Earthquakes and Resonance: Teacher's Notes

Focus question

How does ground motion caused by an earthquake affect the stability of buildings of different heights?

Tools and materials

Two square pieces of wood measuring about 10 cm (4 in) across
30-cm-long (12-in) thin metal strip —we used a thin metal ruler
Small C-clamp
Lump of modeling clay, approximately half the size of a fist, about 100 g (3.5 oz)
Ruler or meter stick
Hammer and nails, or screwdriver and screws, for wood
Stopwatch or timer
Safety goggles

Main ideas and background information

Numerous factors influence the stability of buildings during earthquakes. Some of the more important factors include the magnitude and duration of the earthquake, size and number of aftershocks, underlying geologic material, and age, design, and height of buildings.
Every structure has a natural frequency at which it vibrates after being disturbed by an impact or an initial shaking.
If a structure is subjected to continued vibration by some outside influence, such as an earthquake, the amplitude of the vibration depends very strongly on the correlation between the frequency of the imposed oscillation and the natural frequency of the structure. If the two frequencies are close to being the same, the resulting vibration is at its maximum. This condition is called resonance.
If the frequency of the imposed oscillation is much smaller or much larger than the natural frequency, then the amplitude of the resulting vibration is much smaller.
During some earthquakes, the frequency of passing waves is close to being the same as the natural frequency of buildings. This can cause some buildings to shake and collapse (those for which there is resonance) while adjacent buildings are not damaged.
The frequency range of seismic waves is large, from as high as the audible range (greater than 20 hertz (Hz), or a period of 0.05 sec) to as low as the frequencies of the free oscillations of the whole Earth, with the greatest period being 54 minutes. Attenuation of the waves in rock imposes high-frequency limits, and in small to moderate earthquakes the dominant frequencies extend in surface waves from about 1.0 to 0.1 Hz. (Source: Britannica Online)
A frequency of 1 Hz means that 1 wave per second passes; a frequency of 0.1 Hz indicates that 10 waves pass every second. The formula to find the frequency or period of time is: f = 1/T and T = 1/f (f = frequency; T = time)
For small to moderate earthquakes, the surface wave oscillation period ranges typically from 1 to 10 seconds. This corresponds roughly to the oscillation periods of this activity. According to the table at http://mceer.buffalo.edu/infoservice/reference_services/EQaffectBuilding.asp, a 10-story building could be affected by a surface wave with a period of one second.

Procedural tips

In step 1, students are asked to attach two pieces of wood together with nails or wood screws to make an L-shaped wooden base. You may want to prepare the wooden blocks ahead of time to allow students more in-class time for focusing on the activity. Also in step 1, the clamp should be placed at the top of the wooden block to ensure accuracy.
In step 4, students are asked to steady the wooden base on a table. If you have extra C-clamps, you may want to ask students to clamp the L-shaped wooden block to the tabletop (this clamp is not shown in the photo).
In steps 4 and 5, students measure and calculate the period of the oscillation of the clay ball. Note that an oscillation can be described by its period (how long it takes for one complete oscillation) or its frequency (how many oscillations take place per unit of time). The period and the frequency are the inverse of each other. The oscillation can be described equally well by either the period or the frequency.
In step 7, the height is the independent variable and is plotted along the horizontal axis, while the oscillation period is the dependent variable, plotted along the vertical axis.

Discussion

1. How can studying the effects of earthquakes help engineers improve the safety of buildings and other structures?

By studying how buildings and other structures respond to earthquakes, engineers can recommend suitable building materials and construction techniques. They can also evaluate older structures and find ways to reinforce them so that they are able to withstand an earthquake. Finally, engineers can develop building codes to help prevent structural collapse during an earthquake.

2. Suppose you were a builder who was planning a housing development where earthquakes are likely. What types of land would you avoid for your development? Where would you suggest it would be safe to build?

Earthquake risk is greater on filled land with soft ground than on solid bedrock. This is because earthquake wave energy is transmitted more rapidly, with lesser wave amplitude, in solid bedrock but more slowly, with greater wave amplitude, in loose earth materials. For this reason, a builder would want to avoid building on loose, sandy soil. He or she would suggest constructing buildings on solid rock instead.

Assessment

Describe, in your own words or pictures, how the ground motion caused by an earthquake affects the stability of buildings of different heights.

Extensions and further investigations

Visit other SEED resources and animations on earthquakes:
Ask students to research the effects of resonance on the 1985 earthquake in Mexico City. This earthquake caused severe damage or destruction to about 500 buildings. Ground vibrations were amplified by the vibrational properties of tall buildings. This caused 10- to 14-story buildings to sway even more (at a period of one to two seconds) and resulted in damage to many structures. Nearby shorter and taller buildings were not damaged.
Have students build a “shake table” to study the effects of earthquakes on structures. First, have them staple a plastic coffee can lid to a wooden block, with the lip facing the block. Then, have the students put marbles under the lid. Next, ask them to place the marbles, plastic lid, and block of wood in a cardboard box to contain the amount of movement. Have them design structures and place them on the wooden block. Then they should simulate an earthquake by moving the box in a back-and-forth motion and side-to-side motion. Ask them to vary the frequency of the shaking as well. Give them a chance to redesign their structures to better withstand the movement of the block.
Have groups of students design structures that are earthquake resistant. Give them supplies to build the structures and then have a day in class to test their structures and make revisions to the designs. Have the groups present their buildings to their classmates and allow time for the students to question one another on the design and testing process they used.

Glossary / vocabulary

earthquake: an abrupt shaking of the ground occurring when forces inside the Earth's crust cause a sudden movement in the rock. Earthquakes can be the result of a sudden release of stress along a fracture in the Earth's crust, volcanic activity, or human activity such as an explosion. Most earthquakes occur in the outer 720 km (445 mi) of the crust, where rocks under stress are likely to break rather than bend or flow.
epicenter: the exact location on the Earth's surface directly above the place where the earthquake is focused. The epicenter is the point at which the crust shakes and sends out shock waves.
fault: a fracture or zone of fractures leading to displacement of rock layers in the Earth's crust. Pressure builds up on either side of the fault until the rock snaps and movement takes place. Most faults are underground, but some are visible at the surface.
natural oscillation period: the period of one complete back-and-forth movement of a body or system.

oscillation: the complete cycle of a moving object traveling from one end limit to the other and back.
period: the time needed for the completion of a cycle or a single action.
resonance: a condition in which a vibration affecting an object has about the same period as the natural vibration period of the object.
seismic: pertaining to shock waves of energy that travel through the earth as the result of an earthquake or explosion. Seismic waves are measured by a seismograph and studied by seismologists.

Earthquakes and Man-Made Shocks: /sciencearticle/earthquakes-and-man-made-shocks

Earthquake Epicenters from 1999 to 2003: http://www.planetseed.com/files/uploadedfiles/Science/Laboratory/Earth_Science/
Earthquake_Epicenters/en/index.htm

SEED Science Laboratory Activity: Personal Seismographs: /laboratory/experiment-personal-seismographs

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