Waves, Sound & Light — Chapter Practice, Grade 8

Connect vibrating sources, wave properties, sound, light and information with a complete source–medium–receiver model. This is a required chapter and is included in the course final.

Problem 1

Does no visible motion prove that a source is not vibrating?
Answer and explanation

No. The motion can be too fast or small to detect with the chosen method. A suitable measurement or record is needed.

No. The motion can be too fast or small to detect with the chosen method. A suitable measurement or record is needed.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 2

What is B’s amplitude and what quantity remains unchanged?
Answer and explanation

Amplitude is 3 mm. The cycle count per time, and hence frequency of 200 Hz, is unchanged in this comparison.

Amplitude is 3 mm. The cycle count per time, and hence frequency of 200 Hz, is unchanged in this comparison.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 3

Why is counting only crests without an interval insufficient?
Answer and explanation

Frequency needs the number of complete cycles divided by a defined time. An unscaled drawing alone does not establish hertz.

Frequency needs the number of complete cycles divided by a defined time. An unscaled drawing alone does not establish hertz.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 4

What is missing from a drawing with only a source and an ear?
Answer and explanation

The intermediate medium and interactions, and how the receiver responds. The picture should also identify limits such as scale and omitted biological detail.

The intermediate medium and interactions, and how the receiver responds. The picture should also identify limits such as scale and omitted biological detail.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 5

Illustrative sources A/B/C have amplitudes 1/3/1 mm and complete 4/4/6 cycles respectively in 0.02 s. Compare frequency and amplitude and explain what a receiver prediction would need.
Answer and explanation

A and B are 200 Hz, while C is 300 Hz. B has three times A’s amplitude; C has A’s amplitude but higher frequency. Frequency and amplitude are distinct. Predicting received sound also needs distance, medium, losses and receiver response. The source records alone do not establish an exact perceived loudness.

A and B are 200 Hz, while C is 300 Hz. B has three times A’s amplitude; C has A’s amplitude but higher frequency. Frequency and amplitude are distinct. Predicting received sound also needs distance, medium, losses and receiver response. The source records alone do not establish an exact perceived loudness.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 6

Two sources share 250 Hz but have different amplitudes. Which sound property is expected to differ under comparable conditions?
Answer and explanation

Pitch is associated with the shared frequency, while loudness may differ with amplitude under comparable source, medium, distance and receiver conditions. Neither quantity is a universal perception guarantee.

Pitch is associated with the shared frequency, while loudness may differ with amplitude under comparable source, medium, distance and receiver conditions. Neither quantity is a universal perception guarantee.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 7

Evaluate and correct: A louder sound must always have a higher pitch.
Answer and explanation

Amplitude and frequency can vary independently. Compare graph height and cycles per stated time separately.

Amplitude and frequency can vary independently. Compare graph height and cycles per stated time separately.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 8

Choose one prediction from this unit. Explain a comparison that could test it, specifying observations, changed and matched conditions, and a result that would challenge it.
Answer and explanation

A simplified chain is ruler → nearby air → farther air → receiver. A paper membrane can be a model receiver, but detectable motion depends on many factors. Failure to see it move at quiet volume is not evidence that energy transfer never occurs. The intermediate medium and interactions, and how the receiver responds. The picture should also identify limits such as scale and omitted biological detail.

A simplified chain is ruler → nearby air → farther air → receiver. A paper membrane can be a model receiver, but detectable motion depends on many factors. Failure to see it move at quiet volume is not evidence that energy transfer never occurs. The intermediate medium and interactions, and how the receiver responds. The picture should also identify limits such as scale and omitted biological detail.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 9

A source completes 8 cycles in 0.04 s at amplitude 2 mm. Another completes 8 cycles over the same time at 4 mm. Compare the changed quantity and a limit of predicting what a person hears.
Hints

Distinguish the observed quantities, the proposed mechanism and its conditions.

Answer and explanation

Both have frequency 200 Hz; amplitude doubles. Frequency-related pitch is comparable in the simple model, while received loudness also depends on distance, medium and receiver. The amplitude comparison alone does not fix a person’s perception.

Both have frequency 200 Hz; amplitude doubles. Frequency-related pitch is comparable in the simple model, while received loudness also depends on distance, medium and receiver. The amplitude comparison alone does not fix a person’s perception.

