On December 26, 2004, a great earthquake occurred off the coast of Sumatra and triggered immense waves (tsunami) that killed some 200,000 people. Satellites observing these waves from space measured 800 km from one wave crest to the next and a period between waves of 10 hour. What was the speed of these waves in m/s and in km/h. Does your answer help you understand why the waves caused such devastation?

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Jazmyn Bean · Accepted Answer

We know that the speed of a periodic wave u with wavelength   λ and frequency j is given by:  v  =  f  ∗  λ ...(1)We also know that the relation between the frequency and the time period is given by:  f  =      1    T   ...(2)The distance between one wave crest to the next is the wavelength of the wave which is   λ  =  800  k  m and the period of the wave is T = 1.0h.First, we calculate the frequency of the wave by substituting for T into equation (2), so we get:  f  =      1          1.0      h        =  1.0      h          −      1      Now, we plug our values for f and   λ into equation (1), so we get:  v  =  (  1.0      h          −      1        )  ∗  (  800  )  k  m      /    h  =  (  800  k  m      /    h  )  ×  (            1000      m              /            k      m              3600      s              /            h        )  =  222  m      /    s  ∴  v  =  800  k  m      /    h  =  222  m      /    sThe danger of the wave comes from its high speed, which makes it strick without warning and without taking any action to prevent the damage as possible.But the distruction is measured by the amount of energy carried by this wave which corresponds to the amplitude of the wave.Result:v=800km/h = 222m/sThe danger of the wave comes from its high speed, which makes it strick without warning and without taking any action to prevent the damage as possible.

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