MS-PS4-1: Using Math to Model Waves, Amplitude and Energy
In plain English: MS-PS4-1 is the NGSS middle school performance expectation that asks students to use mathematical representations, such as wave graphs, tables and simple ratios, to describe a model of repeating waves, including how a wave's amplitude is related to its energy. Twice the amplitude means about four times the energy. It is usually taught in grade 6, 7 or 8 physical science.
Use mathematical representations to describe a simple model for waves that includes how the amplitude of a wave is related to the energy in a wave.
Clarification Statement: Emphasis is on describing waves with both qualitative and quantitative thinking.
Assessment Boundary: Assessment does not include electromagnetic waves and is limited to standard repeating waves.
Next Generation Science Standards · Disciplinary Core Idea: Waves and Their Applications in Technologies for Information Transfer · Official standard
Students describe repeating waves with numbers and graphs, then use those tools to find out how a wave's energy depends on its size. A wave is a repeating disturbance that carries energy from place to place without carrying the material along with it. In a simple model, every repeating wave has an amplitude (how far the material moves from its rest position, measured from the rest line to a crest), a wavelength (the distance from one crest to the next) and a frequency (how many waves pass a point each second, measured in hertz, Hz). The key relationship is that a wave's energy grows with the square of its amplitude: twice the amplitude carries 2 × 2 = 4 times the energy, and three times the amplitude carries 9 times the energy.
The NGSS Clarification Statement says: "Emphasis is on describing waves with both qualitative and quantitative thinking." The Assessment Boundary says: "Assessment does not include electromagnetic waves and is limited to standard repeating waves." Every wave on this page is a mechanical wave (rope, water or sound waves) with a steady repeating pattern. Light and other electromagnetic waves are beyond this standard. Energies are given in invented "energy units" that compare waves with each other. All data on this page are invented for teaching.
Learning Objectives
By the end of this lesson, students will be able to:
Read the amplitude, wavelength, crest and trough from a wave graph, and find frequency and period from counts and times
Use the wave model to compare waves with different amplitudes, stating that energy grows with the square of the amplitude
Decide from a data table or graph whether energy grows with amplitude or with the square of amplitude
Describe the same wave qualitatively (in words) and quantitatively (with numbers, tables and graphs)
Prior Knowledge Required
Students should already be comfortable with:
Waves are repeating patterns of motion described by amplitude and wavelength 4-PS4-1
Writing and finding whole-number exponents, such as 3² = 3 × 3 = 9 6.EE.A.1
Ratio language, such as "4 times as much" 6.RP.A.1
Show a short video of small waves on a lake and then of large storm waves at a pier (no sound needed). Ask students to answer the prompt alone, then compare with a partner.
Warm-Up Prompt
"The storm waves look about twice as tall as the lake waves. Do you think they carry twice as much energy, more than twice, or less? Write your guess and one reason."
Tally the guesses on the board. Tell students they will test the guesses with data by the end of the lesson.
Direct Instruction15 minutes
Parts of a wave (Diagram 1). The rest position is where the material sits with no wave. A crest is a high point and a trough a low point. The amplitude is measured from the rest line, not from trough to crest. The wavelength is measured from one crest to the next. The period is the time for one whole wave to pass, and frequency = 1 ÷ period. Extension (beyond MS-PS4-1; the main tool in HS-PS4-1): the wave speed is how far a crest moves each second: wavelength × frequency.
Amplitude and energy. For waves of the same frequency in the same material, energy grows with the square of amplitude: if the amplitude becomes k times as large, the energy becomes k × k = k² times as large. That is why a wave graph of energy against amplitude curves upward (Diagram 2).
Reading a wave graph (a rope wave)
A long rope is tied to a fence post and shaken. A snapshot graph (Diagram 1) shows crests 15 cm above the rest line at 0.3 m, 1.5 m and 2.7 m along the rope, and troughs 15 cm below it.
Result: Amplitude = 15 cm (rest line to crest). Wavelength = 1.5 - 0.3 = 1.2 m (crest to crest). The crest-to-trough height is 2 × 15 = 30 cm, which is twice the amplitude, not the amplitude.
Comparing ocean swells (amplitude and energy)
Invented forecast: on Monday the swell is 1 m from trough to crest; on Tuesday it is 2 m. The waves have the same period.
Result: Amplitudes are half the heights: 0.5 m and 1 m. Tuesday's amplitude is 2 times as large, so each wave carries 2 × 2 = 4 times the energy. A swell that looks twice as big delivers about 4 times as much energy to a seawall.
