HS-PS4-1: Frequency, Wavelength and Wave Speed in Different Media
In plain English: HS-PS4-1 is the NGSS high school performance expectation that asks students to use mathematical representations, such as v = fλ, to support claims about how the frequency, wavelength and speed of waves are related in different media. Students work with light, sound and seismic waves. It is usually taught in Physics or Physical Science.
Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media.
Clarification Statement: Examples of data could include electromagnetic radiation traveling in a vacuum and glass, sound waves traveling through air and water, and seismic waves traveling through the Earth.
Assessment Boundary: Assessment is limited to algebraic relationships and describing those relationships qualitatively.
Next Generation Science Standards · Disciplinary Core Idea: Waves and Their Applications in Technologies for Information Transfer · Official standard
Students use the wave equation v = fλ, ratios and graphs to support claims about how frequency, wavelength and speed are related. They show that in one medium the wavelength is inversely proportional to the frequency, and that when a wave enters a new medium its frequency stays the same while its wavelength changes in proportion to its speed. The data come from light in a vacuum and in glass, sound in air and water, and seismic waves in the Earth.
The NGSS Clarification Statement says: "Examples of data could include electromagnetic radiation traveling in a vacuum and glass, sound waves traveling through air and water, and seismic waves traveling through the Earth." The Assessment Boundary says: "Assessment is limited to algebraic relationships and describing those relationships qualitatively." Every problem on this page uses only algebra (v = fλ, T = 1/f and ratios) together with verbal descriptions. All data sets are invented for teaching, and the reference speeds are standard values stated in the Direct Instruction phase.
Learning Objectives
By the end of this lesson, students will be able to:
Use v = fλ to find any one of speed, frequency or wavelength from the other two, with correct units
Support the claim that, in one medium, wavelength is inversely proportional to frequency, using a table, a ratio or a graph
Support the claim that a wave keeps its frequency when it enters a new medium, while its wavelength changes in proportion to its speed
Apply these relationships to light in a vacuum and glass, sound in air and water, and seismic waves in the Earth
Describe each relationship in words as well as with an equation
Prior Knowledge Required
Students should already be comfortable with:
Describing waves with amplitude, wavelength and frequency MS-PS4-1
Waves being reflected, absorbed or transmitted by materials MS-PS4-2
Rearranging a formula to solve for a quantity HSA.CED.A.4
Speed as distance divided by time, and scientific notation with metric prefixes (nano, kilo, mega, giga)
Play a steady 440 Hz tone from a phone speaker. Then tell students that a swimmer underwater in a pool hears the same tone from an underwater speaker as the same musical note.
Warm-Up Prompt
"Sound travels about four times faster in water than in air, yet the swimmer hears the same note. Which of these must be different underwater: the frequency, the wavelength, or both? Write an equation that could back up your answer."
Record the predictions on the board without judging them. Many students expect the note (the frequency) to change. Come back to the predictions after Example 1.
Direct Instruction15-20 minutes
One relationship, three quantities. For any periodic wave, speed = frequency × wavelength, v = fλ, and the period is T = 1/f. Two facts turn the equation into claims students can support with numbers:
In one medium, waves of every frequency travel at (nearly) the same speed, so λ = v/f: doubling the frequency halves the wavelength. A graph of λ against f is a curve, and a graph of λ against 1/f is a straight line through the origin whose slope is v.
When a wave crosses into a new medium, the frequency stays the same (it is set by the source), so the wavelength changes in proportion to the speed: λ2/λ1 = v2/v1.
Reference speeds used on this page: light in a vacuum 3.00 × 10⁸ m/s (air is almost the same), light in glass about 2.00 × 10⁸ m/s, light in water about 2.25 × 10⁸ m/s, sound in air at 20 °C 343 m/s, in fresh water 1480 m/s, in seawater 1520 m/s, in steel 5960 m/s, and in soft body tissue 1540 m/s. Diagram 1 shows light entering glass and Diagram 2 shows λ against f for sound in air and water.
Sound in air and in water
A 440 Hz tone travels in air (343 m/s) and, from an underwater speaker, in fresh water (1480 m/s).
