An earthquake on the Pacific seafloor creates a tsunami that has a wavelength of

Question

An earthquake on the Pacific seafloor creates a tsunami that has a wavelength of 150 km.

1a. Would this tsunami be a ‘deep water’ wave or a ‘shallow water’ wave? Justify your answer given that the average depth of the Pacific Ocean is 4600 m.

1b. Calculate the speed of the tsunami in units of meters per second AND in units of miles per hour (convert m/s to mph) at the following depths:

D = 4600 m (middle of the ocean)

D = 10 m (close to shore)

1c. Compare the two values and describe how speed changes with depth.

Optional table to help with calculations:

Explanation / Answer

1. We calculate the relative depth d/L = 4600 m/150000 m = 0.0306

Now as the relative depth is less than 0.05 thus it is a shallow water wave.

2. Speed of Tsunami at depth 4600 m = sqrt (gd) = sqrt (9.8*4600) = 212.3 m/sec
now we know that 1 mile = 1609.344 metre
and 1 hour = 3600 sec
Thus speed in miles/ hour = 212.3 * 3600/1609.344 = 474.9 miles/hr

Speed of Tsunami at depth 10 m = sqrt (gd) = sqrt (9.8*10) = 9.8994 m/sec
now we know that 1 mile = 1609.344 metre
and 1 hour = 3600 sec
Thus speed in miles/ hour = 9.8994 * 3600/1609.344 = 22.144 miles/hr

c. We see that the speed of the wave decreases on decreasing the water depth. Thus shallow water wave’s speed is dependent on ocean depth and decreases on decreasing the depth.

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