Final answer:
The statement that amplitudes of waves add up only if they are propagating in the same line is true, pertaining to the principle of the superposition of waves in physics. This principle applies strictly to co-linear waves resulting in constructive or destructive interference.
Step-by-step explanation:
Superposition of Waves
The concept in question relates to the superposition principle in physics, specifically within the topic of wave mechanics. This principle states that when two or more waves meet at a point, the resultant wave's amplitude at that point is the sum of the amplitudes of the individual waves. However, for this algebraic sum to hold true, the waves must meet in the same medium and along the same line.
Linearity is a critical pre-requisite for the superposition principle to apply. It ensures that the waves' amplitudes add algebraically without any distortion. If waves are propagating along different lines or in different dimensions, the manner in which they combine and interact changes, requiring a more complex analysis than simple linear superposition.
Therefore, the statement "The amplitudes of waves add up only if they are propagating in the same line" is True. Waves interfering in the same line, or co-linearly, will have their amplitudes add up algebraically, resulting in constructive interference (when wave crests overlap with crests) or destructive interference (when wave crests overlap with troughs).
In summary, while waves can indeed interfere when propagating in different directions, the simplest form of superposition—that of linear and algebraic summing of amplitudes—applies strictly to waves that are co-linear.
There are numerous examples of this principle in nature and technology, such as sound waves from different sources arriving at a listener or radio waves from multiple transmitters being received by a single antenna. These examples illustrate the practical implications of wave superposition in everyday scenarios.
Implications in Various Fields
The principle of superposition has implications in various fields such as acoustics, electromagnetism, and quantum mechanics, where understanding wave behavior is crucial for comprehension and application. It's essential for explaining phenomena like interference patterns, beats, and the propagation of light.