What is the resultant amplitude when two sine waves of the same frequency with amplitudes $A_1=2.5$ and $A_2=0.5$ undergo anti-phase superposition?

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.

Reasoning, step by step

1. Identify that the middle coordinate system illustrates anti-phase superposition.
2. Observe the blue wave with amplitude 2.5 and the red wave with amplitude 0.5 having opposite phases.
3. Note that the green composite wave has a reduced amplitude compared to the larger individual wave.
4. Apply the formula for anti-phase destructive interference: $A_{total} = |A_1 - A_2|$.
5. Calculate the difference: $|2.5 - 0.5| = 2.0$.

Example

From 00:10 to 00:14, the video shows the middle coordinate system. The script states the blue wave ($A=2.5$) and red wave ($A=0.5$) have opposite phases, resulting in a green composite wave with reduced amplitude. The card confirms the formula $A_{total} = |A_1 - A_2|$.

Common misconceptions

• Thinking that anti-phase always results in zero amplitude (complete cancellation requires equal amplitudes).
• Adding the amplitudes instead of subtracting them for out-of-phase waves.

Watch the explanation

Explore next

• Under what condition would the resultant amplitude be exactly zero in this setup?
• How does the phase of the resultant wave compare to the phase of the dominant input wave?