Physical Science

229 questions

All types229 Multiple choice117 Numeric30 Matching54 Ordering17 Fill in the blank11

An automotive cooling system uses a water pump to continuously circulate liquid coolant through channels in the engine block, carrying thermal energy away from hot metal components to the radiator. Which heat transfer mechanism is primarily responsible for transporting thermal energy throughout the moving liquid?

Conduction

Convection

Radiation

Sublimation

Show answer & explanation

Answer: Convection

Answer

Convection

Convection is the transfer of thermal energy by the bulk movement and circulation of a fluid (either liquid or gas). When the water pump circulates liquid coolant through the engine and out to the radiator, the flowing liquid physically carries the thermal energy with it.

Step-by-Step Solution

Identify the physical medium and method of transport in the scenario.

Thermal energy is carried away by the physical, macroscopic circulation of a liquid fluid (coolant).

Identifying how the matter carrying the heat moves determines the fundamental heat transfer mechanism.

Classify the transport mechanism among standard thermodynamic processes.

Heat transfer via the bulk motion and circulation of fluids is classified as convection.

Conduction occurs via stationary molecular collisions, radiation occurs via electromagnetic waves, and convection occurs through fluid movement.

Key Concept

Convection is the transfer of thermal energy through the bulk movement and circulation of fluids (liquids and gases).

Estimated Time:1m 0s

Question 182Question →

Matter exhibits distinct measurable characteristics that determine how it behaves under mechanical forces, thermal energy, and phase equilibria. Match each physical property of matter on the left with its corresponding scientific description on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Hardness matches with the resistance of a solid substance to surface scratching, localized plastic deformation, or mechanical abrasion; Specific Heat Capacity matches with the quantity of thermal energy required to raise the temperature of one unit mass of a substance by one degree Celsius; Elasticity matches with the capacity of a deformed solid material to return to its original shape and size once applied deforming forces are removed; Vapor Pressure matches with the force per unit area exerted by an evaporated gas in thermodynamic equilibrium with its condensed liquid or solid phase at a given temperature.

Each physical property is correctly paired with its foundational scientific definition: Hardness pertains to surface scratch resistance, Specific Heat Capacity defines the heat required to change temperature per unit mass, Elasticity governs reversible mechanical deformation, and Vapor Pressure quantifies phase equilibrium pressure in a closed container.

Step-by-Step Solution

Analyze the definition of Hardness

Hardness corresponds to resistance to scratching, penetration, or abrasion on a solid surface.

Hardness is evaluated on scales like the Mohs hardness scale by testing which substance can scratch another.

Analyze the definition of Specific Heat Capacity

Specific Heat Capacity corresponds to the amount of heat energy per unit mass needed to raise temperature by

1^\circ\text{C}

Thermal properties govern how substances absorb and transfer heat without undergoing chemical decomposition.

Analyze the definition of Elasticity

Elasticity corresponds to the ability of a material to rebound to its original shape after deforming forces are removed.

Mechanical elasticity is characterized by Hooke's Law within the proportional limit of the material.

Analyze the definition of Vapor Pressure

Vapor Pressure corresponds to the equilibrium pressure created by gas particles above a liquid or solid phase in a closed system.

Volatile substances with weak intermolecular forces display higher vapor pressures at a given temperature.

Key Concept

Physical properties of matter describe observable or measurable characteristics of substances that do not alter their underlying chemical composition.

Estimated Time:1m 0s

Question 183Question →

Household refrigerators transfer thermal energy from a cooler interior to a warmer room through a continuous closed-loop thermodynamic cycle. Starting with the stage where low-pressure refrigerant vapor enters the compressor, what is the correct sequential order of these stages in the refrigeration cycle?

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The compressor pressurizes and heats the vapor, followed by the condenser releasing heat to turn the vapor into liquid, then the expansion valve lowering the pressure and temperature, and finally the evaporator absorbing heat from the interior compartment as the liquid vaporizes.

The correct sequence follows the standard vapor-compression cycle: compression raises the temperature and pressure of the vapor, condensation expels heat to the environment to form a liquid, expansion drops the pressure and chills the liquid, and evaporation absorbs heat from the cold space to turn the fluid back into vapor.