Frequency, period and speed (pond ripples)
A fishing bobber rises and falls 10 times in 5 seconds as ripples pass. Neighboring crests are about 40 cm apart.
Result: Frequency = 10 ÷ 5 = 2 waves per second = 2 Hz. Period = 1 ÷ 2 = 0.5 s. Extension: speed = wavelength × frequency = 0.40 m × 2 = 0.8 m/s. The bobber moves up and down; the energy, not the water, travels across the pond.
Testing the energy model with data (wave tank)
Invented data: a paddle in a lab wave tank makes waves of amplitude 1, 2, 3 and 4 cm. A sensor at the far end measures the energy each wave delivers, compared with the 1 cm wave: 1.0, 4.1, 8.8 and 16.3 energy units.
Result: Squares of the amplitudes: 1, 4, 9, 16. The measurements are within about 5% of the squares, so the data support energy growing with amplitude squared. A doubling model (1, 2, 3, 4) misses badly. Diagram 2 shows both models.
Sound from a guitar string (qualitative and quantitative)
A guitar string is plucked gently, then harder, so its amplitude grows from 1 mm to 3 mm. The note sounds louder but has the same pitch.
Result: In words: louder means more energy reaches your ear; same pitch means the same frequency. In numbers: 3 times the amplitude gives 3 × 3 = 9 times the energy. The frequency does not depend on how hard you pluck.
After each example, ask students to say the result in words first ("bigger waves, much more energy") and then in numbers ("twice the amplitude, four times the energy"). The Clarification Statement asks for both.
Guided Practice15 minutes
Work through this table together. All three waves travel on the same rope at the same frequency.
Three rope waves (invented)
Wave
Amplitude (cm)
Amplitude compared with A
Energy compared with A
A
3
1 time
1 time
B
6
?
?
C
12
?
?
Fill in the third column by dividing each amplitude by 3 cm.
Fill in the fourth column by squaring each number in the third column. (B: 2 × 2 = 4 times; C: 4 × 4 = 16 times.)
On graph paper, plot energy compared with A against amplitude, and describe the shape in words.
Write one sentence in words and one in numbers that compare waves A and C.
Independent Practice25-30 minutes
Pairs run Floor Rope Waves (Activity 1), then complete Model Test: Doubling or Squaring? (Activity 2). Each student writes a short conclusion that answers the warm-up question with numbers from the activities.
Collect the conclusions. Check that amplitude is measured from the rest line, that frequency is waves per second, and that comparisons use the square of the amplitude ratio.
Closure10-15 minutes
Groups do the Wave Card Match (Activity 3). Then each student completes the exit ticket.
Exit ticket: "Return to the warm-up. The storm waves had about twice the amplitude of the lake waves. About how many times as much energy did each storm wave carry? Explain in words and in numbers." Check that students square the ratio instead of doubling.
Differentiation Strategies
For Struggling Students
Give a labeled wave graph template with the rest line drawn, so students mark crest, trough, amplitude and wavelength on top of it
Use a times table of squares (1, 4, 9, 16, 25) as a reference card while comparing energies
Have students act out amplitude with their arms (small and large swings at the same beat) before working with numbers
For Advanced Students
Ask students to work backward: if one wave carries 25 times the energy of another, what is the ratio of amplitudes, and why?
Have students write the model as a rule, energy = c × amplitude², and find c for the Activity 2 data
Ask how the rope data show that wave speed is set by the rope, not by how hard or how often you shake it
Assessment Guidance
What to Look For
Check that students measure amplitude from the rest line, find wavelength crest to crest, and compute frequency as waves per second. When comparing energy, look for the square of the amplitude ratio (2 times the amplitude, 4 times the energy). Listen for students who use the crest-to-trough height as the amplitude, who mix up period and frequency, or who say energy doubles when amplitude doubles.
02
Classroom Activities
3 Activities
1
Floor Rope Waves
25 minPairs
Pairs make waves on a rope lying on the floor and measure amplitude, wavelength and frequency for different kinds of shaking.
Procedure
Lay a 3 m rope straight on a smooth floor. Put masking tape lines along the rope at 10 cm and 20 cm on each side of it to mark amplitudes.
One partner holds the far end still. The other shakes the near end side to side along the floor: (1) gently, to the 10 cm lines, at a steady beat; (2) strongly, to the 20 cm lines, at the same beat; (3) gently but faster.
Film each shake from above next to a meter stick. Use the video to measure the wavelength (crest to crest) and count the waves in 10 seconds.
