Sound Waves Simulator
A virtual sound lab you can hear — wavelength, pitch, loudness, interference & echo
Display Controls
Σ Live equation — values from the set-up on screen
1 Overview
The Sound Waves Simulator is a virtual sound lab: every wave it draws, it can also play, so you can see and hear the same thing. It has five experiments — Anatomy of a wave, Compare two sounds, Superposition, Two speakers and Echo — and four modes: Simulate, Explore, Practice and Quiz.
2 Getting Started
Follow the numbers on the lab: 1 choose an experiment from the strip at the top, 2 press ▶ Play (or 👏 Clap in Echo) on the bar under the canvas: the wave starts moving and you hear it, ❙❙ Pause stops both, and Mute keeps the motion running in silence; 3 change the frequency, amplitude and shape in the panel beside it (the amplitude is the pressure swing in millipascals, and the panel shows how loud that is in decibels), or tap one of the Try a set-up chips, 4 pick the medium and temperature, and 5 work through the Try this challenges, which tick themselves when you get there. Turn the volume down before you start, especially with headphones. The line under the canvas always says in words what is happening.
3 Simulate Mode — the five experiments
- Anatomy of a wave — a loudspeaker drives the air in a tube. The dots are air particles: crowded together they make a compression, spread apart a rarefaction. Under them, on the same distance scale, is the graph of pressure against distance with the crest, trough, wavelength λ and amplitude marked, A microphone partway along has a gold dot that rides the wave up and down once every period T, and a strip under the graph lists the wave’s properties: frequency f, period T = 1/f, wavelength λ = v/f, amplitude p₀ (with its loudness in dB) and speed v = fλ.
- Compare two sounds — waves A (blue) and B (amber) on the same axes. Make B higher in pitch and its crests crowd closer; make it louder and it grows taller. Listen to A, B, both together, or A then B alternately.
- Superposition — wave A, wave B and their sum A + B on one time axis. Shift the phase of B to see and hear constructive and destructive interference; at 180° with equal sine waves the sum is a flat line and the sound stops. Inverted (× −1) turns B upside down, which is what noise-cancelling headphones do: an inverted copy cancels any wave, while a 180° shift cancels a sawtooth only partly (its even harmonics do not flip). Set two close frequencies to hear beats.
- Two speakers — a room seen from above with two loudspeakers playing the same tone. Drag the listener (or use the arrow keys on the canvas) and listen: the sound swells and fades as the path difference passes whole and half wavelengths. Switch the view to the loudness map to see the quiet nodal lines; the phasor diagram shows the two waves adding head to tail.
- Echo — set the distance to a reflecting wall and press Clap. The pulse travels out and back; the microphone trace below shows the clap and the echo in real seconds, with the 0.1 s band in which an echo cannot be heard separately. Choose water for sonar.
The motion on screen is slowed down (the footer says by how much), because a real 440 Hz wave passes 440 crests a second. The sound is always played at the true frequency. ❙❙ Pause (or Space on the canvas) stops the picture so you can read the labels.
4 Explore Mode
Twenty-three concept cards in five groups: Wave basics, Pitch & loudness, Superposition & interference, Echo & reflection, and Speed of sound. Most carry a worked example with real numbers.
5 Practice & Quiz
Practice draws from fourteen kinds of numerical problem: wavelength and frequency from v = fλ, period, the speed of sound at a temperature, echo distance and echo time, sonar depth, the least distance for an echo, beats, decibels (amplitude and intensity), the resultant of two waves, path difference and octaves. Type a number and press Check; Show Solution gives the working. Quiz asks six multiple-choice questions drawn at random from a pool of twenty-two, with the options shuffled, and scores you with up to three stars.
6 Key Concepts
v = fλ: in air at 20 °C, v = 343.2 m/s, so 440 Hz has λ = 0.780 m and T = 2.27 ms. Loudness: L = 20 log₁₀(p / 20 µPa); +6 dB doubles the pressure amplitude, +20 dB multiplies it by 10. Superposition: two equal waves at phase difference φ give AR = 2A|cos(φ/2)|. Echo: t = 2d/v, and a distinct echo needs d ≥ v × 0.1 / 2 = 17.2 m in air. The simulator works in SI units, as sound is taught in SI.
7 Tips & Other Features
Display Controls (top left of the canvas) switch the labels, air particles, beat envelope and phasor diagram; your choices are remembered. Right-click (or long-press) the canvas to save an image, copy the readings or play the sound; PNG also saves the view. The Live equation panel shows the working with the values on screen. Add ?exp=super, ?exp=speakers or ?exp=echo to a link to open a particular experiment. The level slider is the sound-pressure level of the wave; what you actually hear also depends on your volume setting and speakers, so use it to compare sounds, not as a sound-level meter.
Sound Waves Simulator — a Virtual Sound Lab You Can Hear
Sound is easy to hear and hard to see. This sound waves simulator draws the wave and plays it at the same time, so you can link what the ear notices — higher, lower, louder, quieter, a buzz, a silence, an echo — to what the wave is doing. Change the frequency and hear the pitch move while the crests crowd together; raise the amplitude and hear it get louder while the wave grows taller; add two waves until they cancel out.