Result: λair = 343 ÷ 440 = 0.780 m. λwater = 1480 ÷ 440 = 3.36 m. The frequency, and so the note heard, is the same; the wavelength is 1480/343 ≈ 4.3 times longer in water because the speed is 4.3 times larger.
Light in a vacuum and in glass
A green laser gives light with a wavelength of 532 nm in a vacuum. The light enters a glass block, where its speed is 2.00 × 10⁸ m/s.
Result: f = c/λ = (3.00 × 10⁸) ÷ (532 × 10⁻⁹) = 5.64 × 10¹⁴ Hz. In glass: λ = (2.00 × 10⁸) ÷ (5.64 × 10¹⁴) = 3.55 × 10⁻⁷ m = 355 nm, which is 532 × (2.00/3.00).
Seismic waves in the mantle
An earthquake sends P waves (8.0 km/s) and S waves (4.5 km/s) through the upper mantle. Both have a frequency of 0.50 Hz.
Result: λP = 8.0 ÷ 0.50 = 16 km and λS = 4.5 ÷ 0.50 = 9.0 km. Same frequency, different speeds, so different wavelengths: the ratio 16/9.0 equals the speed ratio 8.0/4.5.
Ultrasound in body tissue
A medical ultrasound probe emits 5.0 MHz waves into soft tissue, where sound travels at 1540 m/s.
Result: λ = 1540 ÷ (5.0 × 10⁶) = 3.08 × 10⁻⁴ m ≈ 0.31 mm. The short wavelength is why high frequencies can show small structures.
After each example, ask: "What stayed the same, what changed, and which part of v = fλ shows it?" Stress that a faster medium means a longer wavelength at the same frequency, and that the source, not the medium, sets the frequency.
Guided Practice15 minutes
Pairs use the relationship to fill in a table for a 1000 Hz tone sent through three media, then use the table to support a claim.
Guided practice: a 1000 Hz tone in three media
Medium
Speed of sound (m/s)
Frequency (Hz)
Wavelength (m)
Air, 20 °C
343
1000
?
Fresh water
1480
1000
?
Steel
5960
1000
?
Compute each wavelength with λ = v/f. Key: 0.343 m, 1.48 m and 5.96 m.
Plot wavelength against speed. The points lie on a straight line through the origin with slope 1/f = 0.001 s.
Write a claim: "At a fixed frequency, wavelength is proportional to wave speed." Cite the slope and one ratio (for example 5.96/0.343 ≈ 17.4 and 5960/343 ≈ 17.4) as evidence.
Describe the relationship in words without numbers: in a faster medium, each cycle is stretched over a longer distance.
Independent Practice10-15 minutes
Each student analyzes invented ripple tank data. A glass plate makes one region of the tank shallower than the other, so the two regions act as two media for water waves (about 2 mm of water over the plate and 5 mm elsewhere).
Independent practice data (invented): shallow region
Frequency f (Hz)
3
4
5
6
Wavelength λ (cm)
5.0
3.8
3.0
2.5
Students compute fλ for each row (about 15 cm/s every time) and state a claim about the speed in the shallow region. Then they use one more measurement, λ = 4.4 cm at 5 Hz in the deep region, to find the speed there (22 cm/s) and explain, with the equation, why the wavelength is longer in the deep region when the frequency is the same.
Closure5 minutes
Return to the warm-up predictions and let students vote again. Exit ticket: "A 50 Hz hum from a pump travels through a steel pipe and then into the air of a basement. Which quantities change at the boundary, and by what factor does the wavelength change? Show the equation you used."
Differentiation Strategies
For Struggling Students
Give a v = fλ triangle and a unit table (nm = 10⁻⁹ m, kHz = 10³ Hz, MHz = 10⁶ Hz, GHz = 10⁹ Hz) for every problem
Start with whole-number spring data (1.0 Hz, 3.0 m) before scientific notation with light
Provide a claim frame: "When the wave goes from ___ to ___, its frequency ___ and its speed ___, so its wavelength ___, because λ = v/f."