Safety: keep the rope on the floor, clear the area around it, and do not whip it.
Sample Data (invented)
Gentle shake: amplitude 10 cm, wavelength 1.0 m, 15 waves in 10 s. Strong shake at the same beat: amplitude 20 cm, wavelength 1.0 m, 15 waves in 10 s. Gentle, faster shake: amplitude 10 cm, wavelength 0.6 m, 25 waves in 10 s.
Discussion Questions
Find the frequency for each shake. Extension: find the wave speed (wavelength × frequency) for each shake. What do you notice about the speeds?
Which shake carried more energy, the gentle one or the strong one at the same beat? About how many times as much?
Which change made the wavelength shorter, and why?
Modification for Distance Learning
Students use a phone charging cable or a long scarf on a table at home, or analyze the sample data and a teacher video.
2
Model Test: Doubling or Squaring?
20 minPairs
Pairs test two models against invented data from a lab wave tank: "energy doubles when amplitude doubles" and "energy grows with amplitude squared".
The Data (invented)
A wave tank with a sensor measured these energies: amplitude 1 cm, 0.5 energy units; 2 cm, 2.1 units; 3 cm, 4.4 units; 4 cm, 8.1 units.
Tasks
Graph energy against amplitude on graph paper. Is the graph a straight line through zero, or does it curve upward?
Make a table of predictions for each model, starting from the 1 cm value, and compare them with the data.
Write a claim about which model fits, with two numbers from the table as evidence.
Challenge Variation
Write the rule as energy = c × amplitude² and find a value of c that fits all four points. Then predict the energy of a 5 cm wave.
3
Wave Card Match
15 minGroups of 3
Each group gets 12 cards describing 4 waves on the same rope at the same frequency. For each wave there is a graph card, a numbers card and a words card. Groups sort the cards into 4 sets of 3.
The 12 Cards
Graph cards (4): wave graphs with amplitudes of 2 cm, 4 cm, 6 cm and 1 cm and the same wavelength.
Numbers cards (4): "energy 1 time wave 1's", "energy 4 times wave 1's", "energy 9 times wave 1's" and "energy 1/4 of wave 1's".
Words cards (4): "the reference wave", "a little bigger, much more energy", "the biggest wave, by far the most energy" and "the smallest wave, much less energy".
Discussion Questions
Which card was hardest to match, and what helped you decide?
Why does the words card for the biggest wave say "by far"?
Make a new set of 3 cards for a wave with an amplitude of 8 cm.
Modification for Distance Learning
Use a drag-and-drop slide with the 12 cards, or have students draw the 4 graphs and write the matching cards themselves.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Parts of a Rope Wave
A snapshot of the rope wave in Example 1, drawn to scale from a repeating wave pattern. The amplitude (15 cm) is measured from the rest position to a crest, and the wavelength (1.2 m) from one crest to the next.
Diagram 2: Wave Energy Against Amplitude
Invented wave tank data from Example 4, drawn to scale. The points follow the curve energy = amplitude² (in units of the 1 cm wave's energy), not the dashed straight line a doubling model would give. The curve bends upward because each step up in amplitude adds more energy than the one before.
04
Homework Assignment
~30 min
MS-PS4-1 Homework: Describing Waves with Numbers and Graphs
Directions: Show your work. Describe each answer in words and in numbers. Energy comparisons use "times as much". All data are invented.
Part 1: Read Wave Representations (Problems 1-3)
A snapshot graph of a water wave shows crests at 0.5 m, 2.5 m and 4.5 m. Each crest is 0.3 m above the rest line and each trough is 0.3 m below it. (a) Find the amplitude. (b) Find the wavelength. (c) Find the trough-to-crest height and explain why it is not the amplitude.
An anchored rowboat rises and falls 12 times in 60 seconds as ocean waves pass under it. The crests are about 40 m apart. (a) Find the frequency and the period. (b) Extension (beyond MS-PS4-1): how fast do the crests travel? (c) Does the rowboat travel along with the waves? Explain.
Two waves travel on the same rope with the same wavelength. Wave P has an amplitude of 6 cm and wave Q has an amplitude of 18 cm. (a) Sketch both waves on one graph. (b) How many times as much energy does Q carry? (c) Explain your answer in words.
Part 2: Use the Amplitude and Energy Model (Problems 4-6)
A wave tank measured these energies: amplitude 0.5 cm, 0.26 energy units; 1.0 cm, 1.0 unit; 1.5 cm, 2.3 units; 2.0 cm, 3.9 units. (a) Graph energy against amplitude. (b) Make a table of the predictions of both models (doubling and squaring), starting from the 1.0 cm value. (c) Which model fits better? Give evidence.