Step-by-Step Solution

Identify the initial compression stage.

The compressor does mechanical work to compress the low-pressure vapor into a high-pressure, high-temperature gas.

Raising the pressure and temperature ensures the refrigerant is hotter than the ambient room air.

Follow the refrigerant into the exterior condenser coils.

Heat transfers from the hot refrigerant to the surrounding room, causing the refrigerant to condense into a high-pressure liquid.

Thermal energy naturally transfers from the hotter gas to the cooler room air.

Track the fluid through the expansion valve.

The high-pressure liquid passes through an expansion valve, where pressure suddenly drops, causing a steep decline in temperature.

Rapid fluid expansion and pressure reduction dramatically lower the boiling point and temperature of the refrigerant.

Analyze heat absorption in the interior evaporator coils.

The cold refrigerant absorbs thermal energy from the refrigerator interior and boils into a low-pressure gas.

Because the refrigerant is now colder than the interior air, heat transfers into the fluid, cooling the compartment.

Key Concept

Thermodynamic refrigeration cycle, phase transitions, and forced heat transfer

Estimated Time:1m 0s

Question 184Question →

In classical mechanics, specific physical quantities and principles describe how bodies move and respond to applied forces. Match each mechanical concept on the left with its correct physical definition on the right.

Click a left item, then click its matching right item

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Answer

Inertia matches the natural tendency of an object to resist any change in its state of rest or motion; Acceleration matches the rate at which an object changes its velocity with respect to time; Linear Momentum matches the product of an object's mass and its velocity; Centripetal Force matches a net inward force directed toward the center of curvature that maintains circular motion.

Inertia is the tendency of matter to resist changes in motion; acceleration is the time derivative/rate of change of velocity; linear momentum represents mass in motion (

p = mv

); and centripetal force is the inward radial force that continuously changes the direction of an object in circular motion.

Step-by-Step Solution

Identify the definition of Inertia

Inertia corresponds to the property of mass resisting alterations in its state of rest or uniform motion.

According to Newton's First Law of Motion, inertia is an intrinsic resistance to acceleration.

Identify the definition of Acceleration

Acceleration corresponds to the rate of change of velocity over time (

a = \frac{\Delta v}{\Delta t}

Acceleration describes how rapidly speed or direction changes over a given time interval.

Identify the definition of Linear Momentum

Linear Momentum corresponds to mass multiplied by velocity (

p = mv

Momentum quantifies the motion of a mass and is conserved in isolated systems.

Identify the definition of Centripetal Force

Centripetal Force corresponds to the center-seeking net force in circular motion (

F_c = \frac{mv^2}{r}

An inward radial force is required to continuously deflect an object's velocity vector along a curve.

Key Concept

Fundamental definitions and kinematic relationships governing linear and circular mechanics.

Estimated Time:1m 0s

Question 185Question →

An astronaut collects a rock sample on the Moon and measures its physical properties before transporting it back to Earth. If the gravitational pull on the surface of the Moon is approximately one-sixth of Earth's gravity, how do the mass and weight of the rock sample on the Moon compare to its mass and weight on Earth?

The sample has the same weight on the Moon as on Earth, but its mass is one-sixth of its Earth mass.

The sample has the same mass on the Moon as on Earth, but its weight is one-sixth of its Earth weight.

Both the mass and the weight of the sample are one-sixth of their respective values on Earth.

Both the mass and the weight of the sample remain identical in both locations.

Show answer & explanation

Answer: The sample has the same mass on the Moon as on Earth, but its weight is one-sixth of its Earth weight.

Answer

The sample has the same mass on the Moon as on Earth, but its weight is one-sixth of its Earth weight.

Mass is an intrinsic property of matter that quantifies how much substance an object contains, meaning it remains identical regardless of where the object is located in the universe. In contrast, weight is the gravitational force acting on that mass, expressed as

W = mg

. Because gravity on the surface of the Moon is approximately one-sixth that of Earth, the rock sample weighs one-sixth as much on the Moon while retaining its full mass.

