Chapter 5.2, Problem 17E

Tsunami Waves and Breakwaters This is a continuation of Exercise 16. Breakwaters affect wave height by reducing energy. (See Figure 5.30.) If a tsunami wave of height $H$ in a channel of width $W$ encounters a breakwater that narrows the channel to a width $w$, then the height h of the wave beyond the breakwater is given by $h=H{R}^{0.5}$, where $R$ is the width ratio $R=w/W$.

a. Suppose a wave of height 8 feet in a channel of width $5000\text{feet}$ encounters a breakwater that narrows the channel to $3000\text{feet}$. What is the height of the wave beyond the breakwater?

b. If a channel width is cut in half by a breakwater, what is the effect on wave height?

16. Height of Tsunami Waves When waves generated by tsunamis approach shore, the height of the waves generally increases. Understanding the factors that contribute to this increase can aid in controlling potential damage to areas at risk.

Green’s law tells how water depth affects the height of a tsunami wave. If a tsunami wave has height $H$ at an ocean depth $D$, and the wave travels to a location with water depth $d$, then the new height $h$ of the wave is given by $h=H{R}^{0.25}$, where $R$ is the water depth ratio given by $R=D/d$.

a. Calculate the height of a tsunami wave in water $25\text{feet}$ deep if its height is $3\text{feet}$ at its point of origin in water $15,000\text{feet}$ deep.

b. If water depth decreases by half, the depth ratio $R$ is doubled. How is the height of the tsunami wave affected?