For Advanced Students
Ask students to graph the helium homework data as λ against 1/f and use the slope and intercept to judge the quality of the data
Have students find the wavelength of a 60 Hz power-line hum in air and compare it with the length of the classroom
Ask students to explain why the S-P arrival gap from three seismograph stations can be used to locate an earthquake
Assessment Guidance
What to Look For
Check that students keep the frequency fixed when a wave changes medium, convert units (nm, MHz, km) before dividing, and choose the right form of v = fλ. Look for claims that name a specific number, ratio or slope as evidence and then describe the relationship in words. Listen for the idea that higher frequency means faster, which the data on this page do not support.
02
Classroom Activities
3 Activities
1
Spring Waves: Same Medium, New Medium
25 minGroups of 3-4
Groups make waves on a long spring stretched along the floor. They change the frequency and measure the wavelength in one spring, then join a heavier spring to the end and compare the wavelength on each side at one frequency.
Procedure
Stretch a long coiled spring about 6 m along a smooth floor, with a partner holding the far end still. Put tape marks every 0.5 m beside it.
Shake one end side to side in time with a phone metronome at 60, 90, 120 and 150 beats per minute (1.0, 1.5, 2.0 and 2.5 Hz). Record video and measure the distance between neighboring crests.
Tie a heavier spring to the far end. Shake at 2.0 Hz and measure the wavelength on each spring.
Safety: never let go of a stretched spring, which can snap back, and keep the floor area clear.
Sample Data (invented)
Light spring: 1.0 Hz, 3.0 m; 1.5 Hz, 2.0 m; 2.0 Hz, 1.5 m; 2.5 Hz, 1.2 m. Heavier spring at 2.0 Hz: 0.90 m. Students compute fλ for every row and compare the two springs.
Discussion Questions
What happens to fλ as the frequency changes on the light spring? What does that tell you about the speed in one medium?
At the knot, the frequency is the same on both springs. Use v = fλ to find the speed on the heavier spring and compare it with the light spring.
If you shook at 3.0 Hz, predict the wavelength on each spring before you test it.
Modification for Distance Learning
Students use a free wave-on-a-string simulation, record wavelength at four frequencies, and repeat with a higher string tension to model a second medium.
2
Resonance Tube Speed of Sound
20 minGroups of 3
Groups hold a vibrating tuning fork over a plastic tube standing in a tall cylinder of water and raise the tube until the sound is loudest. For a tube closed at the bottom by the water, the air column at the first loud point is one fourth of a wavelength. The sound wave reaches a little past the open end, by about 0.3 times the tube width (1.2 cm for this tube), so λ = 4(L + 1.2 cm). Students use λ and f to test whether the speed of sound depends on frequency.
Procedure
Stand a 60 cm plastic tube (about 4 cm wide) in a tall cylinder of water. Strike a tuning fork on a rubber block, never on the table, and hold it just above the open end.
Slowly raise the tube and mark the length of air column L where the sound is loudest. Repeat three times per fork.
Use forks of 256, 384 and 512 Hz. Wipe up spilled water right away.
Sample Data (invented)
256 Hz: L = 32.3 cm. 384 Hz: L = 21.1 cm. 512 Hz: L = 15.6 cm. Students compute λ = 4(L + 1.2 cm) and v = fλ for each fork, and compare the results with 343 m/s for air at 20 °C.
Discussion Questions
Do the three speeds agree within 1%? What does that support about the speed of sound at different frequencies?
Which fork gives the longest air column, and how does v = fλ explain it?
If the room were colder, the speed of sound would be a little lower. Predict how L would change for the 384 Hz fork.
Challenge Variation
Groups find the second loud point, where L is three fourths of a wavelength, and use the difference between the two lengths (half a wavelength) as a second measurement.
3
Claim Stations: Waves in Different Media
25 minGroups of 3-4
Four stations each give invented data for one kind of wave in two media. At each station, groups write a claim, show the mathematical representation that supports it (an equation, a ratio or a table), and describe the relationship in words. Groups rotate every 6 minutes.
Station Data
Station 1, red laser: wavelength 650 nm in air and 433 nm inside a glass block.
