Waves & sound lab

Standing waves on a string, two-source interference, and the Doppler effect — three animated sandboxes with the actual wave formulas driving every pixel.

Lessons

Pick your class, read the steps, then try them right in the sandbox below.

Class 11 — Standing waves and harmonics

Concept: a string fixed at both ends only supports certain frequencies — harmonics — where f_n = n·v/(2L), n = 1, 2, 3…

Switch to Standing waves mode.
Set String length L to 1 m and Wave speed v to 50 m/s. Use the Harmonic n stepper to select n = 1 (the fundamental) and note the value in the Frequency stat (25.0 Hz).
Step n up to 2, then 3. Watch the number of nodes increase and check the Frequency stat exactly doubles (50.0 Hz), then triples (75.0 Hz), matching f_n = n·v/(2L).

Takeaway: higher harmonics mean more nodes and proportionally higher frequency — this is exactly how a guitar string produces different overtones.

Class 11 — The Doppler effect

Concept: a moving sound source shifts the frequency you actually hear — higher if it's approaching, lower if it's moving away — even though the source's own frequency never changes.

Switch to Doppler effect mode.
Set Source frequency f to 500 Hz and Source speed to 0 m/s first — confirm Observed freq. reads 500 Hz with no motion.
Increase Source speed while the source moves toward the listener and watch Observed freq. rise above 500 Hz.
Let the source pass and move away — Observed freq. should now drop below 500 Hz.

Takeaway: this is exactly why a passing ambulance siren sounds higher-pitched as it approaches and lower-pitched as it recedes.

Class 12 — Two-source interference

Concept: waves from two sources reinforce (constructive, bright) where their path difference is a whole number of wavelengths, and cancel (destructive, dark) where it's a half-integer number of wavelengths — the same idea behind Young's double-slit experiment.

Switch to Interference mode.
Set Source separation d and Wavelength λ to any values, then drag the detector around the stage.
Find a spot the readout labels "constructive (bright)", then move the detector slightly and find one labelled "destructive (dark)".

Takeaway: whether a point is bright or dark depends only on the difference in distance from the two sources, measured in wavelengths.

The physics behind it

Formulas used in this lab

Wave basics Class 11

Wave speed: v = fλ
Angular frequency and wave number: ω = 2πf, k = 2π/λ
Travelling wave: y = A sin(kx − ωt)

Standing waves on a string Class 11

Wavelength of the n-th harmonic: λ_n = 2L/n, n = 1, 2, 3, …
Frequencies: f_n = nv/2L = nf₁
Standing-wave equation: y = 2A sin(kx) cos(ωt)
Nodes and antinodes: nodes where sin kx = 0 (x = 0, λ/2, λ, …), antinodes halfway between; adjacent nodes are λ/2 apart
Speed on a stretched string: v = √(T/μ)

Interference of two sources Class 12

Path difference: Δ = |r₁ − r₂|
Phase difference: φ = 2πΔ/λ
Constructive (bright): Δ = nλ, n = 0, 1, 2, …
Destructive (dark): Δ = (n + ½)λ
Resultant amplitude and intensity: A_R = 2A|cos(φ/2)|, I ∝ cos²(φ/2), I_max = 4I₀

Doppler effect Class 11

Source moving towards a still observer: f′ = f · v/(v − v_s)
Source moving away: f′ = f · v/(v + v_s)
General case: f′ = f · (v ± v_o)/(v ∓ v_s); upper signs when moving towards each other
Speed of sound used in the lab: v = 343 m/s