Energy, Heat and Waves Lesson Test (40 Questions)

Answer: D

Correct answer: Joule (J). One joule is the work done when a force of one newton moves an object one meter, so 1 J = 1 N·m. Because work, heat and all forms of energy can be converted into one another, they share this unit. The most common confusion is with the watt, which measures power, the rate of energy use: one watt is one joule per second. Food Calories and kilowatt-hours are other energy units that can be converted to joules.

• A: Kelvin is the SI unit for thermodynamic temperature, not energy.
• B: A watt measures power, the rate of energy transfer, not energy itself.
• C: Hertz measures frequency in cycles per second, not energy.
• D (correct): A joule is the SI unit for work, energy and transferred heat.

Answer: B

Correct answer: Kinetic energy. Any object with mass that is moving has kinetic energy, calculated as KE = ½mv². Because speed is squared, doubling the ball's speed gives it four times the energy, which is why fast-moving objects do so much more damage. Potential energy is different: it is stored because of position or shape, like a ball held above the floor or a compressed spring. The word kinetic comes from a Greek word meaning motion.

• A: Gravitational potential energy depends on position in a gravitational field rather than speed.
• B (correct): Kinetic energy is the energy associated with an object’s motion.
• C: Elastic potential energy is associated with deformation such as a compressed spring.
• D: Nuclear energy involves atomic nuclei and is not the direct motion being described.

Answer: A

Correct answer: A book resting on a high shelf. Gravitational potential energy is energy stored because of an object's height in a gravitational field, calculated as PE = mgh. The book is not moving, yet lifting it to the shelf took work, and that energy stays stored until the book falls and converts it into kinetic energy. To spot this type, look for something raised up that could fall. Vibration, sound and light all involve energy that is moving or being transferred, not stored by height.

• A (correct): An elevated book can lose gravitational potential energy when it falls toward the floor.
• B: A speaker playing a note uses vibrations and sound, not stored gravitational height.
• C: Vibration directly indicates motion and kinetic energy rather than primarily elevated position.
• D: Emitted light is energy transported by electromagnetic radiation, not stored height energy.

Answer: B

Correct answer: Conduction. Conduction is heat transfer through direct contact within a material: faster-moving particles at the hot end jostle their neighbors, and in metals free-moving electrons carry energy quickly along. That is why a metal spoon in hot soup soon feels warm at the handle, while a wooden spoon does not. Convection is the tempting wrong choice, but it requires a fluid that flows, and a solid spoon does not flow. Refraction and diffraction describe waves, not heat.

• A: Refraction describes a wave changing direction across a boundary, not warming a spoon.
• B (correct): Conduction transfers energy through particle and electron interactions along the touching metal.
• C: Diffraction is wave spreading around obstacles or through openings, not metal heat transfer.
• D: Convection requires bulk motion of a fluid and is not the principal transfer through stationary metal.

Answer: D

Correct answer: Convection. When air is heated, it expands and becomes less dense, so cooler, denser air sinks and pushes it upward. This circulation, called a convection current, carries thermal energy through the room along with the moving air itself. Convection happens only in fluids, meaning liquids and gases. Conduction is the common mix-up, but it passes energy from particle to particle without the material flowing, as along a metal pan handle.

• A: Reflection changes the direction of waves and does not explain rising warm air.
• B: Conduction transfers thermal energy through microscopic interactions, not the described moving air.
• C: Freezing is a phase change from liquid to solid, not the movement of warm air.
• D (correct): Convection describes bulk motion of a fluid such as heated air that transports thermal energy.

Answer: C

Correct answer: Sound in air. Sound is a mechanical wave: it travels as particles of a medium push on their neighbors, creating compressions and rarefactions. With no particles, as in the vacuum of space, sound cannot travel at all. Light, radio and infrared are all electromagnetic waves, made of changing electric and magnetic fields that need no medium, which is how sunlight reaches Earth. A simple sorting rule: mechanical waves need matter, electromagnetic waves do not.

• A: Radio waves are electromagnetic and can propagate through a vacuum.
• B: Infrared radiation is electromagnetic and can cross empty space.
• C (correct): Sound consists of mechanical disturbances and cannot propagate through a perfect vacuum.
• D: Visible light is electromagnetic and can travel through a vacuum without matter.

