Wave Number Calculator – Guide

Introduction

This is the online Wave Number calculator guide. The calculator supports the R1, R2, and R3 dimensions. Chose from these using the top menu bar of the calculator.

Wave Numbers use Opposite Values. Each Opposite Value consists of 3 parts. The first is the Counter. This gives the magnitude.  

The second part is the Opposite Type that represents the axis where the Opposite Value is located. For example: 1^{^} is on the x-axis, 1i^{^} is on the y-axis and 1j^{^} is on the z-axis. Note that the x-axis does not use a letter.

The third part of an Opposite Value is its Opposite Sign which is either ^{^}, called “Hat” or ^v, called ‘Vee’. It determines which side of 0 on the Wave Number Line that the Opposite Value can be found.

As there is no negative sign in Wave Number expressions, positive signs are optional. It is possible to input 2^{^} + 4i^v + 4j^{^} on the Wave Number calculator without the positive signs as 2^{^} 4i^v 4j^{^}.

Wave Number Calculator Operations

Choose any of the operations of addition, multiplication, division, root, dot product, cross product, rotation, rotication,  memory +,  flipm and memory clear from the second menu  bar of the Wave Number calculator. Note that not all of these operations are available in R1 and R2.

In Wave Numbers, the Operator performs an Operation on the Operand. For example:

• In the R2 equation 4^{^}*6^v = 24^v, 4^{^} is the Operator, multiplication is the Operation and 6^v is the Operand. 
• In the R2 equation 24^v/4^{^} = 6^v, 4^{^} is the Operator, division is the Operation and 24^v is the Operand.

Addition

Click on the + operation for addition. Input Opposite Values into the Operator and Operand fields and click on calculate. The Wave Number calculator then displays the result. For example:

• R1: Operator: 2^{^}, Operand: 5v gives the result: 3v
• R2: Operator: 2^{^} + 4i^v, Operand: 5^v + 6i^{^} gives the result: 3^v + 2i^{^}
• R3: Operator: 2^{^} + 4i^v + 4j^{^}, Operand: 5^v + 6i^{^} + 8j^{^} gives the result: 3^v + 2i^{^} + 12j^{^}

Multiplication

Click on the * operation for multiplication. Input Opposite Values into the Operator and Operand fields and click on calculate. The Wave Number calculator then displays the result. For example:

• R1: Operator: 2^{^}, Operand: 5^v   gives the result: 10^v
• R2: Operator: 2^{^} + 4i^v, Operand: 5^v + 6i^{^}  gives the result: 14^{^} + 32i^{^}
• R3: Operator: 2^{^} + 4i^v + 4j^{^}, Operand: 5^v + 6i^{^} + 8j^{^} gives the result: 66^v + 12i^v + 24j^{^}

An Operator can be a counter in multiplication but an Operand cannot. For example:

• R1: 6*2^v = 12^v
• R2: 6*(2^v + 3i^v) = 12^v + 18i^v
• R3: 6*(2^v + 3i^v + 4j^{^}) = 12^v + 18i^v + 24j^{^}

Division

Click on the / operation for division. Input Opposite Values into the Operator and Operand fields and click on calculate. The Wave Number calculator then displays the result. For example:

• R1: Operator: 2^{^}, Operand: 10^v   gives the result: 5^v
• R2: Operator: 2^{^} + 4i^v, Operand: 14^{^} + 32i^{^}  gives the result: 5^v + 6i^{^}
• R3: Operator: 2^{^} + 4i^v + 4j^{^} , Operand: 66^v + 12i^v + 24j^{^} gives the result: 5^v + 6i^{^} + 8j^{^}

An Operator can be a counter in division but an Operand cannot. For example:

• R1: 8^v/4= 2^v
• R2: (6^v + 12i^v)/3 = 2^v + 4i^v
• R3: (6^v + 12i^v + 24j^{^})/3 = 2^v + 4i^v + 8j^{^}

Root

Click on the Root operation for roots. Input Opposite Values into the Expression, a number > 1 for the root power and click on calculate. The Wave Number calculator then displays the result. For example

• R1:
  • Expression: 64^{^}, Power: 6 gives a result of 2^{^} or 2^v
    • ⁶√64^{^} = 2^{^} or 2^v
• R2:
  • Expression: 16^{^}, Power: 2 gives a result of 4^{^} or 4^v
    • √(16^{^})  = 4^{^} or 4^v
  • Expression: (5^v + 12i^v): Power: 2 gives a result of (2^{^} + 3i^v) or (2^v + 3i^{^})
    • √(5^v + 12i^v) = (2^{^} + 3i^v) or (2^v + 3i^{^})
• R3
  • Expression: (9^v + 16i^{^} + 25j^v ), Power: 2 gives a result of = (3^v + 4i^{^} + 5j^v )
    • √(9^v + 16i^{^} + 25j^v )   = (3^v + 4i^{^} + 5j^v )     
  • Expression: (4^v + 43i^v + 58j^{^}), Power: 3 gives a result of (2^{^} + 3i^v + 4j^{^})
    • ³√(4^v + 43i^v + 58j^{^}) = (2^{^} + 3i^v + 4j^{^})   
  • Please note that for R3 the algorithm to find the cube roots uses simultaneous equations. Sometimes the algorithm times out and a result is not available.

