What is the resultant amplitude when two sine waves of the same frequency and identical phase with amplitudes $A_1=3$ and $A_2=1$ undergo superposition?

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.

Reasoning, step by step

1. Identify that the two waves share the same frequency and are plotted in phase.
2. Observe the animation where the blue wave (amplitude 3) and red wave (amplitude 1) overlap.
3. Note that the green resultant waveform reaches a maximum height equal to the sum of the heights of the blue and red waves.
4. Apply the formula for constructive interference: $A_{total} = A_1 + A_2$.
5. Calculate the sum: $3 + 1 = 4$.

Example

In the top coordinate system shown from 00:05 to 00:10, the script describes plotting two sine curves with Blue $A=3$ and Red $A=1$. The generated green resultant waveform shows that its amplitude equals the sum of the individual amplitudes.

Common misconceptions

• Believing that the resultant amplitude is the average of the two amplitudes.
• Assuming that different amplitudes prevent perfect constructive interference.

Watch the explanation

Explore next

• How does the resultant amplitude change if the waves are exactly out of phase?
• What happens to the phase of the resultant wave if the amplitudes are unequal but phases are slightly shifted?