{"text_format":"3","workbook":"xls","n_sheets":2,"sheets":["Description","Calculation"],"not_rendered":{"charts":3,"external_links":1,"defined_names":62,"comments":5},"read":"whole","date_system":"1900","formulas":"cached_only"}

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[null,null,"Spreadsheet calculates the strength and time of arrival of the initial reflections in a room for a dipole or omnidirectional source."]
[null,null,"The source is assumed to be idealized dipole or omnidirectional loudspeaker, part of a stereo listening setup that may be configured as desired."]
[null,null,"Typical loudspeakers approximate omnidirectional directivity at low frequency but tend to become more directional with frequency depending on the loudspeaker"]
[null,null,"All yellow cells are inputs that may be changed, other values are final and intermediate value results. Wall reflection attenuations are entered as positive values."]
[null,null,"The setup is assumed to be symmetrical in the width aspect of the room. Adjust chart axis scales as necessary."]
[]
[null,null,"The loudspeaker toe-in angle is relative to straight ahead and is not constrained to be the angle to the listener"]
[null,null,"The loudspeaker tilt input is positive for upward tilts, negative for downward tilts. This mainly influences the dipole ceiling and floor reflection result."]
[null,null,"The image azimuth and elevation angles are given as counterclockwise from straight ahead of the listener (upward angles or angles round to the left are positive)"]
[null,null,"Reflections arriving at the same time are given the same order. The floor reflection is not included in the ordering but is generally the first reflection."]
[]
[null,null,"The detectability of a reflection varies with angle, its delay, its relative level, the signal type, presence of other reflections and between individuals."]
[null,null,"Below a certain threshold relative level, which is delay dependent, a reflection becomes inaudible."]
[null,null,"Reflections similar in direction to the direct sound are the least detectible."]

{"sheet":"Calculation","index":1,"n_rows":77,"n_cols":40,"rows_kept":77,"flags":["formulas_cached_only"]}
[{"$nulls":3},"Initial Wall Reflections in a Room for a Dipole or Omnidirectional Source"]
[{"$nulls":5},"Reflection","Closest Sidewall","Front Wall","Front Corner","Rear Wall","Rear Corner","Furthest Sidewall","Ceiling","Floor",{"$nulls":17},"Lines to Listener from Virtual Sources"]
[{"$nulls":5},"Dipole Directivity Adjustment dB",{"v":-35.161570627727464,"d":"-35.2"},{"v":-3.163251531772605,"d":"-3.2"},{"v":-0.07928928001478296,"d":"-0.1"},{"v":-0.7593661044973421,"d":"-0.8"},{"v":-4.251961880698478,"d":"-4.3"},{"v":-2.3000624934999987,"d":"-2.3"},{"v":-5.1188336097887435,"d":"-5.1"},{"v":-3.0102999566398116,"d":"-3.0"},{"$nulls":16},"y","x","x","z"]
