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.

Acoustic Phased Array (Line)

N sources, spacing d/λ and phase ramp: steer audio/sonar-like beams (array factor sketch).

About this model

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.

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