Wave superposition

Adding equal-frequency sinusoids produces a sinusoid at the same frequency. Its amplitude lies between the absolute difference and the sum of the individual amplitudes, calculated by the formula $A=\sqrt{A_1^2+A_2^2+2A_1A_2\cos\phi}$, where $\phi$ is the phase difference.

Conditions: The two waves have the same frequency.; The two waves have an arbitrary phase difference $\phi$.

The amplitude of the resultant sinusoid lies between the absolute difference and the sum of the individual amplitudes, specifically bounded by $|A_1 - A_2| \le A \le A_1 + A_2$. Both the amplitude and the phase position of the resultant wave change relative to the inputs.

Conditions: Two sinusoids have equal frequency.; There is an arbitrary phase difference $\phi$ between them.; Amplitudes are non-zero ($A_1=2, A_2=0.8$ in the demo).

The resultant amplitude is the absolute difference between the two individual amplitudes, which equals 2.0. This is an example of destructive interference where the waves partially cancel each other out.

Conditions: Both waves have the same frequency.; The waves are in anti-phase (phase difference of $\pi$ radians or 180 degrees).; Amplitude of wave A ($A_1$) is 2.5.; Amplitude of wave B ($A_2$) is 0.5.

If two waves of equal frequency are exactly out of phase (phase difference of $\pi$ radians or 180 degrees), they partially cancel each other out. The resultant amplitude is the absolute difference between their individual amplitudes.

Conditions: The two waves have the same frequency.; The two waves are exactly out of phase (anti-phase).

When two waves of the same frequency and identical phase overlap, the amplitude of the resultant wave is the sum of their individual amplitudes. This phenomenon is known as constructive interference.

Conditions: The two waves have the same frequency.; The two waves are in identical phase (phase difference is zero).

The resultant amplitude is the sum of the individual amplitudes, which equals 4. This scenario represents constructive interference where the peaks and troughs align perfectly.

Conditions: Both waves have the same frequency.; The waves are in phase (identical phase).; Amplitude of wave A ($A_1$) is 3.; Amplitude of wave B ($A_2$) is 1.