319:
559:
129:
376:
1044:
66:) is a logarithmic quantity used to measure quantities of which the square is typically proportional to power (for instance, the square of voltage is proportional to power by the inverse of the conductor's resistance), etc., with commonly used units
314:{\displaystyle L_{P}={\frac {1}{2}}\log _{\mathrm {e} }\!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {Np} =\log _{10}\!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {B} =10\log _{10}\!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {dB} .}
554:{\displaystyle L_{F}=\log _{\mathrm {e} }\!\left({\frac {F}{F_{0}}}\right)\!~\mathrm {Np} =2\log _{10}\!\left({\frac {F}{F_{0}}}\right)\!~\mathrm {B} =20\log _{10}\!\left({\frac {F}{F_{0}}}\right)\!~\mathrm {dB} .}
837:
82:
between the quantity and its reference value, though a logarithm may be considered to be a dimensionless quantity. The reference values for each type of quantity are often specified by international standards.
925:
1417:
1531:
1392:
1338:
98:
and related disciplines. Power levels are used for signal power, noise power, sound power, sound exposure, etc. Field levels are used for voltage, current,
1282:
643:(one tenth of a bel) are units of level that are often applied to such quantities as power, intensity, or gain. The neper, bel, and decibel are related by
1559:
1280:
Fletcher, H. (1934), "Loudness, pitch and the timbre of musical tones and their relation to the intensity, the frequency and the overtone structure",
1519:
1096:
772:
1463:
1348:
1039:{\displaystyle L_{f}=\log _{2}\!\left({\frac {f}{f_{0}}}\right)~{\text{oct}}=\log _{10}\!\left({\frac {f}{f_{0}}}\right)~{\text{dec}}.}
1554:
1321:
1111:
1120:
1408:
1106:
1449:
1418:"A Century of Sonar: Planetary Oceanography, Underwater Noise Monitoring, and the Terminology of Underwater Sound"
878:
1438:
Effect of moisturizer and lubricant on the finger‒surface sliding contact: tribological and dynamical analysis
51:
is a logarithmic quantity used to measure power, power density or sometimes energy, with commonly used unit
24:
1116:
87:
40:
722:
The ISO standard defines each of the quantities power level and field level to be dimensionless, with
1476:
1357:
1291:
909:
99:
1459:"A terminology standard for underwater acoustics and the benefits of international standardization"
1510:
1494:
1404:
1373:
915:
746:
91:
1502:
1317:
1101:
17:
1311:
1484:
1365:
1299:
1072:
1059:
1422:
907:) of two frequencies is the logarithm of their ratio, and may be expressed using the unit
1071:
is one hundredth of a semitone. In this context, the reference frequency is taken to be
1480:
1361:
1295:
1548:
1514:
1436:
743:
Power and field quantities are part of a larger class, logarithmic ratio quantities.
727:
1377:
1068:
1050:
78:
The type of level and choice of units indicate the scaling of the logarithm of the
1457:
Ainslie, Michael A.; Halvorsen, Michele B.; Robinson, Stephen P. (January 2022) .
43:
of certain quantities referenced to a standard reference value of the same type.