On a calm day, waves at a harbor wall are 1 m from trough to crest. During a storm they are 3 m from trough to crest. (a) Find both amplitudes. (b) How many times as much energy does each storm wave carry? (c) Explain to a harbor manager, in words, why a wall built for calm days may fail in a storm.
A drum is tapped softly, so its head moves 1 mm from rest, and then hit hard, so it moves 4 mm. The pitch stays the same. (a) How many times as much energy does the hard hit send out as sound? (b) What amplitude would give 4 times the energy of the soft tap? (c) Describe what you would hear differently, and what stays the same.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
Reading Waves
Amplitude from the rest line, wavelength crest to crest, frequency in waves per second, all with units
One quantity misread, such as crest-to-trough height used as amplitude
Energy Model
Squares the amplitude ratio to compare energies and works backward when needed
Uses the ratio without squaring, or squares the amplitudes but compares them wrongly
Graphs and Data
Accurate graph and a model choice backed by two numbers from the data
Graph drawn but the model choice is not backed by numbers
Words and Numbers
Every answer is stated in words and in numbers
Only one of the two is given
05
Quiz: 20 Questions
Interactive, with answers
Instructions
All waves are mechanical waves (rope, water or sound), and all data are invented. In this model, energy grows with the square of the amplitude. Use a calculator if you like.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
On a wave graph, which measurement gives the amplitude?
Answer: C
Amplitude is how far the material moves away from its rest position, so it is measured from the rest line to the top of a crest (or the bottom of a trough). Choice A is the wavelength. Choice B is twice the amplitude. Choice D is half a wavelength.
Question 2 of 20 · Multiple Choice
A graph of a rope wave shows crests 8 cm above the rest line and troughs 8 cm below it. The crests are 50 cm apart. What is the amplitude?
Answer: A
The amplitude is measured from the rest line to a crest: 8 cm. Choice B, 16 cm, is the crest-to-trough height, a common mix-up. Choice C is the wavelength, and D is half the wavelength.
Question 3 of 20 · Multiple Choice
On a wave graph, one crest is at 0.4 m, the next trough is at 0.7 m and the next crest is at 1.0 m. What is the wavelength?
Answer: D
The wavelength is the distance from one crest to the next: 1.0 - 0.4 = 0.6 m. Choice A is only crest to trough (half a wavelength). Choice B reads a position as a length, and C adds the two positions.
Question 4 of 20 · Multiple Choice
A cork on a pond bobs up and down 15 times in 10 seconds as waves pass. What is the frequency of the waves?
Answer: B
Frequency is the number of waves per second: 15 / 10 = 1.5 waves per second, or 1.5 hertz (Hz). Choice A divides the wrong way: 10 / 15 is about 0.67 s, which is the period (seconds per wave), not the frequency. Choice C uses the count without the time.
Question 5 of 20 · Multiple Choice
In a simple wave model, energy grows with the square of the amplitude. A wave's amplitude grows from 2 cm to 10 cm, with nothing else changing. How many times as much energy does it carry?
Answer: C
The amplitude is 10 / 2 = 5 times as large, and energy grows with the square, so the energy is 5 × 5 = 25 times as much. Choice A forgets to square. Choice B uses the difference (10 - 2) instead of the ratio, and choice D squares the new amplitude alone (10 × 10) instead of the ratio.
Question 6 of 20 · Multiple Choice
A wave's amplitude is cut in half, while its frequency and wavelength stay the same. How does its energy change?
Answer: A
Half the amplitude gives (1/2) × (1/2) = 1/4 of the energy. Choice B treats energy as if it grew in step with amplitude. Choice D mixes up speed with energy: the speed is set by the medium, while the energy depends on the amplitude.
Question 7 of 20 · Multiple Choice
Two water waves have the same wavelength. Wave B carries 36 times as much energy as wave A. How many times as large is B's amplitude?
Answer: D
Energy grows with the square of amplitude, so we need a number that times itself gives 36: 6 × 6 = 36, so B's amplitude is 6 times as large. Choice A forgets the square, and choice B halves 36 instead of finding the number that squares to 36.
Question 8 of 20 · Multiple Choice
A student shakes a long rope on the floor. Which change gives the waves more energy while keeping the same wavelength?