Problem 10

Two sources share 250 Hz but have different amplitudes. Which sound property is expected to differ under comparable conditions? Explain a condition that would change this conclusion.
Hints

Distinguish the observed quantities, the proposed mechanism and its conditions.

Answer and explanation

Pitch is associated with the shared frequency, while loudness may differ with amplitude under comparable source, medium, distance and receiver conditions. Neither quantity is a universal perception guarantee.

Pitch is associated with the shared frequency, while loudness may differ with amplitude under comparable source, medium, distance and receiver conditions. Neither quantity is a universal perception guarantee.

Problem 11

Change vibration size without changing cycle rateChange vibration size without changing cycle rateSmaller displacement amplitudeLarger displacement amplitudeSame time window; both complete two cycles.
Both source-position records show two cycles during the same stated time window, with different displacement amplitudes. Amplitude is measured from the middle position to a peak, not from peak to trough. The sketches compare patterns qualitatively; an actual amplitude and frequency require numerical axis scales, as in the OpenSciEd graphs used below.
For this unit’s illustrated case, which record has a higher frequency? What quantity differs, and what additional labels are needed for a numerical amplitude?
Answer and explanation

Neither has a higher frequency in this matched window. Displacement amplitude differs; a numerical vertical position scale and units are needed to measure it.

A cycle is one complete repeat, such as one peak to the next matching peak. A taller trace does not automatically have more cycles. Compare amplitude and frequency one at a time rather than using the word louder for both.

Neither has a higher frequency in this matched window. Displacement amplitude differs; a numerical vertical position scale and units are needed to measure it.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 12

A source-position trace has peaks 0.2 s apart and swings from −3 to +3 mm around zero. Find period, frequency and amplitude, and distinguish amplitude from peak-to-trough span.
Answer and explanation

Period 0.2 s; frequency 5 Hz; amplitude 3 mm; peak-to-trough span 6 mm. The source moves locally rather than traveling across the sound path.

Use matching-peak separation for period and its reciprocal for frequency.

Measure amplitude from the middle position to a peak.

Period 0.2 s; frequency 5 Hz; amplitude 3 mm; peak-to-trough span 6 mm. The source moves locally rather than traveling across the sound path.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 13

OpenSciEd graph A of source position in millimetres against time from 0 to 0.01 seconds, showing repeated vibrations around a mean position of about 20 millimetres.
OpenSciEd 8.2 Sound Waves, Lesson 5: actual position-versus-time record A. Read the labeled axes and estimate a cycle interval before opening the worked guidance. The vertical value is the vibrating point’s position relative to a coordinate origin, not air pressure or sound wavelength. Sound-source vibration graph A · OpenSciEd · 8.2 Sound Waves, Lesson 5, source, CC BY 4.0. Figure excerpt rendered from the PDF and resized for the web.
Read OpenSciEd record A. Estimate a peak-to-peak cycle interval, calculate cycles per second and measure displacement amplitude about the midline. Explain why its mean position near 20 mm is not its amplitude. Approximate graph readings are expected.
Answer and explanation

One cycle takes about 0.0033 s, giving frequency about 300 Hz using cycles per second = 1/period. The midline is near 20 mm and extrema are about 19.2 and 20.8 mm, so displacement amplitude is about 0.8 mm. Amplitude measures departure from the midline, not distance from the coordinate origin. Allow reasonable approximate readings from this source graph.

Compare consecutive peaks: about 0.0033 s per cycle.

Compute 1/period, approximately 300 cycles per second, or Hz.

Amplitude is about 20.8−20 = 0.8 mm (half the peak-to-peak displacement).

Response criteria

  • Read time on the horizontal axis; do not call it wavelength.
  • Estimate frequency from repeats per second.
  • Measure amplitude from the midline and distinguish coordinate origin from equilibrium.

