Geophysicists investigated the seismic wave attenuation properties of synthetic mantle roc… — ACT

Geophysicists investigated the seismic wave attenuation properties of synthetic mantle rock (peridotite) under simulated upper mantle conditions.

In Study 1, five cylindrical peridotite samples with average mineral grain sizes ranging from $15\text{ }\mu\text{m}$ to $250\text{ }\mu\text{m}$ were tested at a constant confining pressure of $3.0\text{ GPa}$ and a fixed temperature of $1,200^\circ\text{C}$ . A torsional oscillation at a frequency of $1.0\text{ Hz}$ was applied to each sample, and the resulting shear wave attenuation factor ( $Q^{-1}$ ) was recorded.

In Study 2, peridotite samples with a fixed average grain size of $50\text{ }\mu\text{m}$ were held at $1,200^\circ\text{C}$ while the confining pressure was varied from $1.0\text{ GPa}$ to $5.0\text{ GPa}$ to measure $Q^{-1}$ .

In Study 3, peridotite samples with a fixed grain size of $50\text{ }\mu\text{m}$ under a constant confining pressure of $3.0\text{ GPa}$ were tested across temperatures from $1,000^\circ\text{C}$ to $1,400^\circ\text{C}$ to measure $Q^{-1}$ .

Based on the experimental procedures described, which of the following correctly identifies the independent variable, dependent variable, and one controlled variable for Study 1, respectively?

Grain size of the peridotite sample; shear wave attenuation factor ( $Q^{-1}$ ); confining pressureAnswer
B
Shear wave attenuation factor ( $Q^{-1}$ ); grain size of the peridotite sample; temperature
C
Confining pressure; shear wave attenuation factor ( $Q^{-1}$ ); grain size of the peridotite sample
D
Grain size of the peridotite sample; temperature; shear wave attenuation factor ( $Q^{-1}$ )

Answer

The independent variable is the grain size of the peridotite sample, the dependent variable is the shear wave attenuation factor (

Q^{-1}

), and a controlled variable is the confining pressure.

In Study 1, researchers explicitly altered the peridotite sample grain size from

15\text{ }\mu\text{m}

250\text{ }\mu\text{m}

(independent variable) and measured the corresponding shear wave attenuation factor

Q^{-1}

(dependent variable), while maintaining constant conditions of

3.0\text{ GPa}

confining pressure and

1,200^\circ\text{C}

temperature (controlled variables).

Step-by-Step Solution

Identify the factor intentionally altered across trials in Study 1 (the independent variable).

The text states that five samples with average grain sizes ranging from

15\text{ }\mu\text{m}

250\text{ }\mu\text{m}

were tested, making grain size the independent variable.

The independent variable is the condition intentionally varied by the experimenter.

Identify the response parameter measured as a result of changing the independent variable (the dependent variable).

The text states that the resulting shear wave attenuation factor (

Q^{-1}

) was recorded for each sample, making

Q^{-1}

the dependent variable.

The dependent variable is the quantitative measurement collected to evaluate the effect of changing the independent variable.

Identify parameters kept identical across all trials in Study 1 (the controlled variables).

Both the confining pressure (

3.0\text{ GPa}

) and temperature (

1,200^\circ\text{C}

) were kept fixed during Study 1.

Controlled variables must be held constant so that any observed change in the dependent variable can be attributed solely to the independent variable.

Key Concept

Identifying Independent, Dependent, and Controlled Variables

Estimated Time:1m 30s

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