Step-by-Step Solution

Define mass in the context of physical properties of matter.

Mass represents the fundamental quantity of matter contained within an object and is invariant regardless of location or external forces.

Mass does not depend on gravitational acceleration.

Define weight and determine how local gravity affects it.

Weight is the force exerted on an object by gravity, given by the relationship

W = mg

. Since lunar gravity is

\frac{1}{6}

of Earth's gravity, the weight of the rock on the Moon is

\frac{1}{6}

of its weight on Earth.

Weight is a force that varies directly with local gravitational field strength.

Synthesize the behavior of both properties.

The rock maintains an identical mass across both environments, while its weight on the Moon is one-sixth of its weight on Earth.

Combining an invariant scalar mass with a variable gravitational force yields the correct comparison.

Key Concept

Mass versus Weight in Gravitational Fields

Question 186Question →

In an occupational safety training session, workers are informed that exposure to steam at $100^\circ\text{C}$ causes significantly more severe burns than exposure to liquid water at $100^\circ\text{C}$ . Which thermodynamic factor directly accounts for this difference?

A higher average molecular kinetic energy in steam molecules than in liquid water molecules

The substantial release of latent heat as steam condenses into liquid upon contact with the skin

A faster transfer of thermal energy driven exclusively by electromagnetic radiation

A rapid exothermic chemical reaction occurring between water vapor and skin tissue

Show answer & explanation

Answer: The substantial release of latent heat as steam condenses into liquid upon contact with the skin

Answer

The substantial release of latent heat as steam condenses into liquid upon contact with the skin

When steam at

100^\circ\text{C}

comes in contact with cooler skin, it undergoes a phase change into liquid water at

100^\circ\text{C}

. During this condensation process, it releases its latent heat of vaporization (approximately

2{}260\text{ J/g}

) directly onto the skin before the resulting water even begins to cool. By contrast, boiling liquid water at

100^\circ\text{C}

only releases sensible heat as its temperature drops (

q = mc\Delta T

), yielding roughly

264\text{ J/g}

when cooling to body temperature. The additional latent heat released by steam transfers nearly ten times as much total energy to the skin, causing far more destructive burns.

Step-by-Step Solution

Analyze the thermal energy transferred by liquid water at

100^\circ\text{C}

Liquid water at

100^\circ\text{C}

transfers sensible heat only as it cools down to body temperature (

37^\circ\text{C}

), which equals approximately

264\text{ J/g}

Liquid water does not undergo a phase change when contacting skin.

Analyze the thermal energy transferred by steam at

100^\circ\text{C}

Steam at

100^\circ\text{C}

must first condense into liquid water at

100^\circ\text{C}

, releasing approximately

2{}260\text{ J/g}

of latent heat of condensation, and then release another

264\text{ J/g}

of sensible heat as the liquid cools.

Phase change from vapor to liquid requires the release of latent heat of vaporization.

Compare total energy delivered to the tissue

Steam delivers nearly ten times more thermal energy per gram than boiling water at the same temperature.

The large latent heat of condensation accounts directly for the greater severity of the burn.

Key Concept

Latent heat of phase change and heat transfer during condensation

Estimated Time:1m 0s

Question 187Question →

A lunar rover has a mass of $90\text{ kg}$ on Earth. While operating on the lunar surface, where gravitational acceleration is approximately $1.6\text{ m/s}^2$ , its electric drive system generates a constant net forward force of $270\text{ N}$ . What is the forward acceleration of the rover?

18.0\text{ m/s}^2

3.0\text{ m/s}^2

4.6\text{ m/s}^2

0.3\text{ m/s}^2

Show answer & explanation

Answer: $3.0\text{ m/s}^2$

Answer

The forward acceleration of the rover is

3.0\text{ m/s}^2

According to Newton's second law of motion, acceleration is directly proportional to the net force applied and inversely proportional to the mass (

a = F_{\text{net}} / m

). Because mass is constant regardless of location, the rover's mass on the Moon is still

90\text{ kg}

. Dividing the net force of

270\text{ N}

90\text{ kg}

yields an acceleration of

3.0\text{ m/s}^2

Step-by-Step Solution

Identify the invariant mass of the rover

m = 90\text{ kg}

Mass measures the amount of matter in an object and remains constant regardless of local gravity.