Problem 14

OpenSciEd graph B of source position in millimetres against time from 0 to 0.01 seconds, showing repeated vibrations around a mean position of about 20 millimetres.
OpenSciEd 8.2 Sound Waves, Lesson 5: actual position-versus-time record B. Read the labeled axes and estimate a cycle interval before opening the worked guidance. The vertical value is the vibrating point’s position relative to a coordinate origin, not air pressure or sound wavelength. Sound-source vibration graph B · OpenSciEd · 8.2 Sound Waves, Lesson 5, source, CC BY 4.0. Figure excerpt rendered from the PDF and resized for the web.
Read OpenSciEd record B. Estimate its period, frequency and amplitude. Compare it with record A, whose frequency is about 300 Hz and amplitude about 0.8 mm. Which vibration property has changed by a factor of two, and which has stayed approximately the same?
Answer and explanation

One cycle takes about 0.0017 s, giving frequency about 600 Hz using cycles per second = 1/period. The midline is near 20 mm and extrema are about 19.2 and 20.8 mm, so displacement amplitude is about 0.8 mm. Amplitude measures departure from the midline, not distance from the coordinate origin. Allow reasonable approximate readings from this source graph. B has about twice A’s frequency and half its period, while displacement amplitude stays approximately 0.8 mm. Faster repetition does not automatically mean a larger vibration.

Compare consecutive peaks: about 0.0017 s per cycle.

Compute 1/period, approximately 600 cycles per second, or Hz.

Amplitude is about 20.8−20 = 0.8 mm (half the peak-to-peak displacement).

Response criteria

  • Read time on the horizontal axis; do not call it wavelength.
  • Estimate frequency from repeats per second.
  • Measure amplitude from the midline and distinguish coordinate origin from equilibrium.

Problem 15

OpenSciEd graph C of source position in millimetres against time from 0 to 0.01 seconds, showing repeated vibrations around a mean position of about 20 millimetres.
OpenSciEd 8.2 Sound Waves, Lesson 5: actual position-versus-time record C. Read the labeled axes and estimate a cycle interval before opening the worked guidance. The vertical value is the vibrating point’s position relative to a coordinate origin, not air pressure or sound wavelength. Sound-source vibration graph C · OpenSciEd · 8.2 Sound Waves, Lesson 5, source, CC BY 4.0. Figure excerpt rendered from the PDF and resized for the web.
Read OpenSciEd record C. Estimate period, frequency and amplitude. The 0.010 s window contains about one and a half cycles. Why would counting only its one fully completed cycle underestimate the frequency? Use the peak-to-peak interval or include the partial cycle.
Answer and explanation

One cycle takes about 0.0067 s, giving frequency about 150 Hz using cycles per second = 1/period. The midline is near 20 mm and extrema are about 19.2 and 20.8 mm, so displacement amplitude is about 0.8 mm. Amplitude measures departure from the midline, not distance from the coordinate origin. Allow reasonable approximate readings from this source graph. About 1.5 cycles in 0.010 s gives 150 Hz. Counting only one ignores the half-cycle and would incorrectly give 100 Hz; use the measured period or account for the partial cycle.

Compare consecutive peaks: about 0.0067 s per cycle.

Compute 1/period, approximately 150 cycles per second, or Hz.

Amplitude is about 20.8−20 = 0.8 mm (half the peak-to-peak displacement).

Response criteria

  • Read time on the horizontal axis; do not call it wavelength.
  • Estimate frequency from repeats per second.
  • Measure amplitude from the midline and distinguish coordinate origin from equilibrium.

Problem 16

A wave has a frequency of 3 Hz and a wavelength of 6 m. Find its speed.
Answer and explanation

18 m/s

v = f × λ = 3 × 6 = 18 m/s.

Problem 17

A wave has a period of 0.5 seconds. What is its frequency?
Answer and explanation

2 Hz

f = 1 ÷ T = 1 ÷ 0.5 = 2 Hz.

Problem 18

A wave travels at 12 m/s and has a frequency of 4 Hz. Find its wavelength.
Answer and explanation

3 m

λ = v ÷ f = 12 ÷ 4 = 3 m.

Problem 19

Which wave property is most directly related to the amount of energy a wave carries?
  1. wavelength
  2. amplitude
  3. period
  4. frequency only
Answer and explanation

amplitude

A bigger amplitude means more energy is being carried by the wave.

Problem 20

The distance from one wave crest to the next crest is the…
  1. amplitude
  2. period
  3. wavelength
  4. frequency
Answer and explanation

wavelength

Wavelength is the distance between two matching points, such as crest to crest.

Problem 21

A wave has a frequency of 50 Hz and travels at 200 m/s. Find its wavelength.
Answer and explanation

4 m

λ = v ÷ f = 200 ÷ 50 = 4 m.

Problem 22

A wave travels at 12 m/s with wavelength 3 m. Find frequency and period. Explain the reasoning in your own words.
Answer and explanation

4 Hz and 0.25 s per cycle.

Frequency=v/λ=12/3=4 Hz.

