Identifying Independent, Dependent, and Controlled Variables

An acoustic engineer conducts an investigation to measure how changing the thickness of fiberglass insulation panels affects the sound intensity level (in decibels) transmitted through a drywall frame assembly. During all test runs, the sound source frequency is held constant at $1,000\text{ Hz}$, the room temperature is maintained at $22^\circ\text{C}$, and the dimensions of the drywall test frame remain identical. Match each experimental element from the study to its correct variable classification.

Oceanographers conducted an investigation to determine how variations in seawater salinity affect the vertical settling rates of marine micro-calcite ($CaCO_3$) particles. Synthetic seawater samples were prepared at four salinity levels ($30\ \text{PSU}$, $33\ \text{PSU}$, $35\ \text{PSU}$, and $38\ \text{PSU}$). In each trial, micro-calcite particles of uniform diameter ($50\ \mu\text{m}$) were dropped into a $1\text{-meter}$ vertical settling column maintained at a constant water temperature of $20^\circ\text{C}$. The elapsed transit time required for each particle to sink through the $1\text{-meter}$ distance was recorded to calculate its terminal sinking velocity.

Match each experimental component from the investigation to its correct variable classification.

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?

Researchers conducted two experiments to investigate the enzymatic activity of cellobiase, an enzyme that hydrolyzes cellobiose into glucose.

*Experiment 1*
Reaction mixtures were prepared using a fixed cellobiase concentration of $0.5\ \text{mg/mL}$ and varying initial cellobiose concentrations ($1.0\ \text{mM}$, $2.5\ \text{mM}$, $5.0\ \text{mM}$, and $10.0\ \text{mM}$). All mixtures were incubated at $37^\circ\text{C}$ and $\text{pH}\ 5.0$. The initial rate of glucose production ($v_0$) was measured for each mixture.

*Experiment 2*
Reaction mixtures were prepared using a constant cellobiose concentration of $5.0\ \text{mM}$ and a constant cellobiase concentration of $0.5\ \text{mg/mL}$. The mixtures were incubated at $\text{pH}\ 5.0$ under four different temperatures ($25^\circ\text{C}$, $37^\circ\text{C}$, $50^\circ\text{C}$, and $65^\circ\text{C}$). The initial rate of glucose production ($v_0$) was measured for each mixture.

Based on the descriptions of both experiments, which variable served as the independent variable in Experiment 1 but was maintained as a controlled variable in Experiment 2?

A team of atmospheric chemists investigated the photochemical formation of secondary organic aerosols (SOAs) in a $5\text{ m}^3$ Teflon smog chamber. Across four distinct experimental runs, researchers introduced constant initial concentrations of $\alpha$-pinene ($100\text{ ppb}$) and ozone ($200\text{ ppb}$) into the chamber alongside ammonium sulfate seed aerosols ($15\ \mu\text{g/m}^3$). Chamber temperature was maintained at $298\text{ K}$ and relative humidity at $50\%$. The ultraviolet (UV) light irradiance was set to a different value for each run ($0\text{ W/m}^2$, $25\text{ W/m}^2$, $50\text{ W/m}^2$, or $100\text{ W/m}^2$). After 4 hours of continuous irradiation, the researchers measured the final total SOA mass concentration ($\mu\text{g/m}^3$) produced in the chamber.

Match each experimental component to its correct variable classification.

A student performed an experiment to study the catalytic decomposition of hydrogen peroxide ($H_2O_2$). In 5 separate trials, the student added $5\text{ mL}$ of a ferric nitrate ($Fe(NO_3)_3$) solution of varying concentrations ($0.1\text{ M}$, $0.2\text{ M}$, $0.3\text{ M}$, $0.4\text{ M}$, and $0.5\text{ M}$) to $50\text{ mL}$ of $3\%\text{ }H_2O_2$ solution in a sealed reaction flask connected to a gas syringe. The initial temperature of all solutions was maintained at $22^\circ\text{C}$. For each trial, the volume of oxygen gas ($O_2$) produced in the first $30\text{ seconds}$ was recorded to determine the initial reaction rate.

Based on the experimental procedure described, which of the following was the independent variable in the student's experiment?

