Question

Tsunamis are fast-moving waves often generated by underwater earthquakes. In the deep ocean their amplitude is barely noticable, but upon reaching shore, they can rise up to the astonishing height of a six-story building.
One tsunami, generated off the Aleutian islands in Alaska, had a wavelength of 732 km and traveled a distance of 3650 km in 4.59 hours.
(a) What was the speed (in m/s) of the wave? For reference, the speed of a 747 jetliner is about 250 m/s. Find the wave's:
(b) frequency and
(c) period

Answer 1

To develop this problem it is necessary to apply the concepts related to the kinematic equations of motion. And from the speed found the relationships between wavelength, frequency and last of the period (which is inversely proportional to the frequency)

PART A) We know that the velocity of a body or a wave is equivalent to the distance traveled over a time interval. So,

$V = \frac{x}{t}$

Where

x = Distance

t = time

$V = \frac{3650*10^{3}}{4.59h(\frac{3600s}{1h})}$

$V = 215.44m/s$

PART B) The frequency would then be defined as

$f = \frac{V}{\lambda}$

Where

$\lambda = Wavelength$

$f = \frac{215.44}{732*10^{3}}$

$f = 2.943*10^{-4}Hz$

PART C) Finally the period is defined as

$T = \frac{1}{f}$

$T = \frac{1}{2.943*10^{-4}}$

$T = \frac{1}{2.943*10^{-4}}$

$T = 3397.89s$