Answer key: Wave Speed, Frequency & Wavelength Worksheet
For teachers. This page is hidden from search engines and not linked from student pages, but it is not password-protected, so please don’t share the link with students. Student worksheet: Wave Speed, Frequency & Wavelength Worksheet.
Goal: Show that wave speed equals frequency × wavelength, and find out which properties of a wave change its speed.
Completed results table
| Setting | Wave speed | Period |
|---|---|---|
| Default (4 m, 0.5 Hz) | 2 m/s | 2 s |
| Long waves (7 m, 0.5 Hz) | 3.5 m/s | 2 s |
| Fast oscillations (4 m, 1.5 Hz) | 6 m/s | 0.667 s |
| Small amplitude (0.3 m) | 2 m/s | 2 s |
| 8 m, 0.25 Hz | 2 m/s | 4 s |
Answers
For each row, multiply the frequency by the wavelength. How does your answer compare with the wave speed readout?
They match, because v = fλ. For example 0.5 Hz × 4 m = 2 m/s and 1.5 Hz × 4 m = 6 m/s.
Did changing the amplitude change the wave speed? Why or why not?
No, the speed stayed 2 m/s. Amplitude is how tall the wave is; it does not appear in v = fλ.
What is the period of the “Fast oscillations” wave, and how is it related to the frequency?
0.667 s. The period is the time for one complete cycle, T = 1 ÷ f = 1 ÷ 1.5 Hz.
The last row has a wavelength of 8 m and a frequency of 0.25 Hz. Why is its speed the same as the default wave?
Doubling the wavelength while halving the frequency keeps fλ the same: 0.25 × 8 = 2 m/s. Its period is 4 s.
In this explorer you can change frequency and wavelength separately. On a real rope, the rope itself sets the wave speed. If you shake the rope faster, what happens to the wavelength?
The wavelength gets shorter. Because the rope fixes the speed, λ = v ÷ f, so doubling the frequency halves the wavelength while the speed stays the same.
Challenge: a wave travels at 6 m/s with a frequency of 1.5 Hz. Predict its wavelength, then set it up in the explorer to check.
4 m, because λ = v ÷ f = 6 ÷ 1.5. That is the “Fast oscillations” setting.