# The Nature of Waves

## Practice

### practice problem 1

Natural phenomena are normally very noisy (in the statistical sense) but from 10:50 to 12:05 local time the changes in sea level at Hanimaadhoo were most nearly periodic. During this time interval determine the tsunami's mean…

- amplitude and
- period

The speed of a tsunami varies with depth. In the open ocean they normally move as fast as a commercial jet airplane (about 250 m/s or 900 kph) but slow down to the speed of a car on a neighborhood street when they reach the shallow waters of the shore (about 15 m/s or 55 kph). Given these speeds, determine the mean wavelength of the segment of the tsunami that arrived in Hanimaadhoo between 10:50 and 12:05 when they were…

- in deep water
- near the shore

One final question.

- How would the amplitude of a tsunami near shore compare to the amplitude of the same wave in the open ocean? Explain your reasoning.

#### solution

### practice problem 2

#### solution

Answer it.

### practice problem 3

#### solution

Answer it.

### practice problem 4

The greatest recorded earthquake (magnitude of 9.5) occurred on 22 May 1960 in Chile. The second largest earthquake (magnitude 9.2) occurred on 27 March 1964 during the Christian Holiday of Good Friday, which is why it is also known as the Good Friday Earthquake. A large earthquake (magnitude 8.8) occurred in Chile on 27 February 2010 that grabbed my attention and motivated me to write this problem. All three earthquakes generated tsunamis for which I was able to find useful data.

Tsunamis are sometimes called "tidal waves" but this name is misleading. Tsunamis, which are seismic in origin, and tides, which are caused by the gravitational pull of the moon and sun, are completely unrelated. The word tsunami is derived from the japanese phrase "harbor wave" (津波) since tsunamis are most intense in harbors where the underlying terrain focuses their energy. The term "tidal wave" is somewhat appropriate since the waves generated by earthquakes result in long period waves that sometimes look like the changes in water depth caused by the tides.

The accompanying tab-delimited text file provides the following data for the tsunamis associated with the three earthquakes described above.

- Location of town, harbor, or facility
- Region (state, province, or country)
- Transit time in minutes after the earthquake began
- Distance from the epicenter in kilometers measured along a great circle (the shortest path on the surface of a sphere)

Use this information to determine the speed of a tsunami in…

- km/min
- km/hr
- m/s
- and mph if you live in the United States

Source: National Oceanic and Atmospheric Administration (NOAA)

- West Coast and Alaska Tsunami Warning Center
- Pacific Tsunami Warning Center

#### solution

Plot distance on the *y* axis and time on the *x* axis so that the slope of the best fit line will be the speed.

It appears that the average speed of a tsunami in the pacific is…

- 11 km/min
- 660 km/h
- 180 m/s
- 410 mph