Aerospace engineers conducted a series of wind tunnel trials to evaluate passive boundary layer control on a swept-wing model using micro-vortex generators (VGs). In Experiment 1, the engineers intentionally varied the VG orientation angle relative to the freestream flow ($\theta$) across five trials while maintaining a constant freestream velocity ($v = 45\text{ m/s}$), wing angle of attack ($\alpha = 12^\circ$), and ambient temperature ($T = 20^\circ\text{C}$). For each trial, they recorded the normalized chordwise position of boundary layer separation ($x_s/c$). Their data are shown in the table below:

Based on Experiment 1, which of the following correctly identifies the independent variable, the dependent variable, and one controlled variable?

An environmental science team investigated the effects of soil moisture on soil microbial respiration rates. In five experimental plots, they adjusted the soil volumetric water content to values ranging from $10\%$ to $50\%$. Throughout all trials, they kept the soil temperature constant at $22^\circ\text{C}$ and maintained a uniform soil bulk density. At the end of 48 hours, they measured the total carbon dioxide ($CO_2$) efflux from each plot.

Match each experimental component listed on the left with its correct variable classification on the right.

A team of biomechanical engineers investigated how stride frequency influences peak knee joint contact force during treadmill running. Ten distance runners completed four trials on an instrumented treadmill at a constant running velocity of $4.0\text{ m/s}$ while wearing identical running shoes. Across trials, stride frequency was set to $150$, $160$, $170$, or $180\text{ steps/min}$ using a rhythmic auditory metronome. Sensors in the treadmill measured the peak knee joint contact force in body weights ($\text{BW}$) during each stance phase. Which of the following identifies the dependent variable in this experiment?

Biomechanical engineers investigated how the initial knee flexion angle affects the peak vertical ground reaction force generated by athletes during a countermovement jump on a stationary force plate. In the experiment, athletes performed jumps starting from pre-determined knee flexion angles (30°, 45°, 60°, and 75°), while force plate sensors continuously recorded the maximum force exerted against the platform during takeoff. All trials were conducted using the same athlete cohort wearing identical athletic footwear under standardized indoor temperature and humidity conditions. Based on this experimental design, match each experimental component to its corresponding variable classification.

A marine biologist conducted an experiment to evaluate how water flow velocity affects the peak bioluminescence intensity produced by the dinoflagellate *Pyrocystis fusiformis*. In four separate experimental trials, cell cultures were exposed to flow velocities of $0.1\text{ m/s}$, $0.5\text{ m/s}$, $1.0\text{ m/s}$, and $2.0\text{ m/s}$. In each trial, the cell density ($1{}000\text{ cells/mL}$), water temperature ($20^\circ\text{C}$), and ambient light intensity ($0\text{ lux}$) were kept constant.

Match each experimental variable category on the left with its corresponding component from the experiment on the right.

A marine geochemist conducted an experiment to evaluate the effect of ocean depth on the dissolution rate of calcium carbonate ($\text{CaCO}_3$). Four sealed pressure vessels were filled with seawater kept at a constant temperature of $2^\circ\text{C}$ and a fixed salinity of $35\text{ psu}$. The hydrostatic pressure in each vessel was set to a different specific level: $100\text{ atm}$, $200\text{ atm}$, $300\text{ atm}$, or $400\text{ atm}$. A synthetic calcite pellet with an initial mass of $5.00\text{ g}$ was placed in each vessel. After $48\text{ hours}$, the pellet was removed and weighed to determine the total mass of dissolved $\text{CaCO}_3$ (in milligrams). Which of the following correctly identifies the independent variable and one of the controlled variables in this experiment?

A team of atmospheric chemists investigated photochemical smog formation by measuring ozone ($O_3$) production in a sealed $10\text{ m}^3$ environmental chamber. Across five experimental trials, the researchers systematically varied the ultraviolet (UV) light irradiance level ($20$, $40$, $60$, $80$, and $100\text{ W/m}^2$). In all trials, chamber temperature ($25^\circ\text{C}$), relative humidity ($50\%$), and initial concentrations of nitrogen dioxide ($NO_2$, $0.5\text{ ppm}$) and volatile organic compounds ($VOCs$, $2.0\text{ ppm}$) were held constant. The rate of $O_3$ concentration accumulation was recorded over a 60-minute period.

Match each experimental component to its correct variable classification.