Apply Newton's second law of motion (

F_{\text{net}} = ma

)

a = \frac{F_{\text{net}}}{m} = \frac{270\text{ N}}{90\text{ kg}} = 3.0\text{ m/s}^2

Horizontal acceleration depends solely on the net horizontal force divided by the object's mass.

Key Concept

Newton's Second Law of Motion and Mass Invariance

Estimated Time:1m 0s

Question 188Question →

During a mass spectrometry investigation, researchers identify an isotope of chromium with a mass number of $52$ and an atomic number of $24$ . How many neutrons are contained in the nucleus of this chromium atom?

24

28

52

76

Show answer & explanation

Answer: $28$

Answer

28

neutrons

The mass number (

A = 52

) is the total number of protons and neutrons in the nucleus. The atomic number (

Z = 24

) indicates the number of protons. Subtracting the atomic number from the mass number (

52 - 24 = 28

) gives the total number of neutrons.

Step-by-Step Solution

Identify the given atomic parameters

Mass number (

A

) =

52

; Atomic number (

Z

) =

24

The mass number represents the sum of protons and neutrons, while the atomic number represents the number of protons.

Apply the neutron calculation formula:

\text{Neutrons} = A - Z

\text{Neutrons} = 52 - 24 = 28

Subtracting the number of protons from the total nucleon count isolates the number of neutrons.

Key Concept

Subatomic Particle Relationships in Atomic Structure

Estimated Time:45s

Question 189Question →

A machinist measures the mass of an irregular steel fastener to be $84\text{ g}$ . To determine its volume, the fastener is submerged in a graduated cylinder filled with $50\text{ mL}$ of water, causing the water level to rise to $62\text{ mL}$ . What is the density of the steel fastener in $\text{g/cm}^3$ ?

Show answer & explanation

Answer: 7

Answer

The density of the steel fastener is

7\text{ g/cm}^3

Density is calculated by dividing mass by volume (

\text{Density} = \frac{\text{Mass}}{\text{Volume}}

). The volume of the irregular fastener is found by subtracting the initial water volume from the final water volume (

62\text{ mL} - 50\text{ mL} = 12\text{ cm}^3

). Dividing the mass of

84\text{ g}

by the volume of

12\text{ cm}^3

gives

7\text{ g/cm}^3

Step-by-Step Solution

Determine the volume of the fastener using the water displacement method

Displaced volume =

62\text{ mL} - 50\text{ mL} = 12\text{ mL} = 12\text{ cm}^3

The volume of an irregular submerged solid equals the volume of fluid it displaces, where

1\text{ mL} = 1\text{ cm}^3

Calculate density by dividing mass by displaced volume

\text{Density} = \frac{84\text{ g}}{12\text{ cm}^3} = 7\text{ g/cm}^3

Density is defined as mass per unit volume (

\rho = \frac{m}{V}

Key Concept

Density and Water Displacement

Estimated Time:1m 0s

Question 190Question →

In modern energy-efficient construction, a radiant barrier made of highly reflective aluminum foil is often installed in attics facing an open air gap. Which heat transfer mechanism is this reflective surface primarily designed to reduce?

Conduction through solid structural framing

Radiation emitted across the open air space

Convection generated by circulating attic air currents

Phase changes caused by moisture condensation

Show answer & explanation

Answer: Radiation emitted across the open air space

Answer

Radiation emitted across the open air space

Thermal radiation travels in the form of electromagnetic infrared waves across open spaces. Radiant barriers possess high thermal reflectivity and low emissivity, meaning they reflect the majority of radiant heat emitted by a hot roof deck rather than absorbing and reradiating it into the attic.

Step-by-Step Solution

Identify the physical properties and placement of the material described in the stem.

The material is a shiny, highly reflective foil facing an open air space.