Dot Product

Click on the Dot Product operation for dot products. This only works for R2 and R3. The result is a Counter. Input Opposite Values into the Operator and Operand fields and click on calculate. It is then displayed. For example:

• R2: Operator: (3^{^} + 2i^{^}), Operand: (1^{^} + 4i^{^}) gives a result of 11
  • (3^{^} + 2i^{^}).(1^{^} + 4i^{^}) = 11
• R3: Operator: (2^v + 8i^v + 10j^{^}), Operand: (2^v  + 2i^{^} + 3j^{^}) gives a result of 18
  • (2^v + 8i^v + 10j^{^}).(2^v  + 2i^{^} + 3j^{^}) = 18

Cross Product

Click on the Cross Product operation for cross products. This only works for R3. Input Opposite Values into the Operator and Operand fields and click on calculate. It is then displayed. For example:

• R3: Operator: (2^v + 8i^v + 10j^{^}), Operand: (2^v  + 2i^{^} + 3j^{^}) gives a result of (44^v + 14i^v + 20j^v)
  • (2^v + 8i^v + 10j^{^}) x (2^v  + 2i^{^} + 3j^{^}) = (44^v + 14i^v + 20j^v)

Rotation

Click on the Rotation operation for rotations. This only works for R2 and R3. Input Opposite Values into the Axis of Rotation and Value Rotation fields. In R2, the Axis of Rotation represents a point. If it is left blank, then assume it is rotation around the z-axis at the origin (0, 0).

In R3, the Axis of Rotation represents a point that together with the origin (0, 0 ,0) form the axis of rotation. If the Axis of Rotation is left blank, then assume it is the z-axis, i.e. the axis is formed by the points (0, 0 , 0) and (0, 0, j^{^}).

Click on calculate and the Wave Number calculator then displays the result. For example:

• R2:
  • Axis of Rotation: (0, 0), Value Rotation: 1^v, and Degree of Rotation: 90^{^} gives i^v
    • π^{^}/2 ↺ 1^v = i^v
  • Axis of Rotation: (0, 0), Value Rotation: 1^{^}, and Degree of Rotation: 45^{^} gives √2/2^{^} + √2/2i^{^}
    • π^{^}/4 ↺ 1^{^} = √2/2^{^} + √2/2i^{^}
  • Axis of Rotation: (7^v, 8i^v), Value Rotation: (3^{^}+ 4i^v), and Degree of Rotation: 90^{^} gives 11^v + 2i^{^}
    • π^{^}/2 ↺^{(7v, 8iv)} (3^{^}+ 4i^v) =   11^v + 2i^{^}
• R3:
  • Axis of Rotation: (0, 0, j^{^}), Value Rotation: (1^{^}, 0, 0), and Degree of Rotation: 90^{^} gives i^{^}
    • π^{^}/2 ↺^z (1^{^},0, 0) = i^{^}
  • Axis of Rotation: (1^{^}, 0, 0), Value Rotation: (1^{^}, 0, 0), and Degree of Rotation: 90^{^} gives 1^{^}
    • π^v/2 ↺^x (1^{^},0, 0) = 1^{^}
  • Axis of Rotation: (4^{^}, 5i^{^}, 6j^{^}), Value Rotation: (1^{^}, 2i^{^}, 3j^{^}), and Degree of Rotation: 60^{^} gives (.456^{^} +  .57i^{^} +  .684j^{^})
    • 60^o ↺^{(4^+ 5i^ + 6j^)} (1^{^} + 2i^{^} + 3j^{^}) = (1.627^{^} +  1.447i^{^} +  3.043j^{^})

Rotication – A New Operation in the Wave Number Calculator

Click on the Rotication operation for rotications. This only works for R2 and R3. Input Opposite Values into the Axis of Rotation and Value Rotation fields. In R2 the Axis of Rotation represents a point. If it is left blank, then assume it is rotation around the z-axis at the origin (0, 0).

In R3 the Axis of Rotation represents a point that together with the origin (0, 0 ,0) form the axis of rotation. If the Axis of Rotation is left blank, then assume it is the z-axis, i.e. the axis formed by the points (0, 0 , 0) and (0, 0, j^{^}).

Click on calculate and the result is then displayed on the Wave Number calculator. For example:

• R2:
  • Axis of Rotation: (0, 0), Value Rotation: 1^v, and Degree of Rotation: 90^{^} gives 0
    • π^{^}/2 R↺ 1^v = 0
  • Axis of Rotation: (7^v, 8i^v), Value Rotation: (3^{^}+ 4i^v), and Degree of Rotation: 90^{^} gives 116.93^v + 21.26i^{^}
    • π^{^}/2 R↺^{(7v, 8iv)} (3^{^}+ 4i^v) =   116.93^v + 21.26i^{^}
• R3:
  • Axis of Rotation: (0, 0, j^{^}), Value Rotation: (1^{^}, 0, 0), and Degree of Rotation: 90^{^} gives i^{^}
    • π^{^}/2 R↺^z (1^{^},0, 0) = i^{^}
  • Axis of Rotation: (1^{^}, 0, 0), Value Rotation: (1^{^}, 0, 0), and Degree of Rotation: 90^{^} gives 1^{^}
    • π^v/2 R↺^x (1^{^},0, 0) = 1^{^}
  • Axis of Rotation: (4^{^}, 5i^{^}, 6j^{^}), Value Rotation: (1^{^}, 2i^{^}, 3j^{^}), and Degree of Rotation: 60^{^} gives (14.28^{^} +  12.7i^{^} +  26.7j^{^})
    • 60^o R↺^{(4^+ 5i^ + 6j^)} (1^{^} + 2i^{^} + 3j^{^}) = (14.28^{^} +  12.7i^{^} +  26.7j^{^})

Wave Number Calculator Memory Operations

The memory operations work on the last result. M+ adds the last result to memory. Clicking the m buttons beside the input fields sets the input to the value in memory. There is no M- button. However the Opposite Sign of the value in memory can be flipped using the FlipM operation. This allows the difference of two values to be calculated. MC clears the memory.

Wave Number Calculator