[{"$nulls":5},"Distance Loss dB [Equivalent to Omni Source]",{"v":-4.771212547196623,"d":"-4.8"},{"v":-5.719475475333596,"d":"-5.7"},{"v":-7.583100312279255,"d":"-7.6"},{"v":-11.817336410295912,"d":"-11.8"},{"v":-12.354312859475879,"d":"-12.4"},{"v":-8.45098040014257,"d":"-8.5"},{"v":-5.1188336097887435,"d":"-5.1"},{"v":-3.0102999566398125,"d":"-3.0"},{"$nulls":15},"Floor R",null,null,{"v":1.7320508075688772,"d":"1.732"},{"v":-1,"d":"-1.000"}]
[{"$nulls":5},"Attenuation via Curvature/Redirection/Abs dB",{"v":3,"d":"3.0"},{"v":3,"d":"3.0"},{"v":6,"d":"6.0"},{"v":3,"d":"3.0"},{"v":6,"d":"6.0"},{"v":3,"d":"3.0"},{"v":3,"d":"3.0"},{"v":3,"d":"3.0"},null,{"v":-11.882727007106201,"d":"-11.9"},"Level of Strongest Reflection dB",{"$nulls":15},{"v":0,"d":"0.000"},{"v":1,"d":"1.000"}]
[{"$nulls":5},"Reflection Level rel Direct dB",{"v":-42.93278317492409,"d":"-42.9"},{"v":-11.882727007106201,"d":"-11.9"},{"v":-13.662389592294037,"d":"-13.7"},{"v":-15.576702514793254,"d":"-15.6"},{"v":-22.606274740174356,"d":"-22.6"},{"v":-13.751042893642568,"d":"-13.8"},{"v":-13.237667219577487,"d":"-13.2"},{"v":-9.020599913279625,"d":"-9.0"},null,{"v":-6.369717608561862,"d":"-6.4"},"Eq. Early Reflected Energy rel Direct dB",{"$nulls":12},"Ceiling R",null,null,{"v":1.7320508075688772,"d":"1.732"},{"v":4,"d":"4.000"}]
[{"$nulls":5},"Delay, msec",{"v":4.246111235572502,"d":"4.2"},{"v":5.40501524073047,"d":"5.4"},{"v":8.086599408203519,"d":"8.1"},{"v":16.810558077300815,"d":"16.8"},{"v":18.252512271037418,"d":"18.3"},{"v":9.545844442241181,"d":"9.5"},{"v":4.65633617199034,"d":"4.7"},{"v":2.4025611923847636,"d":"2.4"},null,{"v":4.246111235572502,"d":"4.2"},"Min Delay, msec",{"$nulls":15},{"v":0,"d":"0.000"},{"v":1,"d":"1.000"}]
[]
[{"$nulls":9},"Room Width m",{"v":4,"d":"4.000"},{"v":13.123359580052496,"d":"13.1"},null,null,"Plan Area m2",{"v":22.928203230275507,"d":"22.9"},{"v":246.7971255868001,"d":"247"},{"$nulls":6},"y","x","z"]
[{"$nulls":5},"Room and Listening Setup Inputs:",null,"feet",null,"Room Depth m",{"v":5.732050807568877,"d":"5.732"},{"v":18.805940969714165,"d":"18.8"},null,null,"Room Volume m3",{"v":57.320508075688764,"d":"57.3"},{"v":2024.2546389993447,"d":"2024"},{"$nulls":5},"Listener",0,0,{"v":1,"d":"1.000"},{"$nulls":3},"Left Wall",{"v":-2,"d":"-2.000"},{"v":2.732050807568877,"d":"2.732"}]
[{"$nulls":5},"Speed of Sound m/s",{"v":344.81,"d":"344.8"},{"v":1131.2664041994751,"d":"1131"},null,"Room Height m",{"v":2.5,"d":"2.500"},{"v":8.202099737532809,"d":"8.2"},{"$nulls":10},"Left L/S",{"v":1.7320508075688772,"d":"1.732"},-1,{"$nulls":5},{"v":-2,"d":"-2.000"},{"v":-3,"d":"-3.000"}]
[{"$nulls":5},"Desired Minimum Delay msec",6,{"$nulls":15},"Right L/S",{"v":1.7320508075688772,"d":"1.732"},1,{"v":1,"d":"1.000"},{"$nulls":3},"Right Wall",{"v":2,"d":"2.000"},{"v":2.732050807568877,"d":"2.732"}]
[{"$nulls":5},"Loudspeaker Separation m",{"v":2,"d":"2.000"},{"v":6.561679790026248,"d":"6.6"},{"$nulls":7},"Omni switch",{"$nulls":6},"Front Left Corner",{"v":2.732050807568877,"d":"2.732"},{"v":-2,"d":"-2.000"},{"v":-1,"d":"-1.000"},{"$nulls":4},{"v":2,"d":"2.000"},{"v":-3,"d":"-3.000"}]
