Correct Option
The correct option is (c) 1 and 3 only.
Explanation
Tsunamis behave as shallow-water waves because their wavelength is extremely long compared to the ocean depth. Their physical characteristics change drastically as they transition from the deep ocean to shallow coastal waters through a process known as shoaling.
Statement-wise Analysis:
- Statement 1 is Correct: In deep water, tsunamis have very long wavelengths (often exceeding 100 km). As the wave approaches the coast, the shallow depth causes the leading edge of the wave to slow down while the trailing part continues at a higher speed. This causes the wave to compress or "bunch up," resulting in a significant decrease in wavelength.
- Statement 2 is Incorrect: The speed of a tsunami is directly related to the depth of the water ($v = \sqrt{g \cdot d}$). In the deep ocean, tsunamis travel at very high speeds (up to 800 km/h). However, as they enter shallow coastal waters, the decrease in depth causes friction with the seabed to increase, leading to a significant reduction in travel speed.
- Statement 3 is Correct: As the wave slows down and the wavelength shortens, the energy flux remains conserved. This energy is compressed into a smaller volume of water, forcing the wave amplitude to rise. Consequently, the height of the wave increases dramatically as it reaches the shore.
Key Takeaway:
As a tsunami moves from deep to shallow water, its speed decreases, its wavelength decreases, and its wave height increases due to the shoaling effect.