Answer: A

Correct answer: Hertz. Frequency counts how many complete wave cycles pass a point each second, so its unit, the hertz, equals one cycle per second, or 1/s. The unit honors Heinrich Hertz, who first demonstrated radio waves. Frequency links to other wave quantities through wave speed = frequency × wavelength. The common confusion is with wavelength, which is a distance measured in meters. A radio station at 100 MHz, for example, sends 100 million cycles each second.

• A (correct): Hertz means complete cycles per second, the unit of frequency.
• B: Meters measure length, including wavelength, but not cycles per second.
• C: Joules measure energy and do not directly count oscillations per second.
• D: Watts measure energy transfer per unit time, not the number of oscillations.

Answer: C

Correct answer: Watt (W). Power is the rate at which energy is transferred or work is done, so it is energy divided by time:

A 100 W light bulb uses 100 joules every second. The frequent mistake is choosing the joule, which measures a total amount of energy, not how fast it is used. Electric bills use kilowatt-hours, which multiply power by time to give an amount of energy rather than a power.

• A: A second measures time alone and cannot directly express power.
• B: A meter measures length, whereas power compares energy with time.
• C (correct): A watt equals one joule per second and is the SI power unit.
• D: A joule measures an amount of energy, not the rate of transfer.

Answer: C

Correct answer: Visible light. Light is an electromagnetic wave, a self-sustaining pattern of changing electric and magnetic fields, so it needs no particles to carry it and can cross the empty space between the Sun and Earth. Water ripples, seismic waves and sound are mechanical waves, which travel only by passing motion from particle to particle. That is why astronauts in space cannot hear each other without radios. Sunlight takes about eight minutes to reach Earth.

• A: Water ripples require liquid water and cannot travel through empty space.
• B: Seismic S waves need an elastic medium and cannot propagate through a vacuum.
• C (correct): Visible light is electromagnetic radiation and can propagate without a material medium.
• D: Sound requires matter and cannot propagate across a vacuum.

Answer: B

Correct answer: It is transferred mostly into thermal energy and other forms. Energy is conserved: it cannot be created or destroyed, only changed from one form to another. When brake pads rub against the wheel rims, friction converts the bicycle's kinetic energy mainly into heat, which is why brakes feel warm after a hard stop. A small share becomes sound, such as a squeal. The energy is not lost; it spreads into the surroundings in a less useful form.

• A: Energy conservation rules out destruction of energy during ordinary braking.
• B (correct): Energy transfers to heating of brakes, tires, air and surroundings, plus some sound.
• C: Braking on level ground does not require all kinetic energy to become height energy.
• D: No conservation principle requires a bicycle’s kinetic energy to become tire mass in this situation.

Answer: D

Correct answer: 24 J. Kinetic energy depends on mass and the square of speed: KE = ½mv². Square the speed first, 4² = 16, then multiply by the mass,

and finally take half, which gives 24 joules. Because speed is squared, doubling the speed would quadruple the energy. The usual mistakes are forgetting the factor of ½ or multiplying by the speed without squaring it.

• A: Forty-eight joules forgets to divide mass times speed squared by two.
• B: Six joules results from treating speed as a simple factor without the square and correct coefficient.
• C: Twelve joules multiplies the mass by the unsquared speed, missing the speed-squared factor.
• D (correct): KE = $\frac{1}{2}$ × 3 × $4^2$ = 24 J using the correct units.

Answer: C

Correct answer: Quadruples. Kinetic energy is KE = ½mv², so it depends on the square of speed, not on speed itself. Whatever factor multiplies the speed gets squared: double the speed and the energy goes up by 2² = 4; triple it and it goes up by 9. The tempting answer is that energy doubles, which would only be true if KE were proportional to v. This is why braking distance grows so sharply with speed.

• A: Tripling does not follow from the square of the speed ratio of two.
• B: Kinetic energy is proportional to speed squared, so doubling speed produces more than twice the energy.
• C (correct): Because ${\left(2v\right)}^2$ = 4v², kinetic energy becomes four times larger.
• D: Changing speed changes kinetic energy unless it is exactly the same speed.

Answer: D

Correct answer: 60 J. Gravitational potential energy gained equals the work done lifting the object against its weight: weight (mg) times the height raised. Here the weight is 2 kg × 10 m/s² = 20 N, and 20 N × 3 m = 60 J. A common slip is to multiply only mass and height, forgetting g, which gives 6 J. Checking units helps: kg × m/s² × m equals N·m, which is joules.