Period=1/f=1/4=0.25 s.

Response criteria

  • Use the stated conditions.
  • Show the evidence or calculation.
  • Explain the conclusion and any stated limitation.

Problem 23

A wave has frequency 5 Hz and wavelength 0.6 m. Find speed. Show the reasoning, not just the conclusion.
Hints

Hz means cycles per second, not meters per second.

Answer and explanation

v=5×0.6=3 m/s.

Problem 24

A floating marker bobs as waves pass. Must it travel across the pond with the wave?
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

No. Waves transfer energy; local matter mainly oscillates in a simple wave model, though real water can also have currents.

Problem 25

A traveling wave and local material motion differA traveling wave and local material motion differt0t1t2Disturbance travels rightMarked rope location moves up/down locally; it does not ride the crest across.
The three conceptual rope snapshots show a pattern shifting along the rope while a marked location retains its horizontal coordinate and changes vertical position. The rope wave carries a disturbance and energy; a piece of rope does not need to move from source to receiver. These qualitative snapshots omit time scales and are not a calibrated wave-speed measurement.
For this unit’s illustrated case, what is wrong with tracing the red rope mark along the moving crest to the far right?
Answer and explanation

That would confuse the traveling pattern with the local motion of the material. The marked rope location oscillates locally rather than being carried across with the crest.

Follow one material marker rather than only a crest. A transverse rope wave has local motion perpendicular to travel. Sound uses a different local-motion direction, so do not assume every mechanical wave looks like a vertical rope curve.

That would confuse the traveling pattern with the local motion of the material. The marked rope location oscillates locally rather than being carried across with the crest.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 26

A supplied wave has wavelength 0.8 m and frequency 5 Hz. Find wave speed. If its matched-model amplitude doubles at the same medium/frequency/duration, what happens to the squared-amplitude energy comparison?
Answer and explanation

Speed 0.8×5 = 4 m/s. The represented energy increases by a factor of four under the stated matched squared-amplitude comparison.

Combine a spatial repeat and a temporal repeat.

Keep all named comparison conditions fixed before using the amplitude pattern.

Speed 0.8×5 = 4 m/s. The represented energy increases by a factor of four under the stated matched squared-amplitude comparison.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 27

Using the speed of sound as 340 m/s, how far away is a thunderstorm if thunder is heard 4 seconds after the lightning flash?
Answer and explanation

1360 m

distance = speed × time = 340 × 4 = 1,360 m.

Problem 28

Sound is what type of wave?
  1. transverse
  2. longitudinal
  3. electromagnetic
  4. standing only
Answer and explanation

longitudinal

Sound particles vibrate in the same direction the wave travels, making it a longitudinal wave.

Problem 29

Increasing the frequency of a sound wave makes the pitch…
  1. higher
  2. lower
  3. louder only
  4. quieter only
Answer and explanation

higher

Higher frequency corresponds to higher pitch.

Problem 30

Sound CANNOT travel through…
  1. water
  2. steel
  3. a vacuum (empty space)
  4. air
Answer and explanation

a vacuum (empty space)

Sound needs a medium of particles to travel through, so it cannot travel through a vacuum.

Problem 31

Using the words compression and rarefaction, explain how a speaker creates sound.
Answer and explanation

The speaker cone vibrates back and forth, pushing air molecules together to create compressions and pulling them apart to create rarefactions. This repeating pattern travels outward through the air as a sound wave.

Problem 32

A sound wave travels at 340 m/s and has a wavelength of 0.85 m. Find its frequency.
Answer and explanation

400 Hz

f = v ÷ λ = 340 ÷ 0.85 = 400 Hz.

Problem 33

An echo returns after 0.4 s. Using sound speed 340 m/s, find the distance to the reflecting wall. Explain the reasoning in your own words.
Answer and explanation

68 m to the wall in this model.

Total path=340×0.4=136 m.

The path goes to the wall and back, so wall distance=136/2=68 m.

Response criteria

  • Use the stated conditions.
  • Show the evidence or calculation.
  • Explain the conclusion and any stated limitation.

Problem 34

A sound has frequency 200 Hz and another 400 Hz. Which is higher pitched under the simple comparison? Show the reasoning, not just the conclusion.
Hints

Remember the return path; the echo delay is not one-way time.

Answer and explanation

The 400 Hz sound, because its frequency is higher.