Station 2, underwater speaker at 2.0 kHz: wavelength 0.76 m in seawater and 0.1715 m in air.
Station 3, seismograph: a station 150 km from an earthquake records the P wave 25 s after the quake and the S wave 43 s after; both waves have a frequency of about 1.5 Hz.
Station 4, steel rail: a hammer strikes a rail 1.0 km away, making a 500 Hz ring; the sound arrives through the rail after 0.168 s and through the air after 2.92 s.
Discussion Questions
At each station, in which medium (or for which wave) is the speed larger, and how do the wavelengths show it?
At Station 1, what is the speed of light in the glass? Use the ratio of wavelengths.
At Station 3, find the speed and the wavelength of each wave. Why does the S wave arrive later even though both waves have the same frequency?
Modification for Distance Learning
Post each station as a slide. Groups work in breakout rooms and submit one claim card per station on a shared document.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Light Entering Glass Keeps Its Frequency
Green laser light (Example 2) crossing from air into glass. The wave is drawn so that the wavelength in glass is exactly 2/3 of the wavelength in air, the same ratio as the speeds. The number of crests passing each point per second (the frequency) is the same on both sides.
Diagram 2: Wavelength Against Frequency for Sound in Air and Water
λ = v/f for sound in air (343 m/s) and fresh water (1480 m/s), computed and drawn to scale from 200 to 1000 Hz. In each medium, doubling f halves λ. At any one frequency the water curve is about 4.3 times higher, the ratio of the speeds. The marked points are the 440 Hz tone of Example 1.
04
Homework Assignment
~30 min
HS-PS4-1 Homework: Frequency, Wavelength and Speed in Different Media
Directions: All data sets are invented for practice. Use c = 3.00 × 10⁸ m/s for light in a vacuum or air and the speeds given in each problem. Show the equation you use, keep units on every number, and end each problem with a one- or two-sentence claim supported by your math.
Part 1: Sound and Light in Two Media (Problems 1-2)
A singer holds middle C (262 Hz). (a) Find the wavelength in air at 20 °C (343 m/s). (b) A swimmer hears the same note through the water of a pool (1480 m/s). Find the wavelength in the water. (c) Write a claim about what changes and what stays the same, and support it with a ratio.
A violet laser produces light with a wavelength of 405 nm in air. (a) Find its frequency. (b) Find its wavelength in glass (speed 2.00 × 10⁸ m/s) and in water (speed 2.25 × 10⁸ m/s). (c) Rank the three media from longest to shortest wavelength and explain the ranking with v = fλ.
Part 2: Analyzing Wave Data (Problems 3-4)
A seismograph 280 km from an earthquake records the P wave 50 s after the quake and the S wave 88 s after. (a) Find the speed of each wave in the crust. (b) Both waves have a frequency of 0.60 Hz. Find each wavelength. (c) Explain why the time between the two arrivals grows for stations farther away.
A student measures the wavelength of sound in a tube of helium: f = 500, 1000, 1500, 2000 Hz gives λ = 2.02, 1.01, 0.671, 0.503 m. (a) Compute fλ for each row. (b) Graph λ against 1/f and find the slope. (c) Compare the speed with the speed in air and support a claim about how the medium affects wavelength at a fixed frequency.
Part 3: Claims and Reasoning (Problems 5-6)
A classmate claims: "When a sound goes from air into water it speeds up, so its frequency must go up too." (a) Use v = fλ and a numerical example of your own to answer the claim. (b) Describe in words what happens to the wavelength and why.
Wi-Fi routers send radio waves at 2.4 GHz and 5.0 GHz through the air. (a) Find each wavelength. (b) A student says the 5.0 GHz signal travels faster because its frequency is higher. Use your answers to support or refute the claim. (c) Describe the relationship between frequency and wavelength for these waves in one sentence without numbers.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
Using v = fλ
Correct equation, rearranged correctly, with units and unit conversions (nm, kHz, km) done right
Correct equation with one unit or arithmetic error
Comparing Media
States that frequency is unchanged at a boundary and that wavelength changes in proportion to speed, with a ratio as evidence
Correct comparison without a ratio or with one reasoning error
Claim and Qualitative Description
Claim is supported by specific numbers and the relationship is also described in words
Claim stated, but support is general or the verbal description is missing
05
Quiz: 20 Questions
Interactive, with answers
Instructions
All data sets are invented. Use c = 3.00 × 10⁸ m/s for light in a vacuum or air, and the other speeds given in each question. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
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
A wave on a rope has a frequency of 4.0 Hz and a wavelength of 0.75 m. What is its speed?
