Enter the amplitude, angular frequency, time, and phase shift of each wave into the calculator to determine the superposition output.

Superposition Formula

The following formula is used to calculate the output of a Superposition Calculator.

SP = ∑ (Ai * sin(ωi * t + φi))


  • SP is the superposition output Ai is the amplitude of the ith wave ωi is the angular frequency of the ith wave (rad/s) t is the time (s) φi is the phase shift of the ith wave (rad)

To calculate the superposition output, for each wave, multiply the amplitude by the sine of the product of the angular frequency and time, plus the phase shift. Sum all these results to get the superposition output.

How to Calculate Superposition?

The following steps outline how to calculate the Superposition using the given formula:

  1. First, determine the amplitude of each wave (Ai).
  2. Next, determine the angular frequency of each wave (ωi) in radians per second (rad/s).
  3. Next, determine the time (t) in seconds (s).
  4. Next, determine the phase shift of each wave (φi) in radians (rad).
  5. Using the given formula SP = ∑ (Ai * sin(ωi * t + φi)), calculate the superposition output (SP).
  6. After inserting the values of Ai, ωi, t, and φi into the formula, calculate the result.

Example Problem:

Use the following variables as an example problem to test your knowledge:

Amplitude of the 1st wave (A1) = 3

Angular frequency of the 1st wave (ω1) = 2

Time (t) = 5

Phase shift of the 1st wave (φ1) = π/4