Superposition: Question 6

Syllabus 8.1

Multiple choice AS 1 mark

The principle of superposition states that when two or more waves meet at a point, the resultant displacement is the vector (algebraic) sum of the individual displacements of each wave at that point.

At a certain instant, two waves overlap at point $X$ . One wave alone would produce a displacement of $+3.5\text{ cm}$ at $X$ , and the other wave alone would produce a displacement of $-1.5\text{ cm}$ at $X$ .

What is the resultant displacement at $X$ at this instant?

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Step 1: Apply the principle of superposition

The principle of superposition says the resultant displacement is the algebraic sum of the individual displacements, keeping their signs: $y_{\text{resultant}} = y_1 + y_2$

Step 2: Substitute the given displacements

$y_{\text{resultant}} = (+3.5) + (-1.5) = 3.5 - 1.5 = 2.0\text{ cm}$

Check (recompute independently): starting from $+3.5\text{ cm}$ and moving $1.5\text{ cm}$ in the negative direction lands at $3.5 - 1.5 = 2.0\text{ cm}$ , the same result.

Step 3: Why the other options are wrong

A ( $+1.0$ cm): this is the average of the two displacements, not their sum.
C ( $+5.0$ cm): this comes from adding the magnitudes $3.5+1.5$ while ignoring that the second wave’s displacement is negative.
D ( $-2.0$ cm): this has the correct magnitude but the wrong sign, from subtracting in the wrong order ( $1.5-3.5$ ).

Final answer

Resultant displacement $= \boxed{+2.0\text{ cm}}$ , option B.