Answer: C
v = fλ = 4.0 × 0.75 = 3.0 m/s. Choice A divides the wavelength by the frequency. Choice B divides the frequency by the wavelength. Choice D adds the two numbers instead of multiplying.
Question 2 of 20 · Multiple Choice
A sound wave has a wavelength of 0.50 m in air (343 m/s) and then passes into fresh water (1480 m/s). Which description of the wave in the water is correct?
Answer: A
The source sets the frequency, so it does not change, and λ grows by the speed ratio: 0.50 × 1480/343 ≈ 2.2 m. Choice B puts the whole change into the frequency. Choice C divides by the speed ratio instead of multiplying. Choice D gets the wavelength right but wrongly changes the frequency.
Question 3 of 20 · Multiple Choice
The frequency of a sound wave in air is tripled, and the air temperature does not change. What happens to its wavelength?
Answer: B
In one medium the speed is fixed, so λ = v/f: tripling f divides λ by 3. Choice A treats wavelength as proportional to frequency. Choice C would be true only if the speed tripled too. Choice D squares the factor, which v = fλ does not do.
Question 4 of 20 · Multiple Choice
A 680 Hz tone travels through air at 343 m/s. What is its wavelength?
Answer: D
λ = v/f = 343 ÷ 680 = 0.504 m. Choice A computes f/v. Choice B multiplies the speed by the frequency. Choice C confuses the wavelength with the frequency value.
Question 5 of 20 · Multiple Choice
A red laser has a wavelength of 633 nm in a vacuum. What is its frequency? (c = 3.00 × 10⁸ m/s)
Answer: A
f = c/λ = (3.00 × 10⁸) ÷ (633 × 10⁻⁹ m) = 4.74 × 10¹⁴ Hz. Choice B multiplies c by the wavelength. Choice C forgets to convert nanometers to meters. Choice D computes λ/c, which is the period, not the frequency.
Question 6 of 20 · Multiple Choice
Light leaves a glass block and passes into air. Which set of changes is correct?
Answer: C
Light is faster in air than in glass, the frequency is unchanged at the boundary, and λ = v/f, so a larger speed means a longer wavelength. Choice A describes light entering glass, the reverse trip. Choice B changes the frequency, which the source sets. Choice D ignores that the speed changes.
Question 7 of 20 · Multiple Choice
A P wave in the lower crust travels at 7.0 km/s with a frequency of 0.40 Hz. What is its wavelength?
Answer: B
λ = v/f = 7.0 ÷ 0.40 = 17.5 km. Choice A multiplies speed and frequency. Choice C divides the frequency by the speed. Choice D adds the numbers.
Question 8 of 20 · Multiple Choice
A 1000 Hz tone has a wavelength of 0.34 m in medium X, 1.5 m in medium Y and 5.0 m in medium Z. In which medium is the wave fastest?
Answer: D
At the same frequency, v = fλ, so the longest wavelength means the largest speed: 1000 × 5.0 = 5000 m/s in Z. Choice A picks the shortest wavelength, the slowest medium. Choice C forgets that the wavelengths differ while the frequency is the same.
Question 9 of 20 · Multiple Choice
For sound in ethanol, a graph of wavelength λ against 1/f is a straight line through the origin that passes through the point (1/f = 0.0020 s, λ = 2.30 m). What is the speed of sound in ethanol?
Answer: A
λ = v × (1/f), so the slope is the speed: 2.30 m ÷ 0.0020 s = 1150 m/s. Choice B divides 1/f by λ, the inverse of the slope. Choice C multiplies the two coordinates. Choice D reads the λ value as the slope.