• A: Fifteen joules would be from unrelated values and fails the stated PE formula.
• B: Six joules incorrectly omits the gravitational acceleration multiplier.
• C: Thirty joules is half the correct value for this particular mass and height.
• D (correct): The gain is ΔPE = mgΔh = 2 × 10 × 3 = 60 J.

Answer: B

Correct answer: 50 J. Work is force times the distance moved in the direction of the force, W = Fd, and one newton acting over one meter is one joule. Because the force and motion point the same way here, the full 10 N counts, giving

Adding or dividing the numbers gives values with the wrong meaning. If the force were perpendicular to the motion, it would do no work at all.

• A: Two joules is a force-to-distance ratio, not the product required for work.
• B (correct): Work by a parallel constant force equals 10 × 5 = 50 J.
• C: Fifteen joules is the sum of the given numbers, not force times distance.
• D: Five hundred joules multiplies in an extra factor of ten absent from the stem.

Answer: A

Correct answer: 40 W. Power measures how fast energy is transferred, so it is energy divided by time, and one watt is one joule per second. Spreading 240 J evenly over 6 s means 40 J each second. Multiplying instead of dividing is the most common error; checking units catches it, since J × s is not a rate. A larger power rating means the same energy is delivered in less time.

• A (correct): Average power = energy/time = $\frac{240}{6}$ = 40 $\frac{\mathrm{J}}{\mathrm{s}}$ = 40 W.
• B: This multiplies joules by seconds, giving the wrong numerical value and unit.
• C: This reverses the division and gives seconds per joule rather than watts.
• D: This adds energy and time instead of dividing, which is not a power formula.

Answer: A

Correct answer: 298.15 K. The kelvin and Celsius scales use the same size degree, so they differ only by where zero is placed. Zero kelvin is absolute zero, which is −273.15 °C, so you always add 273.15 to a Celsius reading to get kelvins. Subtracting instead would put a warm room below the freezing point of water. Room temperature near 25 °C is often rounded to about 298 K.

• A (correct): 25 + 273.15 = 298.15 K, using the correct Celsius-to-kelvin offset.
• B: Taking 273.15 minus 25 gives 248.15, incorrectly reversing the Celsius-to-kelvin offset.
• C: 273.15 K is exactly 0 °C, not 25 °C.
• D: The Celsius and kelvin scales have different zero points despite equal-size intervals.

Answer: B

Correct answer: 68 °F. A Fahrenheit degree is smaller than a Celsius degree: 100 Celsius degrees span the same range as 180 Fahrenheit degrees, a ratio of 9/5. The scales also start at different points, since water freezes at 0 °C but 32 °F. So multiply by 9/5 first, then add 32. Skipping either step gives a wrong value: 36 °F without the offset, or 52 °F without the scaling. A useful check: 20 °C is a mild room, and 68 °F matches that.

• A: About 293 corresponds to 20 °C in kelvins, not Fahrenheit.
• B (correct): 20 × $\frac{9}{5}$ + 32 = 68 °F, the correct Fahrenheit value.
• C: Thirty-six is 20 × 9/5 without adding the 32-degree offset.
• D: Fifty-two adds 32 to 20 but skips multiplying by 9/5.

Answer: C

Correct answer: Thermal radiation. Heat can move in three ways. Conduction passes energy through direct contact between particles, and convection carries it with flowing gas or liquid, so both need matter. Radiation is electromagnetic waves, such as infrared and visible light, which travel through a vacuum at the speed of light. Since space between the Sun and Earth is nearly empty, only radiation can bridge it. You feel the same effect from a campfire's glow on your face.

• A: Evaporation changes liquid into vapor; it is not sunlight transport across space.
• B: Convection currents need a moving gas or liquid to carry heat, and nearly empty space has almost none.
• C (correct): Thermal radiation is electromagnetic energy and can cross a vacuum.
• D: Conduction requires interacting matter and cannot transfer energy across a vacuum gap.

Answer: B

Correct answer: Amount and nature of matter. Temperature reflects the average kinetic energy of particles, while internal energy is the total energy of all particles in a sample. A pool holds vastly more water molecules than a cup, so even at a lower average energy per molecule, the sum can be far larger. The type of substance and its phase also matter. The key mistake is treating temperature and total energy as the same thing.