A team of environmental microbiologists investigated the enzymatic biodegradation of polyethylene terephthalate (PET) microplastics. In five separate bioreactors, identical $1.0\text{ g}$ PET film samples of uniform thickness ($0.05\text{ mm}$) were incubated in $250\text{ mL}$ of synthetic seawater solution. Each bioreactor was inoculated with a different bacterial strain ($S_1$ through $S_5$) of *Ideonella sakaiensis*. All five bioreactors were kept at a constant temperature of $30^\circ\text{C}$ and continuously stirred at $150\text{ rpm}$. After 14 days, the scientists measured the total mass loss (in $\text{mg}$) of the PET film in each bioreactor to evaluate degradation efficiency.

Based on the described experimental design, which of the following correctly pairs the independent variable with a controlled variable?

A team of materials scientists investigated the damping performance of magnetorheological (MR) fluids for automotive suspension systems. Identical $50\text{ mL}$ MR fluid samples at a constant temperature of $25^\circ\text{C}$ were exposed to four different magnetic field strengths ($0.1\text{ T}$, $0.3\text{ T}$, $0.5\text{ T}$, and $0.7\text{ T}$) while maintaining a constant rheometer shear rate of $100\text{ s}^{-1}$. The apparent yield stress of the fluid was measured for each trial.

Match each experimental factor on the left with its correct variable classification on the right.

A team of aerosol scientists investigated the drying kinetics of levitated liquid microdroplets in an acoustic levitation chamber. In four separate trials, the relative humidity inside the chamber was adjusted to $10\%$, $30\%$, $50\%$, or $70\%$. In all trials, the acoustic transducer frequency was maintained at $40\text{ kHz}$, the ambient temperature was held constant at $22^\circ\text{C}$, and each droplet had an initial volume of $5.0\text{ }\mu\text{L}$. The researchers measured the rate of droplet volume reduction over time.

Match each experimental component on the left with its corresponding variable role on the right.

A team of biochemists investigated the catalytic activity of the enzyme $\beta$-glucosidase by measuring the rate of cellobiose hydrolysis across five different incubation temperatures ($20^\circ\text{C}$, $30^\circ\text{C}$, $40^\circ\text{C}$, $50^\circ\text{C}$, and $60^\circ\text{C}$). In each trial, the buffer solution pH ($6.0$), cellobiose concentration ($10\text{ mM}$), and total enzyme volume ($0.5\text{ mL}$) were held constant. The rate of glucose production ($\mu\text{mol/min}$) was recorded after a 10-minute reaction period.

Which of the following correctly identifies the independent variable and the dependent variable in this experiment?

A group of materials engineers evaluated the power conversion efficiency of perovskite solar cells fabricated with different layer thicknesses of a titanium dioxide ($\text{TiO}_2$) electron-transport layer ($50\text{ nm}$, $100\text{ nm}$, $150\text{ nm}$, and $200\text{ nm}$). All solar cell samples were constructed using identical perovskite absorber layers, tested under a constant simulated solar light intensity of $1,000\text{ W/m}^2$, and maintained at a temperature of $25^\circ\text{C}$. Which of the following correctly identifies the independent variable and the dependent variable in this experiment?

Researchers investigated the hydrothermal growth of zinc oxide ($\text{ZnO}$) nanorods for use in piezoelectric nanogenerators. In five separate experimental trials, the reaction vessel temperature was set to $90^\circ\text{C}$, $100^\circ\text{C}$, $110^\circ\text{C}$, $120^\circ\text{C}$, and $130^\circ\text{C}$, respectively. In all trials, the zinc nitrate precursor concentration was maintained at $0.05\text{ M}$, the reaction duration was held at $4\text{ hours}$, and the autoclave fill volume was kept at $100\text{ mL}$. After each trial, the average aspect ratio (length-to-diameter ratio) of the synthesized nanorods was determined using scanning electron microscopy. Match each experimental component to its correct variable classification.

An environmental scientist investigated the rate of nitrate leaching from agricultural soil amended with varying concentrations of biochar. Six identical soil columns were prepared, each containing 5 kg of topsoil. Biochar was added to the columns at concentrations of 0%, 2%, 4%, 6%, 8%, and 10% by mass. All columns were maintained at 22°C and received 50 mL of synthetic rainwater every 24 hours. The concentration of nitrate ($NO_3^-$) in the leachate collected from the bottom of each column was measured daily for 30 days.

In this investigation, which of the following represents the independent variable?