Worksheet

Surf School Buoy: Wave Height, Frequency and Energy

Grade 8 waves practice: read buoy data on wave height, period and wavelength, find amplitude and frequency, and relate amplitude to wave energy.

Grade 8ScienceInteractive · Printable

Aligned toMS-PS4-1

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What’s included

Single worksheet
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1 NGSS standard
Printable answer key
11 questions
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Details

Format: Interactive · Printable
Grade: Grade 8
Subject: Science
Question types: Fill in the blank, Multiple choice, Sorting, Short answer

About this worksheet

What students practice

Students find amplitude from wave height and frequency from period using buoy data.
Students use data to show that wave energy grows with the square of the amplitude.
Students apply the amplitude–energy pattern to predict wave energy and make a decision.

How to use

Sketch one wave on the board and label crest, trough, height and amplitude before students start. Calculators are helpful for the frequency and energy questions.

Curriculum

NGSS standard covered

MS-PS4-1

Use math to describe how a wave's amplitude relates to the energy it carries, and read wavelength and frequency.

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Name Date

Surf School Buoy: Wave Height, Frequency and Energy

Use offshore buoy data to connect amplitude and wave energy.

Reading the buoy log

Read the surf school notes and study the table. Then answer the questions.

Checking the Buoy Before the First Lesson

Every morning before the first lesson, surf instructor Kaimana Reyes checks the readings from a weather buoy anchored far offshore. This summer, eighth grader Beatriz Takahara is helping at the surf school, and Kaimana is teaching her to read the buoy data. The waves at this beach usually start as wind blowing over the open ocean far away, and they can travel for days before they reach the shore. The buoy mostly bobs up and down in place as each wave passes under it, while the wave's energy keeps moving toward the beach. Waves near the shore can look quite different from the buoy readings, because waves change as they move into shallow water.

The buoy reports the wave height, the vertical distance from the bottom of a trough to the top of the next crest. Kaimana sketched a wave on a whiteboard and labeled a crest, a trough and the calm water level halfway between them. She pointed out that wave height is not the same as amplitude. The amplitude is the distance from the calm water level up to a crest, so it is half of the wave height. The buoy also reports the period, the time in seconds (s) between one crest and the next crest passing the buoy. The frequency, in hertz (Hz), is the number of waves that pass each second, so it equals 1 divided by the period.

The buoy's computer also estimates the wavelength, the distance from one crest to the next, and the wave energy for each square meter of sea surface, in joules per square meter (J per m²). Kaimana uses the energy number to decide whether beginners can go in the water. Strong waves can knock a new surfer off a board and push the board hard toward the shore. On days when it is too high, she teaches on the sand instead.

Beatriz copied four mornings of readings into a log. The table shows the wave height, period, wavelength and wave energy for each day. The readings changed from day to day as storms far out at sea grew and faded. On Thursday evening, the forecast for Friday called for waves 4.0 m high.

Beatriz's Buoy Log
Day	Wave height (m)	Period (s)	Wavelength (m)	Energy (J per m²)
Monday	1.0	8	100	1,250
Tuesday	2.0	8	100	5,000
Wednesday	3.0	10	156	11,250
Thursday	1.0	12	225	1,250

Use the buoy log and the notes.

The amplitude of Tuesday's waves was m.

Use the buoy log and the notes.

The frequency of Wednesday's waves was Hz.

Which pattern does the log show?

A. The wavelength stayed about the same all week.
B. Days with taller waves had longer wavelengths.
C. The wavelength got shorter as the period got longer.
D. Days with a longer period had a longer wavelength.

Compared with Monday's waves, Thursday's waves had which of these?

A. A higher frequency and a longer wavelength
B. A lower frequency and a longer wavelength
C. A lower frequency and a larger amplitude
D. A higher frequency and a shorter wavelength

Amplitude and energy

Use the buoy log and the surf school notes to answer the questions.

Compare Tuesday with Monday. Tuesday's amplitude was twice Monday's.

Tuesday's wave energy was times Monday's wave energy.

Compare Wednesday with Monday.

Wednesday's wave energy was times Monday's wave energy.

Which math rule fits the energy data for Monday, Tuesday and Wednesday?

A. Energy doubles each time the amplitude doubles.
B. Energy grows with the period, while amplitude has little effect.
C. Energy grows with the amplitude times itself (amplitude squared).
D. Energy grows by the same amount for each extra 0.5 m of amplitude.

Monday and Thursday had the same wave energy. What does this comparison suggest?

A. In this log, the energy depended on wave height, not on period.
B. Thursday's waves were taller than Monday's waves were.
C. Waves with a longer wavelength carried more energy per square meter.
D. Waves with a longer period carried less energy per square meter.

Friday's forecast calls for waves 4.0 m high. Use the pattern in the log.

The wave energy on Friday would be about J per m².

10.

Kaimana's rule: beginner lessons go in the water only when the wave energy is below 3,000 J per m². Sort each set of waves.

Waves 1.0 m high with a period of 8 sWaves with an amplitude of 1.0 mWaves 0.8 m highWaves with an amplitude of 1.5 mWaves with an amplitude of 0.5 m

Lesson in the water (below 3,000 J per m²)	Lesson moves to the sand

11.

Beatriz's cousin says, "Wednesday's waves were only 3 times as tall as Monday's, so they carried only 3 times as much energy. They can't be that much rougher." Do you agree? Write a claim, give evidence from the log, and explain your reasoning about amplitude and energy.