Problem 35

Why cannot ordinary sound travel through a vacuum between two objects?
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

Sound needs particles of a medium to transmit mechanical disturbances; a vacuum lacks that medium.

Problem 36

Sound as compressions and rarefactionsSound is a pressure variation that needs a mediumcompressionrarefactiontravels through the mediumIn a vacuum there are no particles to compress, so sound does not travel
A sound wave is a pattern of crowding and spreading passing through matter. Drawing it as particles rather than as a curve makes the requirement obvious: remove the particles and there is nothing left to carry the pattern.
For this unit’s illustrated case, what travels from a speaker to the listener in this model?
Answer and explanation

The pressure disturbance and energy travel through the air. Individual particles move locally rather than carrying themselves from speaker to listener.

Draw a line of particles with alternating close and less-close spacing. Show travel and local motion along the same axis in the longitudinal model. Do not show one particle traveling all the way from a speaker to a listener.

The pressure disturbance and energy travel through the air. Individual particles move locally rather than carrying themselves from speaker to listener.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 37

An echo returns after 0.3 s in a supplied air model with sound speed 340 m/s. Find the reflector distance and explain why using the full 102 m as the one-way distance is wrong.
Answer and explanation

Round-trip length is 340×0.3 = 102 m, so reflector distance is 51 m. The measured time includes travel out and back.

Draw both travel legs.

Divide total path by two only under the stated same-path out-and-back comparison.

Round-trip length is 340×0.3 = 102 m, so reflector distance is 51 m. The measured time includes travel out and back.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 38

OpenSciEd graph A of source position in millimetres against time from 0 to 0.01 seconds, showing repeated vibrations around a mean position of about 20 millimetres.
OpenSciEd 8.2 Sound Waves, Lesson 5: actual position-versus-time record A. Read the labeled axes and estimate a cycle interval before opening the worked guidance. The vertical value is the vibrating point’s position relative to a coordinate origin, not air pressure or sound wavelength. Sound-source vibration graph A · OpenSciEd · 8.2 Sound Waves, Lesson 5, source, CC BY 4.0. Figure excerpt rendered from the PDF and resized for the web.
Read OpenSciEd record A. Estimate a peak-to-peak cycle interval, calculate cycles per second and measure displacement amplitude about the midline. Explain why its mean position near 20 mm is not its amplitude. Approximate graph readings are expected.
Answer and explanation

One cycle takes about 0.0033 s, giving frequency about 300 Hz using cycles per second = 1/period. The midline is near 20 mm and extrema are about 19.2 and 20.8 mm, so displacement amplitude is about 0.8 mm. Amplitude measures departure from the midline, not distance from the coordinate origin. Allow reasonable approximate readings from this source graph.

Compare consecutive peaks: about 0.0033 s per cycle.

Compute 1/period, approximately 300 cycles per second, or Hz.

Amplitude is about 20.8−20 = 0.8 mm (half the peak-to-peak displacement).

Response criteria

  • Read time on the horizontal axis; do not call it wavelength.
  • Estimate frequency from repeats per second.
  • Measure amplitude from the midline and distinguish coordinate origin from equilibrium.

Problem 39

OpenSciEd graph B of source position in millimetres against time from 0 to 0.01 seconds, showing repeated vibrations around a mean position of about 20 millimetres.
OpenSciEd 8.2 Sound Waves, Lesson 5: actual position-versus-time record B. Read the labeled axes and estimate a cycle interval before opening the worked guidance. The vertical value is the vibrating point’s position relative to a coordinate origin, not air pressure or sound wavelength. Sound-source vibration graph B · OpenSciEd · 8.2 Sound Waves, Lesson 5, source, CC BY 4.0. Figure excerpt rendered from the PDF and resized for the web.
Read OpenSciEd record B. Estimate its period, frequency and amplitude. Compare it with record A, whose frequency is about 300 Hz and amplitude about 0.8 mm. Which vibration property has changed by a factor of two, and which has stayed approximately the same?
Answer and explanation

One cycle takes about 0.0017 s, giving frequency about 600 Hz using cycles per second = 1/period. The midline is near 20 mm and extrema are about 19.2 and 20.8 mm, so displacement amplitude is about 0.8 mm. Amplitude measures departure from the midline, not distance from the coordinate origin. Allow reasonable approximate readings from this source graph. B has about twice A’s frequency and half its period, while displacement amplitude stays approximately 0.8 mm. Faster repetition does not automatically mean a larger vibration.