Answer: B
Moving the hand farther at the same rate makes a bigger amplitude, and the same rate keeps the same frequency, so the wavelength stays the same. Choice A changes the frequency, which changes the wavelength. A longer rope (C) does not change the waves it carries.
Question 9 of 20 · Short Answer
Invented data from a wave tank: amplitudes of 1, 2 and 3 cm gave energies of 1.0, 3.9 and 9.2 energy units. Does this data fit the model "energy grows with the square of the amplitude" or the model "energy doubles when amplitude doubles"? Explain with numbers.
It fits the square model. Squaring the amplitudes gives 1, 4 and 9, very close to 1.0, 3.9 and 9.2. If energy only doubled when amplitude doubled, the 2 cm and 3 cm waves would have about 2 and 3 units, not about 4 and 9. Full credit needs the comparison for at least two amplitudes.
Question 10 of 20 · Multiple Choice
Each table lists amplitudes of 1, 2 and 3 cm and the energies a wave tank measured. Which table follows the model "energy grows with the square of the amplitude"?
Answer: C
In table C, 2 cm has 4 times the energy of 1 cm (12 = 4 × 3) and 3 cm has 9 times (27 = 9 × 3), so energy grows with the square. Table A grows in step with amplitude and table B doubles at each step. Table D applies the factor 9 to the 2 cm energy (12 × 9 = 108), but 9 times compares the 3 cm wave with the 1 cm wave, so it must multiply the 1 cm energy: 3 × 9 = 27.
Question 11 of 20 · Multiple Choice
On a calm day, waves at a beach are 0.4 m from trough to crest. During a storm they are 1.2 m from trough to crest. About how many times as much energy does each storm wave carry?
Answer: D
The amplitudes are half the heights, 0.2 m and 0.6 m, so the storm amplitude is 3 times as large and the energy is 3 × 3 = 9 times as much. Choice A forgets to square. Choice C multiplies by 3 three times instead of two.
Question 12 of 20 · Multiple Choice
Two waves travel on the same rope at the same frequency. On a wave graph, wave R has crests 4 cm above the rest line, and wave S has troughs 12 cm below the rest line. How many times as much energy does wave S carry?
Answer: A
Amplitude is measured from the rest line, to a crest or to a trough, so the amplitudes are 4 cm and 12 cm. S has 12 ÷ 4 = 3 times the amplitude, so it carries 3 × 3 = 9 times the energy. Choice B forgets to square. Choice D uses the difference (12 - 4 = 8) instead of the ratio, and choice C squares that difference (8 × 8 = 64).
Question 13 of 20 · Short Answer
A water park's wave pool can make waves with an amplitude of 0.3 m or 0.6 m. Use the wave model to compare their energy, and explain why lifeguards might keep small children out of the pool when the bigger setting is on.
The bigger setting has twice the amplitude, so each wave carries 2 × 2 = 4 times as much energy. A wave with 4 times the energy can push much harder on a swimmer and knock a small child over, so the bigger setting is riskier even though the waves are only twice as tall.
Question 14 of 20 · Multiple Choice
Which of these is NOT part of a simple model of a repeating wave?
Answer: B
A simple wave model is described by its wavelength, frequency and amplitude (and the speed that follows from them). The color of the rope or water does not describe the wave pattern. Students sometimes include features of the medium in the wave model by mistake.
Question 15 of 20 · Multiple Choice
A student says: "The wave is 10 cm from trough to crest, so its amplitude is 10 cm." What is wrong with this statement?
Answer: C
Amplitude is measured from the rest position, which is halfway between trough and crest, so it is 10 / 2 = 5 cm. Choice B doubles instead of halving, and choice D is wrong because amplitude can be read from the shape alone.
Question 16 of 20 · Short Answer
Sketch a wave graph for a rope wave with an amplitude of 4 cm and a wavelength of 20 cm, starting at the rest line at 0 cm and rising. Where are the crests and troughs between 0 and 50 cm?
Crests at 5, 25 and 45 cm (4 cm above the rest line); troughs at 15 and 35 cm (4 cm below). The wave crosses the rest line at 0, 10, 20, 30, 40 and 50 cm. Full credit needs a labeled rest line, amplitude and one wavelength marked from crest to crest.
Question 17 of 20 · Multiple Choice
A rope wave takes 0.25 s for one whole wave to pass a point. What is its frequency?
Answer: D
The period is 0.25 s per wave, so the number of waves each second is 1 / 0.25 = 4. Choice A gives the period as if it were the frequency. Choices B and C move the decimal point instead of dividing.
