Wave Speed, Frequency and Wavelength: v = fλ Lesson

A wave moves one wavelength in one period, so its speed is v = fλ: frequency times wavelength. A wave with f = 2 Hz and λ = 4 m travels at 8 m/s. In a given medium the speed is fixed, so a higher frequency means a shorter wavelength.

Learning objectives

• Label wavelength, amplitude, frequency and period on a wave.
• Use v = fλ and T = 1/f.
• Apply them to sound and light.

The opening question

"A guitar plays a higher note. Does its sound reach you sooner?" No: all notes arrive together, at about 343 m/s in air. The higher note has a higher frequency and a shorter wavelength, at the same speed.

The lesson, click by click

1. Click 0: a travelling wave, moving to the right.
2. Click 1: the wavelength λ, crest to crest, and the amplitude A, rest line to crest.
3. Click 2: watch one point: it goes up and down once per period T, while the wave moves forward one λ.
4. Click 3: so v = λ/T = fλ. With f = 2 Hz and λ = 4 m, v = 8 m/s.
5. Click 4: sound: 440 Hz in air (343 m/s) has λ ≈ 0.78 m. Light: an FM radio wave at 100 MHz has λ = 3 m.

Common mistakes to watch for

• Frequency changes speed. In one medium, raising f shortens λ; v stays the same.
• Amplitude changes speed. A bigger wave is not a faster one.
• Amplitude from trough to crest. That is twice the amplitude.
• The medium moves along. In a wave on a rope, each point moves up and down; the shape travels, not the rope.

Check questions

1. A wave has f = 5 Hz and λ = 0.6 m. Its speed? (3 m/s.)
2. Sound at 343 m/s with λ = 1.5 m. Its frequency? (About 229 Hz.)
3. Period of a 50 Hz wave? (0.02 s.)

Building it in Tracé

1. Add a Wave, choose Travelling, and set the Wavelength and Amplitude.
2. Animate Phase (°), animate it to move the wave on a click, or let it loop so the wave keeps moving.
3. Switch to Standing to introduce standing waves on a string.

Questions

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