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Water Wave Properties

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Water Wave Properties

Aotearoa New Zealand’s coastal monitoring team is analysing waves near a harbour. Use the data and wave relationships below to check measurements, interpret changes, and make a justified prediction. Show units in calculations. Assume the waves are periodic and travel in a straight line unless stated otherwise.

Wave model

For a surface wave, v = fλ, where v is wave speed (m s⁻¹), f is frequency (Hz), and λ is wavelength (m). Period T is the time for one cycle, so f = 1/T. Amplitude is the maximum displacement from equilibrium; it is not the same as wave height.

1.A buoy records 18 complete crests passing in 30 s. Calculate the frequency and period of the waves.

2.The measured wavelength is 4.5 m and the frequency is 0.60 Hz. Calculate the wave speed, including units.

3.On a wave profile, the crest is 0.35 m above equilibrium and the trough is 0.35 m below it. What are the amplitude and the vertical crest-to-trough wave height?

4.The wave maker’s frequency is increased while water depth and conditions remain steady. In this model, wave speed stays constant. What happens to wavelength? Explain using v = fλ.

It increases because frequency increases.
It decreases because wavelength must fall when frequency rises at constant speed.
It remains unchanged because speed is constant.
It becomes zero.

Harbour trial data

Technicians repeat measurements at two settings. For each trial they count crests over 20 s and measure the distance across five consecutive wavelengths.

Setting A: 24 crests in 20 s; distance across 5 wavelengths = 10.0 m.

Setting B: 30 crests in 20 s; distance across 5 wavelengths = 9.0 m.

5.Calculate the frequency, wavelength, and wave speed for Setting A. Show how you obtained wavelength from the measured five-wavelength distance.

6.Calculate the frequency, wavelength, and wave speed for Setting B. Compare the speed with Setting A.

7.A student claims the wave speed must be constant because both trials used the same ripple tank. Give one physical factor that could change the speed and explain why the comparison alone does not prove a frequency effect.

Reading a wave profile

Use the stated wave-profile measurements below. The equilibrium level is the reference line; vertical displacement is measured from that level.

8.A wave profile has an amplitude of 0.35 m and a wavelength of 2.0 m. If the frequency is 1.5 Hz, calculate the wave speed.

9.Select every statement that is correct for the wave profile and wave model.

Amplitude is measured from equilibrium to a crest.
Wavelength is the distance from one crest to the next crest.
Frequency is measured in metres.
Wave speed is the distance travelled by the wave pattern per second.
Doubling amplitude necessarily doubles frequency.

10.The measurement team wants a more reliable wavelength estimate. Describe a procedure using repeated spatial measurements and identify one source of uncertainty it would reduce.

11.A long-period swell has T = 12 s and λ = 180 m. Calculate its frequency and speed. Explain what the result says about the wave pattern’s motion, not the net movement of water.

12.A buoy registers a large wave height during a storm. Explain why wave height alone is not enough to calculate wave speed, and name the additional measurements needed using the wave equation.