Question

The principle of superposition in wave motion states that ________.

• A. the net displacement is the vector sum of individual displacements
• B. waves interfere with each other and lose energy
• C. waves cannot occupy the same space at the same time
• D. it is applicable to sound waves only
• E. it is applicable to standing waves only

Hint:

Superposition leads to interference patterns (constructive and destructive).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
This question asks for the definition of the principle of superposition as it applies to waves. This principle is fundamental to understanding wave phenomena like interference and diffraction.
Step 2: Detailed Explanation
The principle of superposition states that when two or more waves of the same type are incident on the same point in a medium, the resultant displacement at that point is the vector sum of the individual displacements that each wave would produce in the absence of the others.
Mathematically, if wave 1 produces displacement \(\vec{y}_1\) and wave 2 produces displacement \(\vec{y}_2\) at a point, the net displacement \(\vec{y}_{net}\) when both are present is:
\[ \vec{y}_{net} = \vec{y}_1 + \vec{y}_2 \] Let's analyze the given options:
(A) the net displacement is the vector sum of individual displacements: Correct. This is the precise statement of the principle. For transverse waves, this means adding the displacements perpendicular to propagation. For longitudinal waves, it's adding the displacements parallel to propagation.
(B) waves interfere with each other and lose energy: Incorrect. Superposition can lead to interference, but the principle itself does not state that energy is lost. In fact, for linear waves, energy is conserved.
(C) waves cannot occupy the same space at the same time: Incorrect. The principle of superposition is precisely about what happens when waves \textit{do} occupy the same space at the same time.
(D) it is applicable to sound waves only: Incorrect. The principle applies to all types of linear waves, including light waves, water waves, waves on a string, and sound waves.
Step 4: Final Answer
The principle of superposition states that the net displacement is the vector sum of individual displacements.