[null,"Standard",{"$nulls":3},"Loudspeaker Upward Elevation Tilt degrees",{"v":0,"d":"0.0"},{"$nulls":8},false,{"$nulls":6},"Front Right Corner",{"v":2.732050807568877,"d":"2.732"},{"v":2,"d":"2.000"},{"$nulls":4},"Front Wall R",0,0,{"v":2.732050807568877,"d":"2.732"},{"v":2.5,"d":"2.500"}]
[null,"30°",{"$nulls":3},"Loudspeaker Toe-in, degrees",{"v":31,"d":"31.0"},{"$nulls":15},"Rear Left Corner",{"v":-3,"d":"-3.000"},{"v":-2,"d":"-2.000"},{"$nulls":5},{"v":-0.9999999999999999,"d":"-1.000"},{"v":3.7320508075688776,"d":"3.732"},{"v":2.732050807568877,"d":"2.732"},{"v":0,"d":"0.000"}]
[null,{"v":1.7320508075688772,"d":"1.732"},{"$nulls":3},"Listener's Distance from line between Loudspeakers m",{"v":1.7320508075688772,"d":"1.732"},{"v":5.682581389661672,"d":"5.7"},{"$nulls":14},"Rear Right Corner",{"v":-3,"d":"-3.000"},{"v":2,"d":"2.000"},{"$nulls":4},"Left Loudspeaker",0,0]
[null,"Min Values for 6 msec Delay",{"$nulls":20},"Floor",{"v":-3,"d":"-3.000"},0,{"$nulls":5},-1,{"v":1.7320508075688772,"d":"1.732"}]
[null,{"v":2.7716956355141815,"d":"2.772"},{"$nulls":3},"Room Height m",{"v":2.5,"d":"2.500"},{"v":8.202099737532809,"d":"8.2"},{"$nulls":15},{"v":2.732050807568877,"d":"2.732"},0,{"$nulls":4},"Left Front Corner R",0,0]
[null,{"v":1.1060053832216872,"d":"1.106"},{"$nulls":3},"Loudspeaker Distance to Front Wall m",{"v":1,"d":"1.000"},{"v":3.280839895013124,"d":"3.3"},{"$nulls":14},"Ceiling",{"v":-3,"d":"-3.000"},2.5,{"$nulls":5},{"v":-2.9999999999999996,"d":"-3.000"},{"v":3.7320508075688767,"d":"3.732"}]
[null,{"v":1.3408979941593722,"d":"1.341"},{"$nulls":3},"Loudspeaker Distance to Closest Sidewall m",{"v":1,"d":"1.000"},{"v":3.280839895013124,"d":"3.3"},{"$nulls":15},{"v":2.732050807568877,"d":"2.732"},2.5,{"$nulls":4},"Left Side Wall R",0,0]
[null,{"v":1.1060053832216872,"d":"1.106"},{"$nulls":3},"Distance to Wall Behind Listener m",{"v":3,"d":"3.000"},{"v":9.842519685039372,"d":"9.8"},{"$nulls":22},{"v":-3,"d":"-3.000"},{"v":1.7320508075688767,"d":"1.732"}]
[]
[{"$nulls":5},"Listener Height m",{"v":1,"d":"1.000"},{"v":3.280839895013124,"d":"3.3"},{"$nulls":14},"Descriptions:",{"$nulls":6},"Left Rear Corner R",0,0]
[{"$nulls":5},"Loudspeaker Height m",{"v":1,"d":"1.000"},{"v":3.280839895013124,"d":"3.3"},{"$nulls":14},"Room: 57 cu.m, 4 m W, 5.732 m L, 2.5 m H",{"$nulls":7},{"v":-2.9999999999999996,"d":"-3.000"},{"v":-7.7320508075688785,"d":"-7.732"}]
[{"$nulls":22},"L/S Spacing 2 m",{"$nulls":6},"Rear Wall R",0,0,{"v":-3,"d":"-3.000"},{"v":2.5,"d":"2.500"}]
[{"$nulls":22},"Room: 57 cu.m, 4 m W, 5.732 m L, 2.5 m H; L/S Spacing 2 m; Order, Level, Delay and Horizontal Angle of Initial Reflections",{"$nulls":7},{"v":-1.0000000000000002,"d":"-1.000"},{"v":-7.732050807568878,"d":"-7.732"},{"v":-3,"d":"-3.000"},{"v":0,"d":"0.000"}]
[{"$nulls":22},"Earliest Room Reflections for a Dipole Source",{"$nulls":6},"Right Side Wall R",0,0]
[{"$nulls":22},"Room: 57 cu.m, 4 m W, 5.732 m L, 2.5 m H; L/S Spacing 2 m; Order, Level, Delay and Vertical Angle of Initial Reflections",{"$nulls":7},{"v":5,"d":"5.000"},{"v":1.7320508075688772,"d":"1.732"}]
