Final answer:
The amplitude of waves can be affected by other waves when they meet, not just when precisely aligned, and waves of different frequencies can superimpose. The Louisiana Purchase indeed doubled the territory of the United States.
Step-by-step explanation:
The statement that the amplitude of one wave is affected by the amplitude of another wave only when they are precisely aligned is false.
Waves can interact or interfere with each other when they meet. This interaction can be constructive or destructive, depending on the phase difference between the waves.
Constructive interference occurs when the waves are in phase, increasing the resultant amplitude, whereas destructive interference occurs when they are out of phase, reducing the resultant amplitude. This principle applies regardless of whether the waves are precisely aligned in space.
Regarding the superposition of waves with different frequencies, the statement is true; waves of different frequencies can still superimpose upon one another to form a resultant wave pattern.
This is seen in the principle of superposition, where the displacement caused by multiple waves at any given point is the sum of the displacements caused by each individual wave.
Last, the statement that the Louisiana Purchase doubled the territory of the United States is also true.
This historic land deal between the United States and France in 1803 approximately doubled the size of the U.S., extending the territory westward.