Reflective materials interact directly with electromagnetic waves rather than direct contact or fluid mass movement.

Differentiate between the three fundamental mechanisms of thermal energy transfer.

Thermal conduction requires direct solid contact, convection requires fluid circulation, and thermal radiation travels as electromagnetic waves across empty or gas-filled space.

Reflective surfaces reflect incoming infrared radiation and have very low thermal emissivity, preventing radiative heat transfer across the air space.

Key Concept

Thermal Radiation and Reflective Barriers

Estimated Time:1m 0s

Question 191Question →

A neutral isotope of zinc has a nucleus containing $36$ neutrons and has an overall mass number of $66$ . During a chemical reaction, this atom forms a $\text{Zn}^{2+}$ cation by losing $2$ electrons. Calculate the total number of electrons present in the $\text{Zn}^{2+}$ ion.

Show answer & explanation

Answer: 28

Answer

28 electrons

The mass number (

66

) minus the number of neutrons (

36

) gives an atomic number of

30

, which corresponds to

30

protons. A neutral atom has

30

electrons, and losing

2

electrons to become

\text{Zn}^{2+}

leaves exactly

28

electrons.

Step-by-Step Solution

Calculate the number of protons (atomic number) in the zinc atom

30 protons

The mass number equals the sum of protons and neutrons (

A = Z + N

), so

Z = 66 - 36 = 30

Calculate the remaining electrons in the

\text{Zn}^{2+}

cation

28 electrons

A neutral atom has an equal number of protons and electrons (30). A

+2

charge indicates the loss of 2 electrons (

30 - 2 = 28

Key Concept

Subatomic particle counts in isotopes and monatomic ions

Estimated Time:1m 0s

Question 192Question →

A stable isotope of silicon has $14$ protons and a total mass number of $30$ . How many neutrons are located inside its nucleus?

Show answer & explanation

Answer: 16

Answer

The nucleus contains 16 neutrons.

The number of neutrons in an atom is found by subtracting the atomic number (number of protons) from the mass number. For this silicon isotope with a mass number of

30

and

14

protons, the calculation is

30 - 14 = 16

neutrons.

Step-by-Step Solution

Identify the given nuclear parameters.

Mass number (

A

) =

30

; number of protons / atomic number (

Z

) =

14

The mass number represents the sum of protons and neutrons in the nucleus, while the number of protons defines the atomic number.

Apply the relationship

N = A - Z

to determine the number of neutrons.

N = 30 - 14 = 16

Subtracting the number of protons from the total mass number yields the number of neutrons.

Key Concept

Calculating Subatomic Particles in an Atom

Estimated Time:45s

Question 193Question →

Wave interactions and behaviors produce distinct physical effects in sound and light. Match each wave phenomenon to its corresponding real-world observation.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Doppler effect matches the shift in pitch of a moving siren; Resonance matches the shattering of a glass at its natural frequency; Total internal reflection matches light confinement in fiber optics; Diffraction matches radio waves bending around hills and structures.

Each wave phenomenon maps directly to its underlying principle: relative motion alters perceived pitch via the Doppler effect; matching natural frequencies drives maximum vibrational amplitude via resonance; optical containment in fiber cores relies on total internal reflection; wave propagation around physical obstacles occurs through diffraction.

Step-by-Step Solution

Analyze the effect of source motion on perceived sound pitch.

Compression and expansion of wavefronts due to motion produces the Doppler effect, matching the approaching and receding siren.

Perceived frequency changes result directly from relative velocity between the source and observer.

Identify the behavior where matching frequencies produce maximum vibration amplitude.

Energy transfer at an object's natural frequency defines resonance, matching the shattering crystal glass.

When forcing frequency matches natural frequency, energy accumulates constructively to cause large mechanical stress.

Examine the mechanism allowing light transmission without leakage in fiber optics.

Complete reflection at the core-cladding boundary beyond the critical angle is total internal reflection, matching fiber-optic light pulses.

Light cannot refract out when traveling from high to low refractive index at incident angles exceeding the critical threshold.