Question 18 of 20 · Short Answer
Wave A has an amplitude of 5 cm and wave B has an amplitude of 10 cm. Both have a frequency of 2 Hz. Which wave carries more energy, and how many times as much? Explain using the model.
Wave B. Its amplitude is 10 / 5 = 2 times as large, and in the simple model energy grows with the square of amplitude, so B carries 2 × 2 = 4 times as much energy as A. The equal frequencies mean amplitude is the only thing that differs.
Question 19 of 20 · Multiple Choice
Invented data: waves with amplitudes of 1, 2 and 3 cm carried 2, 8 and 18 energy units. Using the same pattern, how much energy would a 4 cm wave carry?
Answer: A
The energy is 2 times the amplitude squared: 2 × 1 = 2, 2 × 4 = 8, 2 × 9 = 18, so 4 cm gives 2 × 16 = 32 units. Choice B adds 6 again (the first step), choice C adds 10 again (the last step), and choice D doubles 18 as if the amplitude had doubled.
Question 20 of 20 · Short Answer
A classmate says: "If you double a wave's amplitude, you double its energy." Use these invented data to critique the claim: amplitudes of 1, 2 and 4 cm gave energies of 1.1, 3.9 and 16.2 energy units.
The data do not support the claim. Doubling from 1 to 2 cm raised the energy from 1.1 to 3.9 units, about 4 times, not 2 times. Doubling again from 2 to 4 cm raised it from 3.9 to 16.2, again about 4 times. The data fit the model that energy grows with the square of the amplitude (1, 4, 16).
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does MS-PS4-1 mean?
MS-PS4-1 asks middle school students to use math, such as graphs, tables and ratios, to describe a simple model of waves that includes how amplitude relates to energy. The code means Middle School, Physical Science, core idea 4 (Waves), performance expectation 1. The practice is using mathematics and computational thinking.
Does MS-PS4-1 include light waves?
No. The Assessment Boundary says assessment "does not include electromagnetic waves and is limited to standard repeating waves." Light and radio waves are electromagnetic, so they are beyond this standard. Use rope waves, water waves and sound waves, which travel through a material.
How is amplitude measured?
From the rest position to the top of a crest, or to the bottom of a trough. A common mistake is to measure from trough to crest, which gives twice the amplitude. On a rope lying on the floor, the rest position is the straight line of the rope before anyone shakes it.
Why does energy grow with the square of the amplitude?
A bigger wave moves each bit of material farther in the same time, so each bit moves faster, and the energy of moving material grows faster than its speed. For this standard, students state and use the pattern from data (twice the amplitude, four times the energy) rather than derive it.
What math do students need for MS-PS4-1?
Reading graphs, dividing to find ratios and frequencies, multiplying for wave speed (an extension), and squaring whole numbers and simple decimals. Squaring connects to whole-number exponents (6.EE.A.1). Working backward from an energy ratio to an amplitude ratio uses square roots of perfect squares (8.EE.A.2), so younger classes can stick to forward comparisons.
Does frequency change a wave's energy too?
Yes. For rope and water waves, shaking faster at the same amplitude also delivers energy faster. MS-PS4-1 focuses on amplitude, so every comparison on this page keeps the frequency the same and changes only the amplitude.
What is a standard repeating wave?
A wave whose pattern repeats with the same amplitude and wavelength, like the smooth up-and-down shape in Diagram 1. Single pulses, waves that grow or die out, and messy mixtures of waves are outside the Assessment Boundary.
What are common mistakes with MS-PS4-1?
Using the trough-to-crest height as the amplitude, mixing up period (seconds per wave) and frequency (waves per second), and doubling the energy when the amplitude doubles. Another is thinking the water or rope travels along with the wave, when only the energy and the pattern move forward.
How does MS-PS4-1 connect to MS-PS4-2?
MS-PS4-2 asks how waves are reflected, absorbed or transmitted by different materials. Once students know a wave carries energy that depends on its amplitude, they can describe absorption as a material taking energy out of the wave, which makes the amplitude smaller.
What comes after MS-PS4-1 in high school?
HS-PS4-1 asks students to use the relationship among frequency, wavelength and wave speed in different media, including electromagnetic waves. The wave speed = wavelength × frequency idea from this lesson becomes the main tool there.
07
Related Standards
5 standards
These standards connect to MS-PS4-1: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
4-PS4-1Prerequisite
Model wave patterns of amplitude and wavelength, and show that waves can move objects
Lesson coming soon
6.EE.A.1Prerequisite
Write and evaluate numerical expressions with whole-number exponents
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