• A: Color can affect radiative transfers but cannot alone establish the internal energy of a water sample.
• B (correct): Total internal energy depends on the amount and nature of matter as well as its state.
• C: Boiling point by itself does not tell us how much internal energy is stored in a sample.
• D: Air pressure can affect phase behavior but cannot alone determine the sample’s internal energy.

Answer: C

Correct answer: 5 Hz. Frequency counts how many complete cycles happen each second, so you divide the number of cycles by the elapsed time. Fifteen cycles in 3 s is 5 cycles per second, or 5 hertz. Dividing the other way,

gives the period, the time for one cycle. Frequency and period are reciprocals, so if you get one you can always find the other.

• A: The value 0.2 s would represent the period, not frequency in hertz.
• B: Multiplying oscillations by seconds does not give frequency in cycles per second.
• C (correct): Frequency = 15 cycles / 3 s = 5 Hz.
• D: Three hertz mistakenly uses only the supplied time rather than cycles divided by time.

Answer: A

Correct answer: 0.25 s. Frequency tells how many cycles occur per second, and period tells how many seconds one cycle takes, so each is the reciprocal of the other:

With 4 cycles fitting into each second, each cycle must last one quarter of a second. A quick sense check: higher frequency always means a shorter period, so an answer larger than one second cannot be right for 4 Hz.

• A (correct): Period = 1/f = $\frac{1}{4}$ s = 0.25 s per cycle.
• B: Sixteen seconds comes from squaring the frequency without justification.
• C: Four is the numerical frequency, not the duration of one cycle.
• D: This incorrectly moves the decimal and does not equal one divided by four.

Answer: D

Correct answer: 3 m. The wave equation v = fλ says that in one second a wave advances by as many wavelengths as it has cycles. Rearranged, λ = v/f, so 300 m/s spread over 100 cycles per second makes each cycle 3 m long. Multiplying speed by frequency is the usual error, and its unit, m/s², shows it cannot be a length. Higher frequency at a fixed speed always means a shorter wavelength.

• A: Thirty meters corresponds to dividing speed by ten rather than the given 100 Hz.
• B: Thirty thousand meters incorrectly multiplies wave speed by frequency.
• C: About 0.33 is the reciprocal of 3, not the requested wavelength.
• D (correct): Wavelength λ = $\frac{v}{f}$ = $\frac{300}{100}$ = 3 m.

Answer: A

Correct answer: 68 m. An echo time covers a round trip: the sound travels to the wall and then back to the listener. Speed times time,

is therefore the total path, and the wall is half that distance away. Forgetting to halve is the most common mistake. Sonar on ships and echolocation in bats use the same idea, timing a reflected pulse and halving the round-trip distance.

• A (correct): Wall distance = (340 × 0.4)/2 = 68 m because the trip is out and back.
• B: Three hundred forty meters would result from treating the 0.4-second time as one second.
• C: Thirty-four meters divides the already halved one-way distance by two again.
• D: One hundred thirty-six meters is the entire out-and-back sound path, not the wall distance.

Answer: B

Correct answer: Increasing its frequency. Pitch is how the ear perceives the frequency of a sound wave: more vibrations per second sound higher. Amplitude is a separate property that sets loudness, so making a tone louder does not change its pitch. Distance from a stationary source mainly reduces intensity. A guitar string shows this clearly: tightening or shortening it makes it vibrate faster and sound higher, while plucking it harder only makes it louder.

• A: Decreasing frequency lowers a pure tone’s pitch instead of raising it.
• B (correct): A higher sound-wave frequency corresponds to higher pitch.
• C: Greater amplitude generally affects loudness/intensity, not the frequency that sets pitch.
• D: Greater distance usually reduces intensity; without relative motion it need not increase pitch.

Answer: B

Correct answer: Higher frequency and shorter wavelength. All electromagnetic waves travel at the same speed in a vacuum, so from c = fλ, a higher frequency must come with a shorter wavelength. The spectrum runs from radio waves through infrared, visible light (red to violet) and ultraviolet toward X-rays and gamma rays, with frequency rising along the way. Violet sits at the high-frequency end of visible light, while infrared lies just below red, so violet photons also carry more energy.

• A: They occupy different frequency ranges, so equality of frequency contradicts the comparison.
• B (correct): Violet light is higher-frequency, shorter-wavelength electromagnetic radiation than infrared.
• C: Photon energy increases with frequency, so violet does not have lower photon energy.
• D: Infrared lies below visible light in frequency and is generally longer in wavelength.

