HS-PS4-1

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Use mathematical representations to support a claim regarding relationships among the period, frequency, wavelength, and speed of waves traveling and transferring energy (amplitude, frequency) in various media.

Clarification statement: Examples of data could include descriptions of waves classified as transverse, longitudinal, mechanical, or standing, electromagnetic radiation traveling in a vacuum and glass, sound waves traveling through air and water, seismic waves traveling through Earth, and direction of waves due to reflection and refraction.

Assessment boundary: Assessment is limited to algebraic relationships and describing those relationships qualitatively.

Regents Exam Questions

Released New York State Regents exam questions that assess HS-PS4-1 are listed here by exam and question cluster. Each link opens the question with its answer key.

Exam	Cluster	Question
June 2026 Physics Regents	Kidney Stone Detection and Removal	Question 7
	Kidney Stone Detection and Removal	Question 8
	Kidney Stone Detection and Removal	Question 10
	Emission Spectra and Nuclear Fusion	Question 22
	The Cell Phone	Question 26
	Flashlight Physics	Question 31
	Voice Recognition Software	Question 43
	Voice Recognition Software	Question 44

Vocabulary

Terms from the Physics Glossary that come from this standard or from the released exam questions that assess it.

From this standard

• air
• algebraic relationships
• amplitude
• boundary
• cause and correlation
• cause and effect
• claim
• design solution
• direction
• electromagnetic radiation
• empirical evidence
• energy
• energy transferred
• frequency
• glass
• index of refraction
• investigation
• longitudinal wave
• mathematical representation
• mechanical wave
• medium
• period
• phase
• photon
• reflected ray
• reflection
• refracted ray
• refraction
• ruler and protractor
• seismic wave
• sound wave
• speed
• speed of waves
• standing wave
• support (a claim)
• transverse wave
• type of wave
• vacuum
• water
• wave
• wavelength

From released exam questions

• absorb energy – June 2026
• baseline – June 2026
• edge artifact – June 2026
• filament – June 2026
• hydrogen – June 2026
• image – June 2026
• inversely proportional – June 2026
• justification – June 2026
• laser – June 2026
• lens – June 2026
• light – June 2026
• optically denser – June 2026
• photon energy – June 2026
• refute – June 2026
• relative sound pressure – June 2026
• sampling time – June 2026
• sound – June 2026
• speed of light – June 2026
• speed of sound – June 2026
• visible light – June 2026
• wave motion – June 2026

Implied by this standard

• law of reflection (angle of incidence equals angle of reflection) – implied by "construct the reflected and/or refracted ray(s)"
• Planck's constant – the June 2026 Kidney Stone Detection and Removal rubric uses E_photon = hf with h = 6.63 × 10⁻³⁴ without naming the constant.
• Snell's law – implied by "determine the index of refraction"

Performance Level Descriptions

Every Regents exam question on HS-PS4-1 is written to match one of the performance level descriptions (PLDs) below.

Level 1: Draw a model of a wave with given characteristics or identify the characteristics of a given wave traveling and transferring energy in a medium (period, frequency, wavelength, amplitude, speed, and/or type), or identify the change in characteristics of a wave as the wave hits a boundary. June 2026 · Q31 June 2026 · Q8 June 2026 · Q43

Level 2: Use words, diagrams, and/or graphs to represent the mathematical relationships among the period, frequency, wavelength, and/or speed of waves in a medium, or use mathematical relationships to determine the direction of a wave as the wave hits a boundary (reflection and/or refraction), or given data, model(s), and/or a mathematical representation, compare the phase of points at positions on the wave or the relative amount of energy transferred due to amplitude or frequency, or determine the amount of energy transferred due to the frequency of electromagnetic radiation (photon). June 2026 · Q44

Level 3: Given data, model(s), and/or a mathematical representation, determine the period, frequency, wavelength, or speed of a wave or electromagnetic radiation (photon) traveling and transferring energy in a medium, or use mathematical relationships and a ruler and protractor to construct the reflected and/or refracted ray(s) to show the direction of a wave as it hits a boundary, or determine the index of refraction. June 2026 · Q22 June 2026 · Q7

Level 4: Use mathematical representations to support a claim regarding relationships among the period, frequency, wavelength, and speed of waves traveling and transferring energy (amplitude, frequency) in various media. June 2026 · Q10 June 2026 · Q26

Level 5: Plan and conduct an investigation and use mathematical representations to evaluate claims regarding the relationships among the period, frequency, wavelength, and speed of waves traveling and transferring energy in various media.

Notice: PLD levels!

Resources

Examples and discussion of resources for the learning, teaching, and assessment of HS-PS4-1.

This section could be expanded upon. You can help out by adding to this section.

NGSS Dimensions

Performance expectation HS-PS4-1 was developed using the following elements from the NRC document A Framework for K-12 Science Education:

Science and Engineering Practices

• Using Mathematics and Computational Thinking
  • Use mathematical representations of phenomena or design solutions to describe and/or support claims and/or explanations.

Disciplinary Core Ideas

• PS4.A: Wave Properties
  • The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

Crosscutting Concepts

• Cause and Effect
  • Empirical evidence is required to differentiate between cause and correlation and make claims about specific causes and effects.

Page contributors: Caroline Leonard, Conrad Richman

Physics | HS. Waves and Electromagnetic Radiation