Determine how long-wavelength waves navigate physical terrain barriers.

The bending of waves around large structures without a change in medium is diffraction, matching obstructed radio wave reception.

Waves naturally spread into geometric shadow zones behind obstacles comparable to their wavelength.

Key Concept

Wave behaviors and boundary interactions

Estimated Time:1m 15s

Question 194Question →

A communications antenna emits radio waves that travel through uniform atmospheric air. If the transmitter is adjusted to emit radio waves at a higher frequency, how do the speed and wavelength of the transmitted waves change?

The speed increases, and the wavelength remains unchanged.

The speed increases, and the wavelength increases.

The speed remains constant, and the wavelength decreases.

The speed remains constant, and the wavelength increases.

Show answer & explanation

Answer: The speed remains constant, and the wavelength decreases.

Answer

The speed remains constant, and the wavelength decreases.

In a uniform medium such as air, the speed of an electromagnetic wave is constant. According to the wave equation

v = f \lambda

, when the speed

v

is constant, frequency

f

and wavelength

\lambda

are inversely proportional. Therefore, increasing the frequency causes the wavelength to decrease while the speed remains unchanged.

Step-by-Step Solution

Identify the factor that determines wave propagation speed.

The speed of electromagnetic radio waves is constant in a uniform medium (

v = c

in air).

Wave speed is an intrinsic property of the medium through which the wave travels, not the frequency of the source.

Apply the wave equation relating speed, frequency, and wavelength.

v = f \lambda

, which rearranges to

\lambda = \frac{v}{f}

This relationship mathematically couples frequency and wavelength for a given constant speed.

Determine the effect of increasing frequency on wavelength.

As frequency (

f

) increases while speed (

v

) remains fixed, wavelength (

\lambda

) must decrease proportionally.

Frequency and wavelength are inversely proportional when wave speed is held constant.

Key Concept

The speed of a wave is determined by the transmission medium, creating an inverse relationship between frequency and wavelength (

v = f \lambda

Estimated Time:1m 0s

Question 195Question →

Electromagnetic radiation travels through space as oscillating electric and magnetic fields, with each type characterized by its specific frequency, wavelength, and energy. Arrange the following regions of the electromagnetic spectrum in order of increasing photon energy, from the lowest energy to the highest energy.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from lowest to highest photon energy is Radio waves, Microwaves, Visible light, Ultraviolet radiation, and X-rays.

Photon energy is governed by the relation

E = hf = \frac{hc}{\lambda}

, where

h

is Planck's constant and

c

is the speed of light. Because energy increases directly with frequency and inversely with wavelength, radiation with the longest wavelengths (radio waves) carries the least energy per photon, followed in ascending order by microwaves, visible light, ultraviolet radiation, and X-rays.

Step-by-Step Solution

Recall the fundamental relationship between wave frequency and photon energy.

Photon energy is directly proportional to frequency as defined by Planck's equation,

E = hf

, and inversely proportional to wavelength,

E = \frac{hc}{\lambda}

Establishing that higher frequency and shorter wavelength correspond directly to higher photon energy.

Identify the positions of the given wave types across the continuous electromagnetic spectrum.

In order of increasing frequency: Radio waves (

< 10^9\text{ Hz}

)

\rightarrow

Microwaves (

10^9 - 10^{12}\text{ Hz}

)

\rightarrow

Visible light (

4 \times 10^{14} - 7.5 \times 10^{14}\text{ Hz}

)

\rightarrow

Ultraviolet radiation (

10^{15} - 10^{16}\text{ Hz}

)

\rightarrow

X-rays (

10^{16} - 10^{19}\text{ Hz}

Classifying each radiation type by its frequency band determines its relative energy.

Sequence the items from the lowest photon energy to the highest photon energy.

Radio waves

\rightarrow

Microwaves

\rightarrow

Visible light

\rightarrow

Ultraviolet radiation

\rightarrow

X-rays.

Arranging the items in ascending order of frequency matches the required ascending order of energy.

