question 3 tsunami waves d near shore 5 points this experiment helps us understand the most dang

Step 1: Calculate the new wave height when the depth decreases to 10 m using the relationship A

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Question 3: Tsunami Waves (λ > d) Near Shore (5 points) This experiment helps us understand the most dangerous water wave of all – the tsunami near shore. The waves in this experiment are shallow water waves because their wavelength (λ ~ 5 - 10 cm) is larger than the water depth, d. Tsunami wavelength is so long (100's of km) that they are also shallow water waves even in the deepest oceans. Then, as a tsunami wave approaches the shore, its speed decreases because the depth decreases (see above). Its wavelength λ = vT decreases because the period T is the same. The same wave energy is packed into a smaller distance λ and as a result, the wave amplitude increases with decreasing depth as A ∝ 1/d^4. A wave 0.5 m high at a distance of 500 m from the shore is barely visible and looks unthreatening. Assume that the depth there is 25 m. How high is the wave when d decreases to 10 m? Height = ? How long does it take the wave to travel the 500 m distance to the shore (you can assume an average depth for simplicity)? Time to reach shore = ? These calculations explain why we see photos of unalarmed beachgoers moments before the wave reached the shore. Why is a tsunami wave not easy to detect from a ship at sea, which could then send a warning to coastal areas? (hint: consider the wave speed and its amplitude).

          Question 3: Tsunami Waves (λ > d) Near Shore (5 points)

This experiment helps us understand the most dangerous water wave of all – the tsunami near shore. The waves in this experiment are shallow water waves because their wavelength (λ ~ 5 - 10 cm) is larger than the water depth, d. Tsunami wavelength is so long (100's of km) that they are also shallow water waves even in the deepest oceans. Then, as a tsunami wave approaches the shore, its speed decreases because the depth decreases (see above). Its wavelength λ = vT decreases because the period T is the same. The same wave energy is packed into a smaller distance λ and as a result, the wave amplitude increases with decreasing depth as A ∝ 1/d^4.

A wave 0.5 m high at a distance of 500 m from the shore is barely visible and looks unthreatening. Assume that the depth there is 25 m. How high is the wave when d decreases to 10 m?
Height = ?

How long does it take the wave to travel the 500 m distance to the shore (you can assume an average depth for simplicity)?
Time to reach shore = ?

These calculations explain why we see photos of unalarmed beachgoers moments before the wave reached the shore.

Why is a tsunami wave not easy to detect from a ship at sea, which could then send a warning to coastal areas? (hint: consider the wave speed and its amplitude).

Added by Brian M.

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