Question

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?

Answer 1

28.5714285714 s

6363.64 m

0.0513409510088 m

Step-by-step explanation:

Speed = 7 km/s

f = Frequency = 1.1 Hz

Distance = 200 km

Time is given by

`t=(Distance)/(Speed)`

`t=(200)/(7)\\\Rightarrow t=28.5714285714\ s`

The time elapsed is 28.5714285714 s

Earthquakes are longitudinal waves

Wavelength is given by

`\lambda=(v)/(f)\\\Rightarrow \lambda=(7000)/(1.1)\\\Rightarrow \lambda=6363.64\ m`

The wavelength is 6363.64 m

Horizontal displacement is given by

`A_m=2\pi f^2A\\\Rightarrow 0.25g=(2\pi f)^2A\\\Rightarrow A=(0.25g)/((2\pi f)^2)\\\Rightarrow A=(0.25* 9.81)/((2\pi 1.1)^2)\\\Rightarrow A=0.0513409510088\ m`

The maximum horizontal displacement is 0.0513409510088 m