1388:
1334:
716:
726:. This is motivated by simplifying the expressions involved, as in systems of
1313:
Guide for the Use of the
International System of Units (SI): The Metric System
571:
is the root-power quantity, proportional to the square root of power quantity;
1506:
1498:
1489:
1458:
1369:
95:
1525:
1079:
1064:
1091:
701:
640:
636:
71:
52:
1303:
1211:
1209:
1054:
872:
For the level of a root-power quantity, the base of the logarithm is
832:{\displaystyle L_{Q}=\log _{r}\!\left({\frac {Q}{Q_{0}}}\right)\!,}
882:. For the level of a power quantity, the base of the logarithm is
705:
632:
79:
67:
1472:
1446:
IEEE/ASTM SI 10: American
National Standard for Metric Practice
1346:
Carey, W. M. (2006), "Sound
Sources and Levels in the Ocean",
1215:
913:(symbol: oct) corresponding to the ratio 2 or the unit
928:
775:
379:
132:
16:"Level quantity" redirects here. For other uses, see
596:, and if the reference value of the power quantity,
1038:
831:
553:
313:
1527:ISO 18405:2017 Underwater acoustics – Terminology
999:
952:
825:
799:
536:
510:
485:
459:
431:
405:
296:
270:
245:
219:
194:
168:
1140:
919:(symbol: dec) corresponding to the ratio 10:
1532:International Organization for Standardization
1393:International Organization for Standardization
1339:International Organization for Standardization
1263:
1227:
1057:is a unit used with logarithm base 2 (called
8:
1283:Journal of the Acoustical Society of America
1188:
1176:
1152:
1488:
1028:
1013:
1004:
993:
981:
966:
957:
946:
933:
927:
813:
804:
793:
780:
774:
540:
524:
515:
504:
489:
473:
464:
453:
435:
419:
410:
398:
397:
384:
378:
300:
284:
275:
264:
249:
233:
224:
213:
198:
182:
173:
161:
160:
146:
137:
131:
1251:
1239:
1133:
1097:Power, root-power, and field quantities
749:defines a class of quantities it calls
1216:Ainslie, Halvorsen & Robinson 2022
1200:
1401:ANSI/ASA S1.1: Acoustical Terminology
1164:
7:
1316:, Diane Publishing Co., p. 28,
1464:IEEE Journal of Oceanic Engineering
1349:IEEE Journal of Oceanic Engineering
753:. It defines a level of a quantity
715:Level and its units are defined in
86:Power and field levels are used in
544:
541:
490:
439:
436:
399:
304:
301:
250:
202:
199:
162:
14:
1560:Logarithmic scales of measurement
1385:ISO 80000-8: Quantities and units
1331:ISO 80000-3: Quantities and units
1112:Leveling (tapered floating point)
1121:symmetric level-index arithmetic
1067:is one twelfth of an octave. A
603:, is in the same proportion to
1:
1409:Acoustical Society of America
849:is the base of the logarithm;
1416:Ainslie, Michael A. (2015),
1107:Sound level (disambiguation)
901:logarithmic frequency ratio
895:Logarithmic frequency ratio
349:Field (or root-power) level
1576:
1450:IEEE Standards Association
864:is the reference value of
739:Logarithmic ratio quantity
702:Decibel § Conversions
699:
580:is the reference value of
357:quantity (also known as a
340:is the reference value of
15:
1092:Decibel § Definition
1555:Mathematical terminology
1490:10.1109/JOE.2021.3085947
1370:10.1109/JOE.2006.872214
25:science and engineering
1335:Part 3: Space and Time
1310:Taylor, Barry (1995),
1117:Level-index arithmetic
1040:
833:
588:If the power quantity
555:
331:is the power quantity;
315:
88:electronic engineering
41:logarithmic magnitudes
1078:, four octaves below
1041:
834:
556:
316:
1435:D'Amore, F. (2015),
1141:IEEE/ASTM SI 10 2016
926:
773:
377:
130:
1481:2022IJOE...47..179A
1362:2006IJOE...31...61C
1296:1934ASAJ....6...59F
592:is proportional to
361:quantity), denoted
1405:ANSI/ASA S1.1-2013
1264:ANSI/ASA S1.1 2013
1228:ANSI/ASA S1.1 2013
1036:
829:
747:ANSI/ASA S1.1-2013
734:Related quantities
706:Neper § Units
551:
311:
114:quantity, denoted
92:telecommunications
1389:Part 8: Acoustics
1304:10.1121/1.1915704
1254:, pp. 59–69.
1167:, pp. 61–75.
1143:, pp. 26–27.