Question 10 of 20 · Multiple Choice
A medical ultrasound probe sends 2.5 MHz waves into soft tissue, where sound travels at 1540 m/s. What is the wavelength?
Answer: C
λ = v/f = 1540 ÷ (2.5 × 10⁶) = 6.2 × 10⁻⁴ m, about 0.62 mm. Choice A multiplies instead of dividing. Choice B forgets that MHz means 10⁶ Hz and divides by 2.5 only. Choice D is the speed value in m/s written as if it were a wavelength.
Question 11 of 20 · Multiple Choice
A student claims that high-pitched sounds travel faster in air than low-pitched sounds. Invented data: a 200 Hz tone has λ = 1.72 m and an 800 Hz tone has λ = 0.429 m. What do the data support?
Answer: B
fλ = 200 × 1.72 = 344 m/s and 800 × 0.429 = 343 m/s, so the speeds are the same within measurement error. Choice A assumes frequency sets speed. Choice C reads a longer wavelength as a lower speed without using the frequency. Choice D misses that different wavelengths are expected when the speed is fixed and the frequency changes.
Question 12 of 20 · Multiple Choice
Radio waves and X-rays are both electromagnetic waves. How do their speeds in a vacuum compare?
Answer: D
All electromagnetic waves travel at c in a vacuum; higher frequency comes with shorter wavelength so that fλ = c. Choices A and B each treat one of the two quantities as setting the speed. Choice C confuses the frequency, which the source sets, with the speed, which the medium sets.
Question 13 of 20 · Multiple Choice
The same laser beam passes through a tank of water (light speed 2.25 × 10⁸ m/s) and then a glass block (light speed 2.00 × 10⁸ m/s). What is the ratio of its wavelength in glass to its wavelength in water?
Answer: C
The frequency is the same in both, so λglass/λwater = vglass/vwater = 2.00/2.25 ≈ 0.89: the wavelength is shorter in the slower medium. Choice A inverts the ratio. Choice B assumes the wavelength does not depend on the medium. Choice D squares the ratio.
Question 14 of 20 · Multiple Choice
In a ripple tank, 8.0 Hz waves move from a deep region (24 cm/s) into a shallow region (16 cm/s). What is the wavelength in the shallow region?
Answer: A
The frequency stays 8.0 Hz, so λ = 16 ÷ 8.0 = 2.0 cm (it was 24 ÷ 8.0 = 3.0 cm in the deep region). Choice B is the deep-region wavelength. Choice C multiplies speed and frequency. Choice D divides frequency by speed.
Question 15 of 20 · Short Answer
An underwater speaker plays a 1500 Hz tone in seawater (1520 m/s). Find the wavelength in seawater and the wavelength of the same tone in air (343 m/s). What stays the same?
λseawater = 1520 ÷ 1500 = 1.01 m. λair = 343 ÷ 1500 = 0.229 m. The frequency (1500 Hz) stays the same; the wavelength is longer in seawater in proportion to the larger speed.
Question 16 of 20 · Short Answer
P waves travel at 6.5 km/s and S waves at 3.8 km/s in the crust. How long after the P wave does the S wave reach a seismograph 260 km from the earthquake?
tP = 260 ÷ 6.5 = 40 s and tS = 260 ÷ 3.8 = 68.4 s, so the S wave arrives about 28 s later.
Question 17 of 20 · Short Answer
A blue laser has a wavelength of 450 nm in air. Find its frequency, then its wavelength in water, where light travels at 2.25 × 10⁸ m/s.
f = (3.00 × 10⁸) ÷ (450 × 10⁻⁹) = 6.67 × 10¹⁴ Hz. In water, λ = (2.25 × 10⁸) ÷ (6.67 × 10¹⁴) = 3.38 × 10⁻⁷ m = 338 nm, which is 450 × 0.75.
Question 18 of 20 · Short Answer
A group fills a tube with carbon dioxide from a gas cylinder and measures invented data: 400 Hz, λ = 0.65 m; 800 Hz, λ = 0.33 m; 1200 Hz, λ = 0.215 m. What is the speed of sound in the gas, and what claim do the data support?
fλ = 260, 264 and 258 m/s, an average of about 260 m/s. The speed does not change with frequency, so in this one medium λ is inversely proportional to f. The speed is lower than in air (343 m/s), so any tone has a shorter wavelength in carbon dioxide than in air.