Wavelength, Frequency, Period and Amplitude
A loudspeaker pushes the air back and forth, making a travelling pattern of compressions (air squeezed, pressure a little high) and rarefactions (air spread out, pressure a little low). Because the air moves along the direction of travel, sound is a longitudinal wave. On a graph of pressure against distance a compression is a crest and a rarefaction is a trough.
- Wavelength λ: the distance from one crest to the next.
- Frequency f: the number of waves passing a point each second, in hertz.
- Period T: the time for one wave to pass, T = 1/f.
- Amplitude: the height of a crest above the centre line (not crest to trough).
They are tied together by the wave equation v = fλ. The speed is fixed by the medium, so a higher frequency means a shorter wavelength: in air at 20 °C, 440 Hz has λ = 343.2 / 440 = 0.780 m, and 880 Hz has half that.
Pitch and Loudness
Pitch is what the ear makes of frequency: doubling the frequency raises a note by one octave. Loudness follows the amplitude and is measured as a sound-pressure level in decibels, L = 20 log₁₀(p / 20 µPa). The scale is logarithmic: +6 dB doubles the pressure amplitude and +20 dB multiplies it by ten. The two are independent — a quiet high note and a loud low note are both possible. Two instruments playing the same note at the same loudness still sound different because their waves have different shapes, made of different mixtures of harmonics: their timbre. The simulator’s sine, square, triangle and sawtooth shapes are built from exactly those harmonics, and the sound you hear is built from the same numbers.
Superposition and Interference of Sound Waves
When two waves meet, the total disturbance is the sum of the two: the principle of superposition. Two waves of one frequency arriving in phase add up (constructive interference); arriving 180° out of phase they subtract (destructive interference), and equal waves then cancel out completely. In general the resultant amplitude is AR = √(A² + B² + 2AB cos φ). Two slightly different frequencies drift in and out of step, so the loudness swells and fades at the beat frequency |f₁ − f₂|. From two loudspeakers the same thing happens in space: a listener whose distances to the speakers differ by a whole number of wavelengths hears a loud sound, and one at an odd number of half wavelengths hears a quiet one.
Echo and Reflection of Sound
Sound reflects from large hard surfaces. An echo is the reflection heard as a separate sound; it returns after t = 2d/v. The ear holds a sound for about 0.1 s, so an echo is heard only if 2d/v ≥ 0.1 s. In a room, reflections arrive sooner and blend into reverberation. Ships use the same timing to measure the depth of the sea with sonar.
Speed of Sound in Different Media
| Medium | Speed of sound | Wavelength of 440 Hz | Least distance for an echo |
|---|---|---|---|
| Air at 0 °C | 331.3 m/s | 0.753 m | 16.6 m |
| Air at 20 °C | 343.2 m/s | 0.780 m | 17.2 m |
| Air at 40 °C | 354.7 m/s | 0.806 m | 17.7 m |
| Helium at 20 °C | 1007.4 m/s | 2.290 m | 50.4 m |
| Carbon dioxide at 20 °C | 267.2 m/s | 0.607 m | 13.4 m |
| Water at 20 °C | 1482.0 m/s | 3.368 m | 74.1 m |
| Steel | 5960.0 m/s | 13.545 m | 298.0 m |
The gas speeds come from v = √(γRT/M), so sound is faster in warm air and in light gases; water and steel are handbook values. Every row of this table is computed by the simulator’s own engine.
Who Uses This Simulator?
Students meeting sound and waves in middle school, GCSE and IGCSE, AP Physics 1, IB, CBSE and introductory college physics; teachers who want to show and play a wave at the same time in class; and anyone who wants to hear what destructive interference, beats or an echo actually sound like.
Frequently Asked Questions
How are pitch and frequency related?
Pitch is how high or low a sound seems, and it is set by the frequency: the number of waves passing each second. A higher frequency gives a higher pitch and a shorter wavelength. Doubling the frequency raises the note by one octave, for example from 440 Hz to 880 Hz.
What happens when two sound waves cancel out?
When two waves of the same frequency and amplitude meet exactly out of step (180 degrees apart), every crest of one meets a trough of the other. By the principle of superposition they add to zero, so the pressure stays constant and there is silence. This is destructive interference, and it is how noise-cancelling headphones work.
What is the minimum distance to hear an echo?
The ear can separate two sounds only if they arrive at least about 0.1 s apart. The echo travels to the wall and back, so 2d / v must be at least 0.1 s. In air at 20 degrees Celsius (343 m/s) the wall must be at least 343 x 0.1 / 2 = 17.2 m away.
Explore Related Simulators
- Tuning Fork Simulator: how a fork’s prongs set its frequency, beats between two forks, and the resonance tube.
- Simple Harmonic Motion Simulator: the oscillation behind every sine wave, with amplitude, period and phase.
- Spring-Mass-Damper Simulator: natural frequency, damping and resonance.
- Refraction Simulator: another wave changing speed as it enters a new medium.
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