Compare consecutive peaks: about 0.0017 s per cycle.

Compute 1/period, approximately 600 cycles per second, or Hz.

Amplitude is about 20.8−20 = 0.8 mm (half the peak-to-peak displacement).

Response criteria

  • Read time on the horizontal axis; do not call it wavelength.
  • Estimate frequency from repeats per second.
  • Measure amplitude from the midline and distinguish coordinate origin from equilibrium.

Problem 40

OpenSciEd graph C of source position in millimetres against time from 0 to 0.01 seconds, showing repeated vibrations around a mean position of about 20 millimetres.
OpenSciEd 8.2 Sound Waves, Lesson 5: actual position-versus-time record C. Read the labeled axes and estimate a cycle interval before opening the worked guidance. The vertical value is the vibrating point’s position relative to a coordinate origin, not air pressure or sound wavelength. Sound-source vibration graph C · OpenSciEd · 8.2 Sound Waves, Lesson 5, source, CC BY 4.0. Figure excerpt rendered from the PDF and resized for the web.
Read OpenSciEd record C. Estimate period, frequency and amplitude. The 0.010 s window contains about one and a half cycles. Why would counting only its one fully completed cycle underestimate the frequency? Use the peak-to-peak interval or include the partial cycle.
Answer and explanation

One cycle takes about 0.0067 s, giving frequency about 150 Hz using cycles per second = 1/period. The midline is near 20 mm and extrema are about 19.2 and 20.8 mm, so displacement amplitude is about 0.8 mm. Amplitude measures departure from the midline, not distance from the coordinate origin. Allow reasonable approximate readings from this source graph. About 1.5 cycles in 0.010 s gives 150 Hz. Counting only one ignores the half-cycle and would incorrectly give 100 Hz; use the measured period or account for the partial cycle.

Compare consecutive peaks: about 0.0067 s per cycle.

Compute 1/period, approximately 150 cycles per second, or Hz.

Amplitude is about 20.8−20 = 0.8 mm (half the peak-to-peak displacement).

Response criteria

  • Read time on the horizontal axis; do not call it wavelength.
  • Estimate frequency from repeats per second.
  • Measure amplitude from the midline and distinguish coordinate origin from equilibrium.

Problem 41

A radio wave has a frequency of 1,000,000 Hz. Using the speed of light as 300,000,000 m/s, find its wavelength.
Answer and explanation

300 m

λ = v ÷ f = 300,000,000 ÷ 1,000,000 = 300 m.

Problem 42

Which type of EM wave has the LONGEST wavelength?
  1. gamma rays
  2. visible light
  3. radio waves
  4. X-rays
Answer and explanation

radio waves

Radio waves sit at the long-wavelength end of the electromagnetic spectrum.

Problem 43

Which listed electromagnetic region has the highest energy PER PHOTON?
  1. radio waves
  2. microwaves
  3. visible light
  4. gamma rays
Answer and explanation

gamma rays

Gamma rays have higher photon energy because their frequencies are higher. Total delivered energy also depends on how much radiation arrives and for how long.

Problem 44

When light passes through clear glass, most of it is…
  1. reflected
  2. absorbed
  3. transmitted
  4. turned into sound
Answer and explanation

transmitted

Clear glass mostly transmits light, letting it pass through.

Problem 45

Explain why we see a red apple as red.
Answer and explanation

The apple's surface absorbs most colors of light but reflects red wavelengths back to our eyes, so we perceive the apple as red.

Problem 46

A pencil looks bent when placed in a glass of water because light…
  1. is absorbed at the surface
  2. is only reflected
  3. refracts (bends) when passing from water to air
  4. stops moving inside the water
Answer and explanation

refracts (bends) when passing from water to air

Light bends (refracts) as it passes between materials like water and air, making the pencil appear bent.

Problem 47

A red shirt appears bright under white light but dark under blue light. Explain without changing the shirt's material. Explain the reasoning in your own words.
Answer and explanation

The reflected light depends on both the material and the illumination.

White light contains red wavelengths that the material can reflect toward the eye.

Blue illumination provides little red light to reflect and much may be absorbed.

Response criteria

  • Use the stated conditions.
  • Show the evidence or calculation.
  • Explain the conclusion and any stated limitation.