Answer: D

Correct answer: 35°. The law of reflection says the angle of reflection equals the angle of incidence, with both measured from the normal, an imaginary line perpendicular to the surface. The key trap is the reference line: an angle measured from the mirror surface is the complement, 90° − 35° = 55°. Always check which line an angle is taken from. A ray striking straight along the normal, at 0°, bounces straight back.

• A: Seventy degrees doubles the incident angle, which is not the reflection law.
• B: Fifty-five degrees is measured from the mirror surface, not the stated normal reference.
• C: Zero degrees would be a perpendicular incident ray, unlike this 35° case.
• D (correct): The law of reflection gives equal incident and reflected angles measured from the normal.

Answer: D

Correct answer: A sound-pressure wave. In a longitudinal wave the particles of the medium vibrate back and forth along the same direction the wave travels, creating compressions and rarefactions. In a transverse wave, such as a shaken rope, they move perpendicular to the travel direction. Light and X-rays are electromagnetic waves, which are transverse and need no medium at all. A stretched Slinky pushed along its length is a good model of sound in air.

• A: A wave on an ideal rope is usually transverse rather than longitudinal.
• B: X-rays are electromagnetic radiation and are not pressure waves in air.
• C: Visible light is electromagnetic and does not require air or any other material medium.
• D (correct): Sound propagates via compressions and rarefactions parallel to its direction of travel.

Answer: A

Correct answer: 40%. Efficiency compares useful output to total input: efficiency = useful output ÷ input × 100%. Here 80 J out of 200 J is 0.40, or 40%. The remaining 120 J is not destroyed; it becomes heat, sound and other less useful forms. Mistaking the 80 J itself for a percentage is a common error. No real machine can exceed 100%, since that would mean producing more energy than it receives.

• A (correct): Efficiency = $\frac{80}{200}$ × 100% = 40%, with the rest in other energy transfers.
• B: Eighty percent confuses the useful 80 joules with 80 percent of the input.
• C: A 120-percent output ratio exceeds 100% for the explicitly accounted input and output.
• D: Twenty percent is half the actual efficiency and omits a necessary factor.

Answer: C

Correct answer: Evaporation carries energy away from the skin. Turning liquid water into vapor requires energy, called the latent heat of vaporization. The water molecules that escape take that energy from the skin, so the skin's temperature drops. Energy is conserved; it is moved, not destroyed or turned into some kind of cold. This is also why sweating cools less well in humid air, where evaporation is slow, and why stepping out of a pool on a breezy day feels chilly.

• A: Evaporation moves energy away from the skin; energy is conserved and is never destroyed.
• B: Normal sweat cooling involves evaporation, not freezing water into ice.
• C (correct): Evaporation removes energy as liquid water becomes vapor, often cooling the skin.
• D: “Cold energy” is not a separate energy form produced by sweat.

Answer: B

Correct answer: It decreases. The wave equation v = fλ links speed, frequency and wavelength. Frequency is set by the source, so it stays the same when a wave enters a new medium; only speed and wavelength can change. With f fixed, wavelength is directly proportional to speed, so slower speed means shorter wavelength. Light entering glass behaves this way: it slows down and its wavelength shortens, while its frequency and color stay the same.

• A: Wavelength cannot remain fixed if speed changes and frequency stays fixed under this relationship.
• B (correct): From v = fλ, a smaller speed at the same frequency means a smaller wavelength.
• C: A normal propagating wave does not need zero wavelength when speed decreases.
• D: At fixed frequency, higher—not lower—speed would give a larger wavelength.

Answer: C

Correct answer: 120 J. With no friction, mechanical energy is conserved, so all the potential energy lost on the way down becomes kinetic energy. The potential energy at the start is mgh =

and at the reference level it is zero. The shape of the slope does not matter, only the height dropped. Answers above 120 J would require energy appearing from nowhere, which conservation rules out.

• A: Sixty joules halves the correct mgh transfer without justification.
• B: Two hundred forty joules doubles the available energy and violates the idealized conservation calculation.
• C (correct): Initial PE = 1.5 × 10 × 8 = 120 J, entirely converted into KE in the idealized situation.
• D: Twelve joules omits the factors of gravitational acceleration and sufficient height.