[]
[{"$nulls":29},"Intermediate Results:",null,null,"Check"]
[{"$nulls":29},"L/S Distance to Furthest Sidewall m",{"v":3,"d":"3.000"},{"v":9.842519685039372,"d":"9.8"}]
[{"$nulls":29},"Loudspeaker Toe-in re Listener Axis degrees",{"v":0.9999999999999964,"d":"1.0"}]
[{"$nulls":29},"Directivity Loss to Listener dB",{"v":-0.0013230038154304342,"d":"-0.0"},{"$nulls":3},"Order","Level dB","Delay","Angle","Ordered Delay"]
[{"$nulls":29},"Distance to Ceiling Image of Loudspeaker m",{"v":3.605551275463989,"d":"3.606"},{"v":11.829236468057708,"d":"11.8"},null,null,2,{"v":-13.237667219577487,"d":"-13"},{"v":4.65633617199034,"d":"5"},{"v":30.000000000000004,"d":"30"},{"v":0,"d":"0.00"},1]
[{"$nulls":29},"Distance to Front Wall Image of Loudspeaker m",{"v":3.8637033051562732,"d":"3.864"},{"v":12.676191946050768,"d":"12.7"},{"v":3.8637033051562737,"d":"3.864"},null,3,{"v":-11.882727007106201,"d":"-12"},{"v":5.40501524073047,"d":"5"},{"v":14.999999999999998,"d":"15"},{"v":4.246111235572502,"d":"4.25"},2]
[{"$nulls":29},"Listener Distance to Loudspeaker m",{"v":2,"d":"2.000"},{"v":6.561679790026248,"d":"6.6"},null,null,0,0,0,{"v":30.000000000000004,"d":"30"},{"v":4.65633617199034,"d":"4.66"},3]
[{"$nulls":29},"Distance to Front Corner Image of Loudspeaker m",{"v":4.788340341942655,"d":"4.788"},{"v":15.709778024746246,"d":"15.7"},{"v":4.7883403419426545,"d":"4.788"},null,4,{"v":-13.662389592294037,"d":"-14"},{"v":8.086599408203519,"d":"8"},{"v":38.79397688699689,"d":"39"},{"v":5.40501524073047,"d":"5.41"},4]
[{"$nulls":29},"Distance to Closest Sidewall Image of Loudspeaker m",{"v":3.4641016151377544,"d":"3.464"},{"v":11.365162779323343,"d":"11.4"},{"v":3.4641016151377544,"d":"3.464"},null,1,{"v":-42.93278317492409,"d":"-43"},{"v":4.246111235572502,"d":"4"},{"v":60.00000000000001,"d":"60"},{"v":8.086599408203519,"d":"8.09"},5]
[{"$nulls":29},"Distance to Rear Corner Image of Loudspeaker m",{"v":8.293648756176411,"d":"8.294"},{"v":27.210133714489544,"d":"27.2"},{"v":8.293648756176411,"d":"8.294"},null,7,{"v":-22.606274740174356,"d":"-23"},{"v":18.252512271037418,"d":"18"},{"v":158.7939768869969,"d":"159"},{"v":9.545844442241181,"d":"9.55"},6]
[{"$nulls":29},"Distance to Rear Wall Image of Loudspeaker m",{"v":7.796448530634094,"d":"7.796"},{"v":25.578899378720784,"d":"25.6"},{"v":7.796448530634095,"d":"7.796"},null,6,{"v":-15.576702514793254,"d":"-16"},{"v":16.810558077300815,"d":"17"},{"v":172.63074021243006,"d":"173"},{"v":16.810558077300815,"d":"16.81"},7]
[{"$nulls":29},"Distance to Furthest Sidewall Image of Loudspeaker m",{"v":5.291502622129181,"d":"5.292"},{"v":17.360572907247974,"d":"17.4"},{"v":5.291502622129181,"d":"5.292"},null,5,{"v":-13.751042893642568,"d":"-14"},{"v":9.545844442241181,"d":"10"},{"v":-70.89339464913091,"d":"-71"},{"v":18.252512271037418,"d":"18.25"},8]
