:0.260965:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 vibración de una cuerda :@0.079018:0.291034:0.242453:0.291034:0.242453:0.276094:0.079018:0.276094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 se basa en cómo las ondas :@0.079018:0.306163:0.258688:0.306163:0.258688:0.291223:0.079018:0.291223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 mecánicas generadas :@0.079018:0.321292:0.225573:0.321292:0.225573:0.306352:0.079018:0.306352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 por la cuerda vibrante :@0.079018:0.336421:0.227382:0.336421:0.227382:0.321481:0.079018:0.321481:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 producen sonido, donde :@0.079018:0.351550:0.246442:0.351550:0.246442:0.336610:0.079018:0.336610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la frecuencia determina :@0.079018:0.366679:0.238139:0.366679:0.238139:0.351739:0.079018:0.351739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el tono percibido. La física :@0.079018:0.381808:0.253213:0.381808:0.253213:0.366868:0.079018:0.366868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de materiales también es :@0.079018:0.396937:0.248537:0.396937:0.248537:0.381997:0.079018:0.381997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 clave, ya que la tensión :@0.079018:0.412066:0.234534:0.412066:0.234534:0.397126:0.079018:0.397126:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 modifica la elasticidad :@0.079018:0.427195:0.228770:0.427195:0.228770:0.412255:0.079018:0.412255:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de la cuerda y afecta la :@0.079018:0.442324:0.232498:0.442324:0.232498:0.427384:0.079018:0.427384:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 velocidad de las ondas :@0.079018:0.457453:0.232461:0.457453:0.232461:0.442513:0.079018:0.442513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y, en consecuencia, la :@0.079018:0.472581:0.224797:0.472581:0.224797:0.457642:0.079018:0.457642:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 frecuencia. Las :@0.079018:0.487710:0.178822:0.487710:0.178822:0.472771:0.079018:0.472771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 derivadas:@0.178668:0.487710:0.245579:0.487710:0.245579:0.472556:0.178668:0.472556:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.245554:0.487710:0.249218:0.487710:0.249218:0.472771:0.245554:0.472771:0.000000 entran en juego para :@0.079018:0.502839:0.221206:0.502839:0.221206:0.487899:0.079018:0.487899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 analizar cómo cada :@0.079018:0.517968:0.210095:0.517968:0.210095:0.503028:0.079018:0.503028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 variable, como la tensión :@0.079018:0.533097:0.246889:0.533097:0.246889:0.518157:0.079018:0.518157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ), la longitud ( ) y la :@0.079018:0.548226:0.220955:0.548226:0.220955:0.533286:0.079018:0.533286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 T:@0.083386:0.548226:0.090765:0.548226:0.090765:0.533312:0.083386:0.533312:0.000000 L:@0.180492:0.548226:0.187420:0.548226:0.187420:0.533312:0.180492:0.533312:0.000000 densidad lineal ( ) afecta :@0.079018:0.563355:0.246713:0.563355:0.246713:0.548415:0.079018:0.548415:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ρ:@0.186533:0.563355:0.195235:0.563355:0.195235:0.548440:0.186533:0.548440:0.000000 la frecuencia al derivar :@0.079001:0.578484:0.229511:0.578484:0.229511:0.563544:0.079001:0.563544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 parcialmente la fórmula :@0.079001:0.593613:0.239134:0.593613:0.239134:0.578673:0.079001:0.578673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.079018:0.615476:0.083712:0.615476:0.083712:0.599069:0.079018:0.599069:0.000000 = :@0.083638:0.615476:0.136348:0.615474:0.136348:0.599040:0.083638:0.599042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.106989:0.608637:0.115971:0.608637:0.115971:0.592203:0.106989:0.592203:0.000000 2:@0.103215:0.625029:0.112198:0.625029:0.112198:0.608596:0.103215:0.608596:0.000000 L:@0.112124:0.625029:0.119745:0.625029:0.119745:0.608623:0.112124:0.608623:0.000000 T:@0.140411:0.608637:0.148529:0.608637:0.148529:0.592231:0.140411:0.592231:0.000000 ρ:@0.139675:0.625029:0.149247:0.625029:0.149247:0.608623:0.139675:0.608623:0.000000 . :@0.161956:0.614451:0.168533:0.614451:0.168533:0.599511:0.161956:0.599511:0.000000:0.000000 Esto es esencial para que :@0.079023:0.749779:0.247091:0.749779:0.247091:0.734839:0.079023:0.734839:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 músicos y fabricantes de :@0.079023:0.764908:0.244876:0.764908:0.244876:0.749968:0.079023:0.749968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 instrumentos logren el :@0.079023:0.780037:0.232218:0.780037:0.232218:0.765097:0.079023:0.765097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tono y la calidad de sonido :@0.079023:0.795166:0.260361:0.795166:0.260361:0.780226:0.079023:0.780226:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 deseados en un violín.:@0.079023:0.810295:0.225863:0.810295:0.225863:0.795355:0.079023:0.795355:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000