Key Concept

Photon energy across the electromagnetic spectrum is directly proportional to wave frequency (

E = hf

) and inversely proportional to wavelength (

E = hc/\lambda

Estimated Time:1m 0s

Question 196Question →

An acoustic engineer tests a noise-reduction device that emits a secondary sound wave exactly half a wavelength ( $180^\circ$ ) out of phase with an incoming noise wave of identical frequency and amplitude. What occurs when these two sound waves overlap in the air?

The waves undergo constructive interference, resulting in a sound wave with twice the original amplitude.

The waves undergo destructive interference, resulting in the cancellation of sound with zero net amplitude.

The waves undergo refraction, resulting in a permanent doubling of the wave's frequency.

The waves undergo dispersion, resulting in the sound separating into different component frequencies.

Show answer & explanation

Answer: The waves undergo destructive interference, resulting in the cancellation of sound with zero net amplitude.

Answer

The waves undergo destructive interference, resulting in the cancellation of sound with zero net amplitude.

When two waves with equal frequency and amplitude meet half a wavelength (

180^\circ

) out of phase, the crests of the first wave precisely coincide with the troughs of the second wave. According to the principle of superposition, their individual displacements subtract from each other, resulting in complete destructive interference and zero resultant amplitude.

Step-by-Step Solution

Analyze the phase relationship of the two sound waves.

The two waves have identical frequency and amplitude but are half a wavelength (

180^\circ

) out of phase.

Determining phase alignment indicates whether wave crests and troughs align constructively or destructively.

Apply the principle of wave superposition to calculate the net displacement.

Every positive peak (crest) of the primary wave perfectly aligns with an equal negative peak (trough) of the secondary wave, summing to zero net displacement (

A - A = 0

The principle of superposition states that overlapping waves combine algebraically at every point in space.

Identify the corresponding wave phenomenon.

Destructive interference.

Complete destructive interference occurs when opposing wave displacements of equal magnitude cancel each other out.

Key Concept

Destructive Wave Interference and Superposition

Estimated Time:1m 0s

Question 197Question →

An atom of bromine has an atomic number of $35$ and a mass number of $81$ . What is the total number of neutrons contained in its nucleus?

35

46

81

116

Show answer & explanation

Answer: $46$

Answer

The nucleus contains

46

neutrons.

The mass number of an atom is the total count of protons and neutrons in the nucleus (

A = \text{protons} + \text{neutrons}

). Given that the atomic number is

35

(protons =

35

) and the mass number is

81

, the number of neutrons is calculated as

81 - 35 = 46

Step-by-Step Solution

Identify the given values from the problem statement.

Atomic number (

Z

) =

35

(which equals the number of protons); Mass number (

A

) =

81

(total nucleons in the nucleus).

The atomic number defines the number of protons, and the mass number represents the sum of protons and neutrons.

Apply the relationship between mass number, protons, and neutrons:

\text{Mass Number } (A) = \text{Protons } (Z) + \text{Neutrons } (N)

N = A - Z

To find the unknown number of neutrons, rearrange the standard subatomic relationship.

Substitute the known integer values into the equation:

N = 81 - 35

N = 46

Subtracting

35

from

81

gives the total number of neutrons in the nucleus.

Key Concept

The mass number (

A

) of an atom equals the sum of its protons (

Z

) and neutrons (

N

). The number of neutrons is found by subtracting the atomic number from the mass number (

N = A - Z

Estimated Time:45s

Question 198Question →

Wave properties describe the spatial and temporal behavior of mechanical and electromagnetic oscillations. Which of the following correctly matches each wave parameter on the left with its standard physical definition on the right?

Click a left item, then click its matching right item

Show answer & explanation

Answer

Wavelength pairs with the spatial distance between two consecutive identical points on adjacent wave cycles; Frequency pairs with the number of complete wave cycles that pass a fixed reference point per second; Amplitude pairs with the maximum displacement of an oscillation from its central equilibrium position; and Wave speed pairs with the rate at which a wave disturbance propagates through a given medium.

Each fundamental wave term corresponds directly to its standard physical definition: wavelength is the distance between consecutive identical points on adjacent cycles; frequency is the number of cycles passing a reference point per second; amplitude is the maximum displacement from equilibrium; and wave speed is the propagation rate of the wave disturbance through a medium.