1102:Logarithmic scale
1031:
1027:
1019:
984:
980:
972:
819:
539:
530:
488:
479:
434:
425:
299:
290:
248:
239:
197:
188:
154:
18:Level measurement
1567:
1541:
1540:
1539:
1518:
1492:
1453:
1441:
1431:
1412:
1396:
1380:
1342:
1326:
1306:
1267:
1261:
1255:
1249:
1243:
1237:
1231:
1225:
1219:
1213:
1204:
1198:
1192:
1186:
1180:
1177:ISO 80000-8 2007
1174:
1168:
1162:
1156:
1153:ISO 80000-3 2006
1150:
1144:
1138:
1045:
1043:
1042:
1037:
1032:
1029:
1025:
1024:
1020:
1018:
1017:
1005:
998:
997:
985:
982:
978:
977:
973:
971:
970:
958:
951:
950:
938:
937:
888:
881:
855:is the quantity;
838:
836:
835:
830:
824:
820:
818:
817:
805:
798:
797:
785:
784:
725:
695:
689:
687:
686:
683:
680:
669:
663:
661:
660:
657:
654:
560:
558:
557:
552:
547:
537:
535:
531:
529:
528:
516:
509:
508:
493:
486:
484:
480:
478:
477:
465:
458:
457:
442:
432:
430:
426:
424:
423:
411:
404:
403:
402:
389:
388:
370:, is defined by
320:
318:
317:
312:
307:
297:
295:
291:
289:
288:
276:
269:
268:
253:
246:
244:
240:
238:
237:
225:
218:
217:
205:
195:
193:
189:
187:
186:
174:
167:
166:
165:
155:
147:
142:
141:
123:, is defined by
64:root-power level
37:root-power level
1575:
1574:
1570:
1569:
1568:
1566:
1565:
1564:
1545:
1544:
1537:
1535:
1524:
1456:
1444:
1434:
1423:Acoustics Today
1415:
1399:
1383:
1345:
1329:
1324:
1309:
1279:
1276:
1271:
1270:
1262:
1258:
1250:
1246:
1238:
1234:
1226:
1222:
1214:
1207:
1199:
1195:
1187:
1183:
1175:
1171:
1163:
1159:
1151:
1147:
1139:
1135:
1130:
1088:
1076:
1009:
1000:
989:
962:
953:
942:
929:
924:
923:
905:frequency level
903:(also known as
897:
883:
873:
863:
809:
800:
789:
776:
771:
770:
765:
741:
736:
723:
713:
708:
693:
684:
681:
678:
677:
675:
674:1 dB = 0.1 B =
673:
667:
658:
655:
652:
651:
649:
647:
627:
618:
609:
602:
579:
520:
511:
500:
469:
460:
449:
415:
406:
393:
380:
375:
374:
369:
353:The level of a
351:
339:
280:
271:
260:
229:
220:
209:
178:
169:
156:
133:
128:
127:
122:
108:
35:(also called a
21:
12:
11:
5:
1573:
1571:
1563:
1562:
1557:
1547:
1546:
1543:
1542:
1522:
1454:
1442:
1432:
1413:
1397:
1381:
1343:
1327:
1322:
1307:
1275:
1272:
1269:
1268:
1256:
1244:
1232:
1220:
1205:
1193:
1181:
1169:
1157:
1145:
1132:
1131:
1129:
1126:
1125:
1124:
1114:
1109:
1104:
1099:
1094:
1087:
1084:
1074:
1047:
1046:
1035:
1023:
1016:
1012:
1008:
1003:
996:
992:
988:
976:
969:
965:
961:
956:
949:
945:
941:
936:
932:
896:
893:
870:
869:
861:
856:
850:
840:
839:
828:
823:
816:
812:
808:
803:
796:
792:
788:
783:
779:
761:
740:
737:
735:
732:
712:
709:
698:
697:
691:
671:
665:
623:
614:
607:
600:
586:
585:
577:
572:
562:
561:
550:
546:
543:
534:
527:
523:
519:
514:
507:
503:
499:
496:
492:
483:
476:
472:
468:
463:
456:
452:
448:
445:
441:
438:
429:
422:
418:
414:
409:
401:
396:
392:
387:
383:
365:
350:
347:
346:
345:
337:
332:
322:
321:
310:
306:
303:
294:
287:
283:
279:
274:
267:
263:
259:
256:
252:
243:
236:
232:
228:
223:
216:
212:
208:
204:
201:
192:
185:
181:
177:
172:
164:
159:
153:
150:
145:
140:
136:
118:
107:
104:
100:sound pressure
76:
75:
56:
13:
10:
9:
6:
4:
3:
2:
1572:
1561:
1558:
1556:
1553:
1552:
1550:
1533:
1529:
1528:
1523:
1520:
1516:
1512:
1508:
1504:
1500:
1496:
1491:
1486:
1482:
1478:
1474:
1470:
1466:
1465:
1460:
1455:
1451:
1447:
1443:
1440:
1439:
1433:
1429:
1425:
1424:
1419:
1414:
1410:
1406:
1402:
1398:
1394:
1390:
1386:
1382:
1379:
1375:
1371:
1367:
1363:
1359:
1355:
1351:
1350:
1344:
1340:
1336:
1332:
1328:
1325:
1323:9780788125799
1319:
1315:
1314:
1308:
1305:
1301:
1297:
1293:
1289:
1285:
1284:
1278:
1277:
1273:
1265:
1260:
1257:
1253:
1252:Fletcher 1934
1248:
1245:
1241:
1236:
1233:
1230:, entry 3.01.
1229:
1224:
1221:
1217:
1212:
1210:
1206:
1202:
1197:
1194:
1190:
1185:
1182:
1178:
1173:
1170:
1166:
1161:
1158:
1154:
1149:
1146:
1142:
1137:
1134:
1127:
1122:
1118:
1115:
1113:
1110:
1108:
1105:
1103:
1100:
1098:
1095:
1093:
1090:
1089:
1085:
1083:
1081:
1077:
1070:
1066:
1062:
1061:
1056:
1052:
1033:
1021:
1014:
1010:
1006:
1001:
994:
990:
986:
974:
967:
963:
959:
954:
947:
943:
939:
934:
930:
922:
921:
920:
918:
917:
912:
911:
906:
902:
894:
892:
890:
886:
880:
876:
867:
860:
857:
854:
851:
848:
845:
844:
843:
826:
821:
814:
810:
806:
801:
794:
790:
786:
781:
777:
769:
768:
767:
764:
760:
756:
752:
748:
744:
738:
733:
731:
729:
728:natural units
720:
718:
710:
707:
703:
672:
646:
645:
644:
642:
638:
634:
629:
626:
622:
617:
613:
610:, the levels
606:
599:
595:
591:
583:
576:
573:
570:
567:
566:
565:
548:
532:
525:
521:
517:
512:
505:
501:
497:
494:
481:
474:
470:
466:
461:
454:
450:
446:
443:
427:
420:
416:
412:
407:
394:
390:
385:
381:
373:
372:
371:
368:
364:
360:
356:
348:
343:
336:
333:
330:
327:
326:
325:
308:
292:
285:
281:
277:
272:
265:
261:
257:
254:
241:
234:
230:
226:
221:
214:
210:
206:
190:
183:
179:
175:
170:
157:
151:
148:
143:
138:
134:
126:
125:
124:
121:
117:
113:
105:
103:
101:
97:
93:
89:
84:
81:
73:
69:
65:
61:
57:
54:
50:
46:
45:
44:
42:
38:
34:
30:
26:
19:
1536:, retrieved
1526:
1468:
1462:
1445:
1437:
1427:
1421:
1403:, vol.
1400:
1387:, vol.
1384:
1353:
1347:
1333:, vol.
1330:
1312:
1287:
1281:
1259:
1247:
1240:Ainslie 2015
1235:
1223:
1196:
1189:D'Amore 2015
1184:
1172:
1160:
1148:
1136:
1058:
1051:music theory
1048:
914:
908:
904:
900:
898:
891:
884:
874:
871:
865:
858:
852:
846:
841:
762:
758:
754:
750:
745:
742:
721:
714:
630:
624:
620:
615:
611:
604:
597:
593:
589:
587:
581:
574:
568:
563:
366:
362:
358:
354:
352:
341:
334:
328:
323:
119:
115:
111:
109:
106:Power level
85:
77:
63:
59:
48:
36:
32:
28:
22:
1475:: 179–200.