Question 19 of 20 · Short Answer
Explain in words, without numbers, why the wavelength of light gets shorter when it enters glass while its frequency does not change.
The frequency is the number of crests the source makes each second, and every crest that reaches the glass enters it, so the number per second cannot change. In glass each crest moves more slowly, so in one period it covers a shorter distance, and the crests bunch closer together: a shorter wavelength.
Question 20 of 20 · Short Answer
An FM station broadcasts at 100.3 MHz. Find the wavelength of its radio waves in air, and the frequency a radio wave would need to have a wavelength of 1.0 m.
λ = (3.00 × 10⁸) ÷ (100.3 × 10⁶) = 2.99 m (about 3.0 m). For λ = 1.0 m, f = (3.00 × 10⁸) ÷ 1.0 = 3.0 × 10⁸ Hz = 300 MHz.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HS-PS4-1 mean?
HS-PS4-1 asks students to use mathematical representations, mainly v = fλ, to support claims about how frequency, wavelength and speed are related for waves in different media. The code means High School, Physical Science, core idea 4 (Waves and Their Applications in Technologies for Information Transfer), performance expectation 1.
Is HS-PS4-1 taught in physics or physical science?
It is usually taught in Physics or Physical Science, in the waves unit, and sometimes in an integrated science course. The math is algebraic: multiplying, dividing, rearranging v = fλ and working with ratios and scientific notation.
What is the assessment boundary for HS-PS4-1?
The official Assessment Boundary is: "Assessment is limited to algebraic relationships and describing those relationships qualitatively." Students work with v = fλ, T = 1/f and ratios, and they describe the relationships in words. Trigonometric wave equations, Snell's law angle calculations and the physics of why a medium has a given speed are beyond this standard.
Does the frequency of a wave change when it enters a new medium?
No. The frequency is set by the source, and it is the same on both sides of a boundary. The speed changes with the medium, and the wavelength changes by the same factor as the speed.
Why does sound travel faster in water than in air?
Sound is a pressure wave, and water pushes back much more strongly when it is compressed than air does, which lets the disturbance pass along faster even though water is denser. For HS-PS4-1, students only need to use the measured speeds (about 343 m/s in air and 1480 m/s in fresh water) and describe the effect on wavelength.
Does light slow down in glass?
Yes. Light travels at 3.00 × 10⁸ m/s in a vacuum and at about 2.0 × 10⁸ m/s in ordinary glass, the exact value depending on the glass. Example 2 and Diagram 1 show what this means for its wavelength. Air slows light by only about 0.03%, so it is usually treated as a vacuum.
Does wave speed depend on frequency?
For the waves in this standard, the speed in a given medium depends on the medium, not the frequency. Changing the frequency changes the wavelength instead, so that fλ stays equal to the speed. Small differences, such as colors of light traveling at slightly different speeds in glass, are real but beyond this standard.
How do seismic waves fit HS-PS4-1?
The Clarification Statement names seismic waves traveling through the Earth. P waves are faster than S waves in the same rock, and both change speed in different layers. Students can use distances and arrival times to find speeds, then use v = fλ to find wavelengths, which gives a real data set for the same relationship.
What math do students need for HS-PS4-1?
Students should be able to rearrange v = fλ for any of the three quantities, convert units such as nanometers, kilohertz, megahertz and kilometers, use scientific notation, and compare two situations with a ratio. Graphing λ against 1/f to get the speed as a slope is another representation of the same algebraic relationship.
What comes after HS-PS4-1?
HS-PS4-3 asks students to evaluate the wave and particle models of electromagnetic radiation, and HS-PS4-5 asks how devices use wave behavior to transmit and capture information. Both use the relationships among frequency, wavelength and speed from HS-PS4-1.
07
Related Standards
6 standards
These standards connect to HS-PS4-1: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
MS-PS4-1Prerequisite
Use math to describe a simple wave model relating amplitude to wave energy
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