Acoustic Phased Array (Line)
This simulator illustrates a **uniform linear phased array** for sound (or sonar): several coherent sources radiate sinusoidal pressure at frequency f with a fixed progressive phase shift Δφ between neighbors. In the far field the amplitude pattern is proportional to the **array factor** AF(θ) = |sin(Nψ/2)/sin(ψ/2)| with ψ = 2π(d/λ)sinθ + Δφ, where N is the number of elements, d is the center-to-center spacing, and λ = c/f is the wavelength in a medium with sound speed c. Steering the main lobe to angle θ is achieved by tuning Δφ; for narrowband signals this approximates true time delays on each channel. The model is idealized: identical isotropic elements, no mutual coupling, no boundary reflections or attenuation—yet it captures how interference shapes directivity, the same mathematics used in sonar arrays, ultrasound imagers, and concert line arrays.
Who it's for: Undergraduate students in waves, acoustics, and fields; engineers learning phased arrays and their acoustic analogue.
Key terms
- Array factor
- Phased array
- Path length difference
- Main lobe
- Wavelength
- Narrowband approximation
- Interference
- Radiation pattern
How it works
Several loudspeakers driven with controlled phase shifts add constructively in chosen directions — the acoustic analogue of beam steering used in sonar arrays and concert line arrays.
Frequently asked questions
- How is this different from the electricity phased-array page?
- The **array-factor** mathematics for a uniform linear array is identical; what changes are typical values of **c** and **f** (sound in air or water versus electromagnetic waves) and whether you interpret pressure or field amplitude. The dedicated waves page foregrounds acoustic applications and shows **λ** and physical **d** explicitly.
- Why do sharp nulls appear at certain angles?
- Nulls occur when sin(Nψ/2) = 0 while sin(ψ/2) ≠ 0: the N phasors in the complex plane close to zero. These are **grating**/**pattern** nulls of the discrete array; their locations depend on **d/λ**, **N**, and **Δφ**.
- Does phase steering work for broadband music or speech?
- For wide bandwidth, true **time delays** per channel are preferred to a single phase shift tuned at one frequency—otherwise the phase shift that steers one f is wrong for others. The simulator is intentionally **narrowband** to isolate the classic **AF(θ)** formula.
- How do d/λ and physical spacing d relate?
- **d/λ** is the spacing measured in wavelengths. With **c** and **f** you get λ = c/f and **d = (d/λ)·λ** in meters—useful for comparing air versus water designs.
More from Waves & Sound
Other simulators in this category — or see all 35.
Chladni Figures
Plate mode sin(mπx)sin(nπy); nodal contrast + grains drift to nodes (model).
Cymatics: Circular Membrane
Drum eigenmodes J_m(k_{mn}r) cos(mθ); angular m, radial n, shimmer.
Echo & Echosounder
Round-trip time t = 2d/v; pulse to a wall and back with adjustable sound speed.
Wave Speed: String vs Rod
v = √(T/μ) for a string vs v ≈ √(E/ρ) for longitudinal bar waves.
LC Oscillator (Undamped)
Ideal series LC: q(t), I(t), ω₀ = 1/√(LC); U_C + U_L constant; vs RLC AC.
Larsen Effect (Feedback Loop)
Mic + speaker + delay: loop gain and saturation in a toy discrete feedback model.