Superposition Calculator

Formula

The formula to calculate the Superposition Output (SP) is:

\[ SP = \sum (A_i \times \sin(\omega_i \times t + \phi_i)) \]

Where:

\( SP \) is the Superposition Output
\( A_i \) is the Amplitude of the \(i\)th wave
\( \omega_i \) is the Angular Frequency of the \(i\)th wave (rad/s)
\( t \) is the Time (seconds)
\( \phi_i \) is the Phase Shift of the \(i\)th wave (radians)

What is Superposition?

The principle of superposition states that when two or more waves overlap in space, the resulting wave is the sum of the individual waves. This concept is essential in physics and engineering, particularly in the study of wave interference, sound waves, and light waves. The superposition principle allows us to calculate the resulting wave pattern by adding together the contributions from each wave at a given point in time.

Example Calculation

Let's consider an example with two waves:

Wave 1: \(A_1 = 2\), \(\omega_1 = 1\) rad/s, \(\phi_1 = 0\) radians
Wave 2: \(A_2 = 1\), \(\omega_2 = 2\) rad/s, \(\phi_2 = \pi/4\) radians
Time \(t = 3\) seconds

Using the formula to calculate Superposition Output:

\[ SP = 2 \times \sin(1 \times 3 + 0) + 1 \times \sin(2 \times 3 + \frac{\pi}{4}) \]

This means that the resulting superposition output at \(t = 3\) seconds is the sum of the contributions from both waves.