Final answer:
The amplitudes of waves can add up regardless of whether they are propagating in the same line or not, through interference which can be either constructive or destructive. Waves of different frequencies can superimpose, and standing waves are formed by two identical waves traveling in opposite directions.
Step-by-step explanation:
The statement that the amplitudes of waves add up only if they are propagating in the same line is False. When two waves interfere with each other, their amplitudes combine through a process known as superposition. This process occurs regardless of whether the waves are propagating in the same line or not. The resulting amplitude can be larger (constructive interference) or smaller (destructive interference) and sometimes, if precisely out of phase, can even cancel each other out completely.
Moreover, the amplitude of one wave can affect another wave when they intersect and interact, not only when they are precisely aligned. As for frequencies, waves of different frequencies can indeed superimpose, forming complex wave patterns; this occurrence is common in sound waves and electromagnetic waves. Lastly, a standing wave is actually formed by the superposition of two identical waves with the same amplitude and frequency, traveling in opposite directions, not the same direction as suggested by the prompt.