1201:Taylor 1995
717:ISO 80000-3
628:are equal.
110:Level of a
60:field level
49:power level
33:field level
29:power level
1549:Categories
1538:2022-12-20
1521:(22 pages)
1274:References
1165:Carey 2006
757:, denoted
700:See also:
355:root-power
1515:243948953
1507:0364-9059
1499:1558-1691
1356:(1): 61,
1290:(2): 59,
1119:(LI) and
711:Standards
96:acoustics
1378:30674485
1086:See also
1080:middle C
1065:semitone
1060:interval
724:1 Np = 1
70:(Np) or
1534:, 2022
1477:Bibcode
1358:Bibcode
1292:Bibcode
688:
676:
662:
650:
641:decibel
72:decibel
53:decibel
1513:
1505:
1497:
1452:, 2016
1411:, 2013
1395:, 2007
1376:
1341:, 2006
1320:
1055:octave
1053:, the
1026:
979:
916:decade
910:octave
842:where
751:levels
704:, and
648:1 B =
639:, and
564:where
538:
487:
433:
324:where
298:
247:
196:
39:) are
31:and a
1511:S2CID
1495:eISSN
1471:(1).
1374:S2CID
1128:Notes
1123:(SLI)
1063:). A
766:, as
694:10 Np
668:10 Np
633:neper
359:field
112:power
80:ratio
74:(dB).
68:neper
55:(dB).
1503:ISSN
1473:IEEE
1318:ISBN
1069:cent
899:The
631:The
619:and
62:(or
27:, a
1485:doi
1430:(1)
1366:doi
1300:doi
1049:In
1030:dec
991:log
983:oct
944:log
887:= e
791:log
690:log
664:log
637:bel
502:log
451:log
395:log
262:log
211:log
158:log
23:In
1551::
1530:,
1509:.
1501:.
1493:.
1483:.
1469:47
1467:.
1461:.
1448:,
1428:11
1426:,
1420:,
1407:,
1391:,
1372:,
1364:,
1354:31
1352:,
1337:,
1298:,
1286:,
1208:^
1082:.
995:10
889:.
877:=
730:.
719:.
685:20
635:,
506:10
498:20
455:10
266:10
258:10
215:10
102:.
94:,
90:,
58:A
47:A
1517:.
1487::
1479::
1368::
1360::
1302::
1294::
1288:6
1266:.
1242:.
1218:.
1203:.
1191:.
1179:.
1155:.
1075:0
1073:C
1034:.
1022:)
1015:0
1011:f
1007:f
1002:(
987:=
975:)
968:0
964:f
960:f
955:(
948:2
940:=
935:f
931:L
885:r
879:e
875:r
868:.
866:Q
862:0
859:Q
853:Q
847:r
827:,
822:)
815:0
811:Q
807:Q
802:(
795:r
787:=
782:Q
778:L
763:Q
759:L
755:Q
696:.
692:e
682:/
679:1
670:;
666:e
659:2
656:/
653:1
625:P
621:L
616:F
612:L
608:0
605:F
601:0
598:P
594:F
590:P
584:.
582:F
578:0
575:F
569:F
549:.
545:B
542:d
533:)
526:0
522:F
518:F
513:(
495:=
491:B
482:)
475:0
471:F
467:F
462:(
447:2
444:=
440:p
437:N
428:)
421:0
417:F
413:F
408:(
400:e
391:=
386:F
382:L
367:F
363:L
344:.
342:P
338:0
335:P
329:P
309:.
305:B
302:d
293:)
286:0
282:P
278:P
273:(
255:=
251:B
242:)
235:0
231:P
227:P
222:(
207:=
203:p
200:N
191:)
184:0
180:P
176:P
171:(
163:e
152:2
149:1
144:=
139:P
135:L
120:P
116:L
20:.
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