Question

On December 26, 2004, a violent earthquake of magnitude 9.1 occurred off the coast of Sumatra. This quake triggered a huge tsunami (similar to a tidal wave) that killed more than 150,000 people. Scientists observing the wave on the open ocean measured the time between crests to be 1.0 h and the speed of the wave to be 800 km/h. Computer models of the evolution of this enormous wave showed that it bent around the continents and spread to all the oceans of the earth. When the wave reached the gaps between continents, it diffracted between them as through a slit.
(a) What was the wavelength of this tsunami?
(b) The distance between the southern tip of Africa and northern Antarctica is about 4500 km, while the distance between the southern end of Australia and Antarctica is about 3700 km. As an approximation, we can model this wave’s behavior by using Fraunhofer diffraction. Find the smallest angle away from the central maximum for which the waves would cancel after going through each of these continental gaps.

Answer 1

Answer:

a) 800 km

b) 9.79° & 12.47°

Explanation:

It is known that the wavelength of any material or substance is given by the relation 入 = v/f

From the question, the time between the crest is given as 1.0 h, therefore, t = 1.0 h

Also, remember that frequency, f can be represented by

f = 1/t, and thus,

f = 1/1.0 h = 1.0 h^-1. This is our frequency, and would be used in the primary stated formula

入 = v/f, from the question, the speed is already stated as 800 km/h, so we apply directly

入 = 800 / 1

入 = 800 km. Therefore, the wavelength of the tsunami is 800 km

B,

the smallest angle between the Southern tip of Africa is

Sinθ = 800 / 4500

Sinθ = 0.17

θ = Sin^-1 0.17

θ = 9.79°

The smallest angle between the Southern end of Australia is

Sinθ = 800 / 3700

Sinθ = 0.216

θ = Sin^-1 0.216

θ = 12.47°