Answer: D

Correct answer: 3 m. Frequency is fixed by the source, so it does not change when a wave crosses into a new material. Only speed and wavelength change, and they stay proportional through v = fλ. In material B, dividing 150 m/s by 50 Hz gives 3 m. The information about material A is a distractor: 6 m there implies 300 m/s, so cutting the speed in half also halves the wavelength, confirming 3 m.

• A: Two meters would imply 100 $\frac{\mathrm{m}}{\mathrm{s}}$, below the stated speed in material B.
• B: Six meters is the wavelength in A and does not reflect the changed speed.
• C: One meter would imply a propagation speed of only 50 $\frac{\mathrm{m}}{\mathrm{s}}$ at 50 Hz.
• D (correct): λB = $\frac{150}{50}$ = 3 m; the frequency stays constant across the boundary.

Answer: C

Correct answer: 28 J. Net work equals the total work done by all forces, which is the same as the net force times the displacement. The applied force does +48 J, while friction acts opposite the motion and does −20 J, so the total is 28 J. Using the 12 N force alone ignores friction. By the work-energy theorem, this 28 J is exactly the crate's gain in kinetic energy.

• A: Twenty joules is the magnitude of friction’s work, with its negative sign omitted.
• B: Forty-eight joules is work by the applied force alone, ignoring friction.
• C (correct): Net horizontal force is 12−5 = 7 N; net work = 7 × 4 = 28 J.
• D: Sixty-eight joules incorrectly adds opposing force magnitudes rather than subtracting them.

Answer: A

Correct answer: 90,000 J. Power is energy per unit time, so energy equals power multiplied by time. Because a watt is one joule per second, the time must be in seconds: 2 minutes is 120 s. Multiplying 750 by 2 without converting gives 1,500 J, which is the most common mistake. The answer can also be written as 90 kJ, and it shows how quickly even modest appliances transfer energy.

• A (correct): E = Pt = 750 $\frac{\mathrm{J}}{\mathrm{s}}$ × 120 s = 90,000 J.
• B: This multiplies 750 by 2 but fails to convert minutes to seconds.
• C: Forty-five thousand joules uses only half the actual 120-second running time.
• D: Three hundred seventy-five is a quotient unrelated to constant-power energy transfer.

Answer: C

Correct answer: 10 °C. Specific heat capacity is the energy needed to raise 1 kg of a substance by 1 °C, so heat absorbed is Q = mcΔT. Solving for the temperature change gives ΔT = Q ÷ (mc). Here the sample needs

J per degree, and 2,000 J supplies ten such degrees. Substances with high specific heat, like water, warm up slowly for this reason.

• A: Twenty degrees results from using twice the correct temperature increase.
• B: Two and a half degrees arises from multiplying the given mass and capacity incorrectly.
• C (correct): ΔT = 2000/(0.4 × 500) = 10 °C, which is also a 10 K interval.
• D: Four degrees would require a larger effective heat capacity than the one supplied.

Answer: A

Correct answer: 25 m/s. One peak every 0.02 s at a fixed point means one full cycle passes each 0.02 s, so that is the period. Frequency is the reciprocal,

Wave speed then follows from v = fλ, 50 × 0.5. An equivalent shortcut is v = λ/T, since the wave moves one wavelength each period. Multiplying period by wavelength is the trap, and its units, m·s, are not a speed.

• A (correct): The period is 0.02 s, so f = 50 Hz and v = 50 × 0.5 = 25 $\frac{\mathrm{m}}{\mathrm{s}}$.
• B: Ten meters per second would be correct for a lower frequency of 20 Hz.
• C: 0.01 is a product of period and wavelength rather than speed.
• D: Two hundred fifty meters per second assumes a tenfold shorter period.

Answer: B

Correct answer: Wavelength halves; photon energy doubles. In a vacuum all electromagnetic radiation moves at the same speed c, and c = fλ, so frequency and wavelength are inversely related: one doubles, the other halves. Photon energy follows E = hf, where h is Planck's constant, so energy is directly proportional to frequency. That is why high-frequency ultraviolet and X-rays can damage cells while lower-frequency radio waves cannot.

• A: A wavelength increase contradicts constant c with a higher frequency.
• B (correct): From c=fλ, doubling f halves λ; from E=hf, photon energy doubles.
• C: This reverses both relationships between frequency, wavelength, and photon energy.
• D: Neither wavelength nor photon energy is unchanged if frequency doubles.