Step-by-Step Solution

Identify the spatial parameter describing the length of a full cycle

Wavelength (

\lambda

) is the physical distance between consecutive corresponding points, such as crest to crest or compression to compression.

This establishes the spatial periodicity of the wave.

Identify the temporal rate parameter measuring wave oscillations per unit time

Frequency (

f

) is the count of complete wave cycles passing a stationary point per unit time, measured in Hertz (

\text{Hz}

This establishes the temporal oscillation rate of the wave.

Identify the parameter measuring wave height or disturbance magnitude

Amplitude (

A

) is the maximum displacement of the medium or field from its central baseline equilibrium position.

This parameter indicates the energy carried by the wave, relating to loudness in sound and brightness in light.

Identify the propagation rate of the wave disturbance

Wave speed (

v

) is the distance a wave crest travels per unit time through a medium, determined by

v = f \lambda

This connects spatial wavelength and temporal frequency to linear propagation speed.

Key Concept

Fundamental wave parameters: wavelength, frequency, amplitude, and propagation speed

Estimated Time:1m 0s

Question 199Question →

An ion with a $+3$ positive charge has $10$ electrons and a mass number of $27$ . How many neutrons are located inside the nucleus of this ion?

Show answer & explanation

Answer: 14

Answer

14 neutrons

For any atom or ion, the mass number equals the total count of protons and neutrons in the nucleus. Because this ion has a

+3

charge and

10

electrons, it must contain

13

protons (

10 + 3

). Subtracting

13

protons from the mass number of

27

gives exactly

14

neutrons.

Step-by-Step Solution

Calculate the atomic number (number of protons) using the ion's charge and electron count.

The atom has

13

protons.

A positive charge (

+3

) indicates that the atom has lost

3

electrons relative to its proton count. Therefore,

\text{Protons} = \text{Electrons} + \text{Charge} = 10 + 3 = 13

Calculate the number of neutrons using the mass number and the proton count.

The nucleus contains

14

neutrons.

Mass number is the sum of protons and neutrons (

A = Z + N

). Thus,

\text{Neutrons} = \text{Mass Number} - \text{Protons} = 27 - 13 = 14

Key Concept

Relationship between mass number, atomic number (protons), net ionic charge, and subatomic particle counts.

Estimated Time:1m 0s

Question 200Question →

A naval research vessel uses active sonar to determine the depth of the ocean floor. The ship's transducer transmits an acoustic pulse downward into seawater where sound travels at an average speed of $1{}500\text{ m/s}$ . If the reflected echo is recorded by the receiver exactly $4.0\text{ seconds}$ after transmission, what is the depth of the ocean floor?

6{}000\text{ meters}

750\text{ meters}

3{}000\text{ meters}

375\text{ meters}

Show answer & explanation

Answer: $3{}000\text{ meters}$

Answer

3{}000\text{ meters}

Sonar relies on reflected sound waves (echoes). Because the sound pulse must travel down to the seafloor and then back up to the ship's receiver, the

4.0\text{ seconds}

represents two-way travel time. The one-way travel time is

2.0\text{ seconds}

. Multiplying the speed of sound in seawater (

1{}500\text{ m/s}

) by the one-way time (

2.0\text{ s}

) gives an ocean depth of

3{}000\text{ meters}

Step-by-Step Solution

Calculate the total distance traveled by the sound wave during the round trip

\text{Total distance} = \text{speed} \times \text{total time} = 1{}500\text{ m/s} \times 4.0\text{ s} = 6{}000\text{ meters}

The acoustic pulse travels from the ship down to the ocean floor and reflects back up to the surface.

Divide the total round-trip distance by two to obtain the one-way depth

\text{Depth} = \frac{6{}000\text{ m}}{2} = 3{}000\text{ meters}

Sonar distance measurement involves two equal legs of travel (downward and upward).

Key Concept

Calculation of distance using sound wave reflection and two-way travel time

Estimated Time:1m 0s

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