Final answer:
The statement that tsunami waves may be only inches higher than the ocean surface in deep water is true. The distance between tsunami wave crests traveling at 600 km/h, occurring every 15 minutes, is 150 km. Waves can superpose with different frequencies, and the statement that waves propagate faster in a less dense medium if the stiffness is the same is false.
Step-by-step explanation:
True, in the open ocean, the waves of even the largest tsunamis may be only inches higher than the ocean surface. When a tsunami is in deep water, its height on the ocean's surface can be less than 30 cm, and it can travel very rapidly, up to speeds of 700 km/hr. However, as it reaches shallow water near the coast, the speed of the tsunami decreases, and the wave can rise dramatically, often reaching heights of up to 30 meters due to the wave dynamics where the top part of the wave travels faster than the bottom.
The distance between tsunami wave crests can be calculated using their speed and frequency of approach. If a tsunami travels at 600 km/h and has a frequency of one wave crest every 15 minutes, the distance between the wave crests would be the product of speed and time which is 150 km (600 km/h * 0.25 hours).
Waves can superimpose, or add together, even if their frequencies are different. This is true because waves of different frequencies can interact to form a complex wave pattern. The amplitude of one wave is affected by another wave only when they coincide at the same point, and hence they constructively or destructively interfere with each other, a concept known as superposition.
Concerning the amplitude of waves propagating on the same line, the statement that their amplitudes add up only if they are propagating in the same line is false. Waves traveling in different directions can still influence each other's amplitude through the principle of superposition when they intersect or overlap.
Lastly, the statement that waves propagate faster in a less dense medium if the stiffness is the same is false. Wave propagation speed depends on both the density and the stiffness (elastic properties) of the medium, and waves typically travel slower in less dense media if the stiffness is unchanged.