TwiddleLab / Physics / Waves and Sound

Frequency, Wavelength, Speed

Lesson 2 of 10 · 7 min · Free, no account needed

What you will learn

• Frequency f: how many crests pass a point each second, in hertz (Hz). The period T = 1/f is the time for one.
• Wavelength λ: the distance from one crest to the next.
• The medium sets the wave speed v. Shake faster and the crests just get closer: v = f λ.

Start the lesson

How the lesson goes

1. Wi-Fi at 5 GHz and 2.4 GHz travels at the same speed. So what is different about the waves?

   Start with a rope. If the shaker goes twice as fast, where is the next crest?

2. Turn the shaker until the crests are exactly 1 m apart.

   Watch the sun flag riding a crest. Does it speed up?

   The crests always move at the rope's speed, 2 m/s. In one second the first crest goes 2 m. If 2 crests leave in that second, they share those 2 m, so they are 1 m apart.

3. Measure the gap between two neighbouring crests.

   This shaker runs at 2.5 Hz.

   In one second 2.5 crests leave the shaker and line up 0.8 m apart, so the front one has gone 2.5 × 0.8 = 2 m. That distance per second is the speed.

4. Three numbers describe a steady wave.

   Frequency f: crests per second, in hertz (Hz). 2 Hz means 2 crests a second. The period T = 1/f is the time for one: here 0.5 s.

   Wavelength λ: the distance from one crest to the next, in metres.

   Wave speed v: how fast a crest travels. The medium sets it. Then v = f λ: crests per second × metres apart.

   Wi-Fi: both bands travel at the speed of light. 5 GHz has more crests per second, so its waves are shorter (about 6 cm against 12 cm).

5. Game: Buoy hit. Make every buoy ride a crest at the same moment.

   Set the frequency, then Lock in. No extra crests between buoys.

6. Tap every crest that will reach the shore within 1 second.

   Crests move 2 m in a second, so only the ones within 2 m arrive in time. They are 0.5 m apart, so 2 m holds 4 of them: 4 per second, the frequency.

7. Math: frequency and period are flips of each other. Which trace is 2 Hz?

   This is the wave at one point, over 2 seconds: up and down in time.

   If one wave takes T seconds, then 1 second holds 1/T of them. A 0.5 s period gives 1 ÷ 0.5 = 2 waves a second.

8. This shaker runs at 5 Hz and its crests are 0.4 m apart. How fast do they travel?

   Every second 5 crests leave, each 0.4 m behind the last, so the first one is 5 × 0.4 = 2 m away after one second.

9. Your first buoy frequency, playing.

Previous lesson: A Wave Moves, the Rope Doesn't · Next lesson: Sound Is a Pressure Wave · Part of the course: Waves and Sound

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