Tsunamis are fast moving waves often generated by underwater earthquakes. In the

Question

Tsunamis are fast moving waves often generated by underwater earthquakes. In the deep ocean their amplitude is barely noticeable, but upon reaching shore, they can rise up as high as a six story building. A recent tsunami has been estimated by some to have a wavelength of 750km and was suspected to travel a distance of 3700km in about 5.3 hours. Determine the wave's a.) speed, b.) frequency, c.) period. As a reference, d.) also compare the wave's speed to that of standard passenger jets, 250 m/s. Assuming that hte wave would have an amplitude of the six story building with 4m per story, e.) write the equation of the wave (as a cosine wave).

Explanation / Answer

The wavelength of the wave is = 750 km The distance travelled d = 3700 km The time taken for the travell is t = 5.3 hrs a) Wave speed v = d/t = 3700 km/5.3 hr = 193.92 m/s b) frequency f = v/ = 193.92 m/s / 750000 m = 0.258 mHz c) Period T = 1/f = 3.875*103 s d) The speed of the jet is v' = 250 m/s The speed of the wave is v = 193.92 m/s = 0.776*250 m/s = 0.776v' e) The amplitude of the wave is A = 24 m The wave equation will be of the form y = Acos(kx+t) k = 2/ = 2/750000 m = 8.37*10-6 m-1 = 2f = 2*0.258*10-3 Hz = 1.62*10-3 s-1 The wave equation is y = (24 m)cos[(8.37*10-6 m-1)x+(1.62*10-3 s-)t] The wave equation is y = (24 m)cos[(8.37*10-6 m-1)x+(1.62*10-3 s-)t]

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