[{"$nulls":29},"Distance to Floor Image of Loudspeaker m",{"v":2.8284271247461903,"d":"2.828"},{"v":9.279616551004562,"d":"9.3"},null,null,2,{"v":-13.237667219577487,"d":"-13"},{"v":4.65633617199034,"d":"5"},{"v":68.9482755646271,"d":"69"}]
[{"$nulls":34},"F",{"v":-9.020599913279625,"d":"-9"},{"v":2.4025611923847636,"d":"2"},-45]
[{"$nulls":29},"Front Wall Reflection Loudspeaker Angle degrees",{"v":14.999999999999998,"d":"15.0"}]
[{"$nulls":29},"L/S Angle to Listener degrees",{"v":30.000000000000004,"d":"30.0"},"°"]
[{"$nulls":18}," ",{"$nulls":10},"Front Corner Reflection Loudspeaker Angle degrees",{"v":38.79397688699689,"d":"38.8"}]
[{"$nulls":29},"Closest Sidewall Reflection Loudspeaker Angle degrees",{"v":60.00000000000001,"d":"60.0"}]
[{"$nulls":29},"Rear Corner Reflection Loudspeaker Angle degrees",{"v":158.7939768869969,"d":"158.8"}]
[{"$nulls":29},"Rear Wall Reflection Loudspeaker Angle degrees",{"v":172.63074021243006,"d":"172.6"}]
[{"$nulls":29},"Furthest Sidewall Reflection Loudspeaker Angle degrees",{"v":-70.89339464913091,"d":"-70.9"}]
[{"$nulls":29},"Ceiling Reflection Angle, Listener L/S Axis degrees",{"v":68.9482755646271,"d":"68.9"}]
[{"$nulls":29},"Floor Reflection Angle, Listener L/S Axis degrees",{"v":-45,"d":"-45.0"}]
[{"$nulls":31},"Image Dipole Polarity"]
[{"$nulls":29},"Angle of Front Wall Reflection re Loudspeaker Axis degrees",{"v":134,"d":"134.0"},"Opposite"]
[{"$nulls":29},"Angle of Front Corner Reflection re Loudspeaker Axis degrees",{"v":187.7939768869969,"d":"187.8"},"Opposite"]
[{"$nulls":29},"Angle of Closest Sidewall Reflection re Loudspeaker Axis degrees",{"v":91,"d":"91.0"},"Opposite"]
[{"$nulls":29},"Angle of Rear Corner Reflection re Loudspeaker Axis degrees",{"v":52.20602311300311,"d":"52.2"},"Same"]
[{"$nulls":29},"Angle of Rear Wall Reflection re Loudspeaker Axis degrees",{"v":23.630740212430055,"d":"23.6"},"Same"]
[{"$nulls":29},"Angle of Furthest Sidewall Reflection re Loudspeaker Axis degrees",{"v":-39.89339464913091,"d":"-39.9"},"Same"]
[]
[{"$nulls":29},"Horizontal Separations on Listener to L/S Axis"]
[{"$nulls":29},"Front Wall to L/S m",{"v":1.1547005383792517,"d":"1.155"}]
[{"$nulls":29},"L/S to Listener m",{"v":2,"d":"2.000"}]
[{"$nulls":29},"Listener to Rear Wall m",{"v":3.464101615137755,"d":"3.464"}]
[{"$nulls":31},"Check"]
[{"$nulls":29},"Listener to L/S m",{"v":2,"d":"2.000"},{"v":2,"d":"2.000"}]
[{"$nulls":29},"Elevation Angle of Listener rel L/S degrees",{"v":0,"d":"0.0"}]
[{"$nulls":29},"L/S Axis Elevation Angle to Listener degrees",{"v":0,"d":"0.0"}]
[{"$nulls":29},"Angle to Ceiling Reflection Point degrees",{"v":56.309932474020215,"d":"56.3"}]
[{"$nulls":29},"L/S Axis Angle to Ceiling Reflection Point degrees",{"v":56.309932474020215,"d":"56.3"}]
[{"$nulls":29},"Ceiling Reflection Angle rel Direct degrees",{"v":56.309932474020215,"d":"56.3"}]
[{"$nulls":29},"L/S Axis Angle to Floor Reflection Point degrees",{"v":-45,"d":"-45.0"}]
[]
[]
[{"$nulls":29},"Reflection Detection Threshold: Speech, No Reverberation",0,-15]
[{"$nulls":30},20,-15]
[{"$nulls":30},80,-45]