Problem 48

White light splits into colors through a prism. What property differs among the colors? Show the reasoning, not just the conclusion.
Hints

Compare speed in the same medium; do not confuse frequency with speed.

Answer and explanation

Frequency and wavelength differ; frequency remains unchanged when light passes between stationary media, while speed and wavelength can change.

Problem 49

Why can sunlight cross space while ordinary sound cannot?
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

Light is electromagnetic and needs no material medium; sound is a mechanical disturbance requiring matter.

Problem 50

Energy per photon differs from total energy arrivingEnergy per photon differs from total energy arrivingLower-frequency caseEnergy per photon: 1 relative unit(s)Total for matched area/time: 8Higher-frequency caseEnergy per photon: 2 relative unit(s)Total for matched area/time: 6
The deliberately simplified lower-frequency case has eight photons at one relative energy unit each; the higher-frequency case has three at two units each. Totals are eight and six under the matched area/time comparison. The circles are a counting aid rather than literal photon shapes. Higher frequency means higher energy per photon, but total exposure also depends on how many arrive and the comparison conditions.
For this unit’s illustrated case, which case has more energy per photon, and which has more total supplied energy for the matched comparison?
Answer and explanation

The higher-frequency case has more per photon (2 versus 1). The lower-frequency case has more total (8 versus 6), because it has more supplied photons.

A photon is a quantum of electromagnetic radiation. Per-photon energy, arrival amount and exposure duration are distinct. Do not replace a total-energy comparison with a frequency-only slogan when the photon counts or duration also change.

The higher-frequency case has more per photon (2 versus 1). The lower-frequency case has more total (8 versus 6), because it has more supplied photons.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 51

For the same measured incoming 120 energy-units, a sheet reflects 30 and transmits 70. Find the absorbed amount in the stated complete account and explain why color under one lamp does not fix appearance under every lamp.
Answer and explanation

Absorbed amount is 120−30−70 = 20 units. Appearance depends on the incident wavelengths and the surface’s reflection toward the observer; a different lamp can change it.

Keep reflected, transmitted and absorbed pathways distinct.

Name both source and surface in a color explanation.

Absorbed amount is 120−30−70 = 20 units. Appearance depends on the incident wavelengths and the surface’s reflection toward the observer; a different lamp can change it.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 52

Why does a fixed magnet alone not explain a complete changing sound?
Answer and explanation

The time-varying input and resulting changing force are also needed to produce the membrane’s varying motion and air disturbance.

The time-varying input and resulting changing force are also needed to produce the membrane’s varying motion and air disturbance.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 53

What must two people agree on before flashes form a reliable message?
Answer and explanation

The encoding rules, timing and how to distinguish message boundaries and symbols; the physical carrier alone does not define the meaning.

The encoding rules, timing and how to distinguish message boundaries and symbols; the physical carrier alone does not define the meaning.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 54

Does digital transmission prevent all error?
Answer and explanation

No. Noise can cause incorrect symbol decisions, especially near a threshold. Reliability depends on the system and code, not merely the digital label.

No. Noise can cause incorrect symbol decisions, especially near a threshold. Reliability depends on the system and code, not merely the digital label.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 55

What distinguishes the sound pathway from the magnetic pathway?
Answer and explanation

Sound requires material interactions in a medium. Magnetic interactions can occur across a vacuum; the two effects do not share the same air requirement.

Sound requires material interactions in a medium. Magnetic interactions can occur across a vacuum; the two effects do not share the same air requirement.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 56

Illustrative received values are 0.15, 0.85, 0.48 and 0.88 with threshold 0.5. A drawing shows electrical input jumping directly to an ear with no speaker or air. Decode the values, identify the less robust reading and revise the drawing with intermediate interactions.
Answer and explanation

The decoded sequence is 0101. The 0.48 value is closest to the threshold, so small noise could change its symbol. Add the coil–magnet interaction, attached membrane vibration, successive air interactions and receiver. The drawing should not imply that charge or air particles travel the entire information path unchanged.

The decoded sequence is 0101. The 0.48 value is closest to the threshold, so small noise could change its symbol. Add the coil–magnet interaction, attached membrane vibration, successive air interactions and receiver. The drawing should not imply that charge or air particles travel the entire information path unchanged.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 57

A magnet still attracts another magnet in a vacuum, but a distant ordinary sound cannot be heard through the gap. Is the evidence contradictory?
Answer and explanation

No. Magnetic fields can mediate an interaction through a vacuum, while ordinary sound requires a material medium. Different mechanisms predict the different observations.

