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In 2003, an earthquake in Japan generated 1.1 Hz waves that traveled outward at 7.0 km/s. 200 km to the west, seismic instruments recorded a maximum acceleration of 0.25g along the east-west axis.
a. How much time elapsed between the earthquake and the first detection of the waves?
b. Was this a transverse or a longitudinal wave?
c. What was the wavelength?
d. What was the maximum horizontal displacement of the ground as the wave passed?

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boffeemadrid

Answer:

28.5714285714 s

6363.64 m

0.0513409510088 m

Explanation:

Speed = 7 km/s

f = Frequency = 1.1 Hz

Distance = 200 km

Time is given by

[tex]t=\dfrac{Distance}{Speed}[/tex]

[tex]t=\dfrac{200}{7}\\\Rightarrow t=28.5714285714\ s[/tex]

The time elapsed is 28.5714285714 s

Earthquakes are longitudinal waves

Wavelength is given by

[tex]\lambda=\dfrac{v}{f}\\\Rightarrow \lambda=\dfrac{7000}{1.1}\\\Rightarrow \lambda=6363.64\ m[/tex]

The wavelength is 6363.64 m

Horizontal displacement is given by

[tex]A_m=2\pi f^2A\\\Rightarrow 0.25g=(2\pi f)^2A\\\Rightarrow A=\dfrac{0.25g}{(2\pi f)^2}\\\Rightarrow A=\dfrac{0.25\times 9.81}{(2\pi 1.1)^2}\\\Rightarrow A=0.0513409510088\ m[/tex]

The maximum horizontal displacement is 0.0513409510088 m

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