In 2003, an earthquake in Japan generated 1.1 Hz waves that...

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?

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?

Key Concepts

Sinusoidal Motion and Maximum Displacement

In oscillatory systems, particularly those that can be modeled by simple harmonic motion, acceleration, displacement, and angular frequency are interrelated. The concept involves using the maximum acceleration and the angular frequency (related to the wave frequency) to calculate the maximum displacement or amplitude experienced during the wave’s passage.

Relationship Between Frequency, Wavelength, and Speed

This core wave principle, expressed by the equation wavelength equals speed divided by frequency, connects these three key parameters. It is essential for analyzing wave phenomena and calculating one property when the other two are known, regardless of the wave's nature.

Types of Seismic Waves

This concept explains the difference between transverse and longitudinal waves. Knowing which type of wave is detected depends on the direction of particle motion relative to the direction of wave propagation, which is critical in interpreting seismic data and understanding the behavior of Earth’s interior during an earthquake.

Wave Speed and Travel Time

This concept involves understanding how waves travel through a medium at a constant speed and how the time it takes to cover a certain distance is calculated by dividing the distance by the wave speed. It is fundamental in determining the delay between the origin of a disturbance and its detection at a remote location.

Transcript

00:01 In this question, there's an earthquake with frequency 1 .1.

00:05 Also, it generates, during the earthquake, it generates 1 .1 hertz waves.

00:10 It travels at the speed of 7 kilometers per second.

00:14 And then there's a point, 300 kilometers to the west.

00:22 So just take it to be to the west.

00:24 Yeah, it should be right now on the diagrams to the east, but the idea is the same.

00:33 Then there's a seismic vibration is east west as along the east west direction and then the maximum acceleration is 0 .25 a quarter of the acceleration due to gravity.

00:47 Okay.

00:48 So there are four parts in this question.

00:52 In part a, how much time, how much time it takes for the for the wave for the waves to be detected from the earthquake.

01:04 So the time, delta t is d over v.

01:11 So 200 divided by 7.

01:14 So you have 29 seconds.

01:21 Then part b was the direction of, what kind of wave is that? it's a longitude and a wave.

01:32 Because the vibration is along east -west.

01:42 Okay, the traveling direction is also along east -west.

01:45 Okay.

01:49 The wavelength is v over f, so 7 ,000 meters per second, divided by 1 .1 hertz...