Ripples on water, sound, a wiggle running along a rope — all of them are waves. This guide makes waves you can see and hear using a rope and rubber bands, then uses an interactive simulation with adjustable frequency and amplitude to untangle the three most easily confused concepts: wavelength, frequency and amplitude.

Safety first (read this before you start)

  • Make sure there's plenty of clear space before swinging a rope — keep the free end away from people and objects, and never use the rope as a whip.
  • When stretching rubber bands, keep them away from eyes and faces in case they snap loose.

Materials and equipment

  • A fairly long, soft rope, or a slinky (coil spring toy);
  • A few rubber bands of different thicknesses;
  • Optional: a shallow tray of water for watching water waves.

Two effects to see first

Effect one: transverse waves on a rope. Have one student hold one end of the rope while another shakes the far end up and down. Shake slowly and long, gentle waves appear; shake fast and the waves become short and tightly packed. Notice that the rope only moves up and down — yet the wave travels across to the other side.

Effect two: pitch and frequency. Stretch a rubber band tight, pluck it, and listen to the pitch. Stretch it tighter (so it vibrates faster) and the pitch rises. Comparing thick and thin rubber bands, you can hear the difference too.

The key distinction: a wave transmits the "shape" of the vibration and its energy; each point of the medium only vibrates in place. The faster you shake, the more waves you generate per second — that is frequency. The distance between two neighboring crests is the wavelength.
Interactive simulation: this experiment has a drag-and-play simulator in our Interactive Lab. The lab interface is currently Chinese-only — the controls are simple sliders and switches, so it is still easy to explore.

Three small experiments worth writing down

"Seeing a wave" isn't enough — each of the following three steps produces a result you can record in a notebook.

  1. Count the waves. Have one student time 10 seconds on a phone while another shakes the rope up and down as steadily as possible, silently counting the shakes. Shakes divided by 10 gives the hand's frequency in hertz. A slow shake is about 1 Hz; a fast one reaches 3–4 Hz.
  2. Measure the wavelength. Once the shaking is steady, have a bystander snap a photo, then measure the distance between the tops of two neighboring humps in the photo and convert it to real length. That is this trial's wavelength.
  3. Change the rope and repeat. Pull the rope tighter, shake at the same frequency, and measure the wavelength again. It comes out longer — the tighter the rope, the faster waves travel along it.

Recording what you see

Log each trial in three columns — frequency / wavelength / rope tension — and three patterns should emerge:

  • On the same rope at the same tension, the faster you shake, the shorter the wavelength — roughly in inverse proportion: double the frequency, halve the wavelength;
  • Swing your hand through a bigger arc (larger amplitude) and the crests get visibly taller, but the number of waves across the rope barely changes: amplitude does not affect wavelength or frequency;
  • Tighten the rope and the same frequency now gives a longer wavelength: change the medium, and the wave speed changes.

The rubber bands are worth recording too: the tighter the band, the higher the pitch (higher frequency); the harder the pluck, the louder the sound (larger amplitude). The two effects are independent of each other — exactly matching the rope waves.

The science: wavelength, frequency and wave speed

Three quantities describe a wave:

  • Frequency f: vibrations per second, measured in hertz (Hz). It determines a sound's pitch — the higher the frequency, the higher the pitch;
  • Wavelength λ: the distance between two neighboring crests (or troughs);
  • Amplitude A: the maximum distance from the rest position. It determines a sound's loudness — the larger the amplitude, the louder the sound.

They are tied to the wave speed v by one essential relationship:

v = f × λ

Within one medium the wave speed is roughly constant, so the higher the frequency, the shorter the wavelength. That is exactly why turning up the frequency in the simulator packs the waves tighter. Amplitude only changes how tall the crests are (loudness) — it changes neither wavelength nor frequency.

Do the math. Sound travels through 15 °C air at about 340 m/s. The A above middle C on a piano is 440 Hz, so its wavelength is λ = v ÷ f = 340 ÷ 440 ≈ 0.77 m — about the span of an outstretched arm. Try another: the lowest frequency humans can hear is about 20 Hz, wavelength 340 ÷ 20 = 17 m; the highest is about 20,000 Hz, wavelength just 1.7 cm. In the very same air, wavelengths span a factor of a thousand — all set by frequency.

Transverse and longitudinal waves: on a rope, the medium moves up and down while the wave moves forward — vibration perpendicular to travel — a transverse wave. Sound in air is different: the air is squeezed and stretched in layers, vibration parallel to travel — a longitudinal wave. A slinky shows both beautifully: shake it side to side for a transverse wave; push a section forward and let it spring back and you'll see a "compressed zone" run along the coil — that is a longitudinal wave. v = f × λ holds for both.

Waves in everyday life

  • Speech and song are sound waves, carried to your ears by vibrating air;
  • Tuning an instrument, or the difference between high and low voices, is all frequency; tightening a guitar string to raise its pitch is the same physics as tightening the rope;
  • Bats and parking sensors use ultrasound, above 20,000 Hz — inaudible to us; the restlessness of some animals before earthquakes may be linked to infrasound below 20 Hz;
  • Water waves, seismic waves, light and radio waves all obey v = f × λ too. Your phone's "2.4 G band" simply means electromagnetic waves at a frequency of about 2.4×10⁹ Hz.

Four things students mix up most often

  • "The wave carries the rope along with it." It doesn't. Tie a small piece of colored tape onto the rope: as you shake, the tape only bobs up and down in place — it never travels forward. A wave transports energy and the pattern of vibration, not the medium itself. A leaf on a pond bobbing up and down without drifting with the ripples is the same fact.
  • "Shake harder and the wave travels faster." No. Shaking harder only increases the amplitude; wave speed is set by the medium (the rope's tension and thickness). To make the wave travel faster, tighten the rope — don't whip it harder.
  • "A high pitch means a loud sound." The most commonly lost point on tests. Pitch is set by frequency; loudness by amplitude. A soprano singing softly is "high pitch, low loudness"; a bass bellowing is "low pitch, high loudness."
  • "The wavelength is the height of the crest." Crest height is the amplitude; wavelength is the horizontal distance between neighboring crests. Mark each with its own arrow when you sketch a wave and you'll never swap them again.

Tips for teachers and parents

  • Timing and groups: 30 minutes; needs a good-sized open space; groups of three — shaker, timer, recorder.
  • Say it before hands touch equipment: nobody stands within the rope's swing range.

The step most people skip. After the transverse wave, always follow up with a longitudinal wave on the slinky — otherwise students will equate "wave" with humps on a rope. And tying a piece of colored tape to the rope is the most effortless way ever invented to show "the vibration travels, the material doesn't."

How to tell they really understand. If a student can separate pitch (frequency) from loudness (amplitude), and use v = fλ to explain "shake faster, waves get denser," they've met the standard.

Take it further

  • In the simulator, double the frequency and check whether the number of waves on screen roughly doubles while the wavelength halves.
  • Change only the amplitude and confirm that wavelength and frequency stay put — loudness and pitch really are two different things.
  • Record a plucked rubber band with a phone audio app (many show a spectrum) and watch the peak shift right as the pitch rises.
  • Think about it: lightning and thunder happen at the same instant — why do you see the flash first and hear the rumble later? If the thunder arrives 3 seconds after the flash, estimate with 340 m/s: about how far away was the strike?

When students can use "frequency, wavelength, amplitude, wave speed" to explain why faster shaking packs the waves closer together, this experiment has achieved its goal.