Answer: D

Correct answer: 120 m. An echo time covers the trip to the wall and back. Multiplying speed by time,

gives that full round-trip path, so the wall is half as far away. Forgetting to halve is the usual error, and doubling instead makes it worse. Depth sounders and ultrasound imaging use the same halving step when they convert a reflected pulse's travel time into a distance.

• A: The 240 m value is the complete two-way sound path, not one-way wall distance.
• B: Four hundred eighty meters incorrectly doubles rather than halves the full path.
• C: Eighty meters results from using the wrong speed or time conversion.
• D (correct): Distance = 320 × 0.75 ÷ 2 = 120 m because sound reaches the wall and comes back.

Answer: D

Correct answer: Its efficiency is 25%; all 600 J is accounted for. Efficiency is useful output divided by total input, so only the 150 J of work counts as useful. The other 450 J has not vanished; it was converted to heating and sound, and together with the work it adds up to the full 600 J. Conservation of energy always holds, while efficiency describes how much of the energy goes where you want.

• A: Seventy-five percent is the fraction transferred as other forms, not the useful work fraction.
• B: One hundred fifty percent contradicts the given energy accounting and the efficiency ratio.
• C: Heating and sound cannot automatically be counted as the specified useful mechanical output.
• D (correct): Useful efficiency = $\frac{150}{600}$ × 100% = 25%; 150+450 = 600 J is conserved.

Answer: A

Correct answer: 0.8 m then 0.9 m. Frequency is fixed by the vibrating source, so changing the air temperature changes only the speed and wavelength. From λ = v/f, wavelength is proportional to speed when frequency is constant: 320 ÷ 400 gives the initial value and 360 ÷ 400 the final one. Faster sound in warmer air therefore stretches each wavelength. Sound generally travels faster in warmer air because its molecules move faster.

• A (correct): Initially λ=$\frac{320}{400}$=0.8 m; finally λ=$\frac{360}{400}$=0.9 m at constant frequency.
• B: These values reverse the correct initial and final wavelengths for the stated speed increase.
• C: These values copy wave speeds as wavelengths and ignore the frequency.
• D: These wavelengths use an unrelated divisor instead of the given 400 Hz.

Answer: D

Correct answer: 10 m/s. Only the drop in height matters: 20 m − 15 m = 5 m. With no friction, lost potential energy becomes kinetic energy, so

and the mass cancels.

• A: This uses the 15 m height of the second hill as the drop; the car has only fallen 20 − 15 = 5 m.
• B: This is the speed at ground level after a full 20 m drop, not at the top of a 15 m hill.
• C: This is the value of 2gh = 100 before taking the square root; the speed is the square root of that.
• D (correct): The car has dropped 5 m, so each kilogram has gained 50 J of kinetic energy, giving a speed of 10 m/s.

Answer: B

Correct answer: 1,000 W. Useful output:

Input energy = useful output ÷ efficiency =

Power drawn = 30,000 J ÷ 30 s = 1,000 W.

• A: This is the useful output power (24,000 J ÷ 30 s); the motor must draw more than that because 20% is wasted.
• B (correct): The crate gains 24,000 J, so the input is 24,000 ÷ 0.80 = 30,000 J, and 30,000 J ÷ 30 s = 1,000 W.
• C: This multiplies the useful power by 0.80; efficiency means input is larger than output, so divide, not multiply.
• D: This divides by 0.80 twice; once is enough to go from 800 W of useful output to the input power.

Answer: C

Correct answer: 20 °C. Energy = mass × specific heat × temperature change, so temperature change = energy ÷ (mass × specific heat).

For aluminum:

The water warms only about 4.3 °C because its specific heat is much higher.

• A: This uses water's specific heat; that is the water's rise, not the aluminum's.
• B: This divides the specific heat by the energy; the energy must be divided by mass times specific heat.
• C (correct): Temperature change = 18,000 ÷ (1 × 900) = 20 °C, much more than the water's rise because aluminum's specific heat is lower.
• D: This is a place-value slip, dividing 18,000 by 9,000 instead of by 900.

Answer: A

Correct answer: About 2.5 km. Light arrives almost instantly, so the delay is the sound's one-way travel time. Sound in air travels about 343 m/s, roughly 1 km every 3 s.

Distance ≈ 7.5 s ÷ 3 s per km = 2.5 km (343 × 7.5 ≈ 2,570 m).