No. Magnetic fields can mediate an interaction through a vacuum, while ordinary sound requires a material medium. Different mechanisms predict the different observations.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 58

Evaluate and correct: A digital message cannot be corrupted.
Answer and explanation

Noise can cause a reading to cross the decision threshold; a code and receiver design influence error detection and reliability.

Noise can cause a reading to cross the decision threshold; a code and receiver design influence error detection and reliability.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 59

Choose one prediction from this unit. Explain a comparison that could test it, specifying observations, changed and matched conditions, and a result that would challenge it.
Answer and explanation

In a supplied vacuum comparison, magnets can still interact while no ordinary airborne sound crosses an empty gap. The magnetic force and sound transmission need different models. Use evidence about the actual gap rather than claim that all effects require air. Sound requires material interactions in a medium. Magnetic interactions can occur across a vacuum; the two effects do not share the same air requirement.

In a supplied vacuum comparison, magnets can still interact while no ordinary airborne sound crosses an empty gap. The magnetic force and sound transmission need different models. Use evidence about the actual gap rather than claim that all effects require air. Sound requires material interactions in a medium. Magnetic interactions can occur across a vacuum; the two effects do not share the same air requirement.

Response criteria

  • Use the supplied conditions and relevant evidence.
  • Explain the scientific mechanism or calculation.
  • State a meaningful limitation or testable next step.

Problem 60

Received values 0.3 and 0.7 use threshold 0.5. Decode the two symbols and explain why replacing an air gap with a vacuum distinguishes sound from magnetic interaction.
Hints

Distinguish the observed quantities, the proposed mechanism and its conditions.

Answer and explanation

Symbols are 0 and 1. Ordinary sound requires material interactions and cannot use a vacuum gap as an air medium. Magnetic interaction can act across a vacuum. The threshold rule can still make errors if noise alters the values.

Symbols are 0 and 1. Ordinary sound requires material interactions and cannot use a vacuum gap as an air medium. Magnetic interaction can act across a vacuum. The threshold rule can still make errors if noise alters the values.

Problem 61

A magnet still attracts another magnet in a vacuum, but a distant ordinary sound cannot be heard through the gap. Is the evidence contradictory? Explain a condition that would change this conclusion.
Hints

Distinguish the observed quantities, the proposed mechanism and its conditions.

Answer and explanation

No. Magnetic fields can mediate an interaction through a vacuum, while ordinary sound requires a material medium. Different mechanisms predict the different observations.

No. Magnetic fields can mediate an interaction through a vacuum, while ordinary sound requires a material medium. Different mechanisms predict the different observations.

Problem 62

A physical signal and its interpreted message differA physical signal and its interpreted message differOne chosen code: three short pulses means “ready”.pulsepulsepulseCarrier: changing physical pattern. Message: meaning assigned by a code.A larger pulse does not automatically change this three-pulse message.
Three pulses form a changing physical pattern. Under the explicitly chosen classroom code they mean ready. The material disturbance is the carrier, while the meaning depends on a shared code and receiver. A different code could assign different meaning to the same pulses. Changing pulse size within a readable range need not change the encoded pulse count.
For this unit’s illustrated case, would a receiver that has never learned the three-pulse code automatically know the message? What information is missing?
Answer and explanation

No. It can detect a pattern but needs the agreed code/context to interpret ready. Physical detection and message interpretation are different steps.

A signal is an observable changing pattern used to convey information. A code links a pattern to meaning. Explain both the physical mechanism carrying it and the rule used to interpret it.

No. It can detect a pattern but needs the agreed code/context to interpret ready. Physical detection and message interpretation are different steps.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 63

A continuous signal is recorded every 0.1 s and rounded to only three allowed levels. Name two kinds of lost detail and explain why merely taking samples faster does not solve both.
Answer and explanation

Changes between sample times and finer level differences are lost. Faster sampling improves temporal coverage but does not add more allowed amplitude levels; the encoding and reconstruction also matter.

Separate sampling times from quantized levels.

State which omitted detail each proposed change addresses.

Changes between sample times and finer level differences are lost. Faster sampling improves temporal coverage but does not add more allowed amplitude levels; the encoding and reconstruction also matter.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

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