• A (correct): Sound covers about 1 km every 3 s, so 7.5 s ÷ 3 s per km gives about 2.5 km.
• B: This halves the distance as if it were an echo; thunder travels only one way from the strike to the listener.
• C: This multiplies the delay by 3 instead of dividing; it takes about 3 s per kilometer, not 3 km per second.
• D: This assumes sound travels 1 km each second; sound in air is closer to 343 m/s, about 1 km every 3 s.

Answer: D

Correct answer: Radio waves. The electromagnetic spectrum, from lowest to highest frequency, runs radio, microwave, infrared, visible, ultraviolet, X-ray and gamma. Radio waves are at the low-frequency, long-wavelength end.

• A: Gamma rays sit at the opposite end of the spectrum, with the highest frequency and shortest wavelength.
• B: Ultraviolet is beyond violet, the high-frequency end of visible light, so its frequency is high.
• C: Microwaves have low frequency, but they come just after radio waves, which are lower still.
• D (correct): Radio waves begin the spectrum order and have the lowest frequency and longest wavelength.

Answer: C

Correct answer: A higher pitch while it approaches and a lower pitch as it moves away. This is the Doppler effect. As the train comes closer, each crest is emitted from a slightly closer point, so crests arrive bunched together and the pitch sounds higher. As it moves away the crests spread out and the pitch drops, even though the horn itself never changes.

• A: This reverses the Doppler effect; waves bunch up in front of an approaching source, raising the pitch.
• B: Loudness does change, but the received frequency also shifts because the source is moving relative to the listener.
• C (correct): An approaching source bunches its wave crests, raising the received frequency; a receding source spreads them, lowering it.
• D: The horn's emitted frequency never changes; only the frequency the listener receives shifts.

Answer: D

Correct answer: 253.15 K. First convert to Celsius by reversing the Fahrenheit formula: °

Then add 273.15:

K.

• A: This adds 273.15 directly to the Fahrenheit reading; the reading must first be converted to Celsius.
• B: This uses +20 °C instead of −20 °C; a reading below 32 °F is below 0 °C.
• C: This subtracts 32 but skips multiplying by 5/9, treating −36 Fahrenheit degrees as Celsius degrees.
• D (correct): Converting gives −20 °C, and −20 + 273.15 = 253.15 K.

Answer: C

Correct answer: It slows the flow of the camper's body heat out to the cold air. Insulation does not create warmth; it slows energy transfer. Heat flows from the warm camper toward the cold air, and the still air trapped in the bag's filling conducts poorly and stops convection, so the body's own energy escapes more slowly.

• A: Insulation does not generate any energy; the only warmth comes from the camper's body.
• B: Cold is not something that flows; energy flows from the warm camper outward.
• C (correct): Trapped still air in the filling conducts poorly and blocks convection, so energy leaves the body more slowly.
• D: Cold is not a form of energy that can be reflected; the bag reduces outward energy loss.

Answer: A

Correct answer: 3.0 m. A plane mirror forms an image as far behind the mirror as the object is in front of it. The image is 1.5 m behind the mirror, so the total distance from the sailor to his image is

• A (correct): The image appears 1.5 m behind the mirror, and the sailor is 1.5 m in front, so they are 3.0 m apart.
• B: This is the distance from the mirror to the image, not from the sailor to the image.
• C: This halves the distance; a plane mirror image is as far behind the mirror as the object is in front.
• D: The image is not on the mirror's surface; it appears behind the mirror.

Answer: A

Correct answer: Amplitude. Volume, or loudness, is controlled by amplitude: how far the medium moves from its rest position. Since the note's pitch is unchanged, the frequency, and therefore the wavelength in the same air, stay the same.

• A (correct): Louder sound means the air is displaced farther from rest, which is a larger amplitude.
• B: Frequency sets pitch; the note stays the same, so frequency does not change.
• C: Wavelength depends on wave speed and frequency, and neither changes when the volume is raised.
• D: The speed of sound depends on the air, not on how loud the sound is.

Answer: B

Correct answer: 0.5 J. Use

• A: This skips squaring the compression, computing ½ × 400 × 0.05 instead of using 0.05².
• B (correct): Elastic energy = ½ × 400 × (0.05)² = ½ × 400 × 0.0025 = 0.5 J.
• C: This squares the compression but leaves out the factor of ½.
• D: This simply multiplies k by x, which gives a force in newtons, not stored energy.