Why does the whistle pick a particular pitch?

Real loops have **frequency-dependent** gain and phase. The audible tone corresponds to a frequency where **|G(ω)|** is large and the total phase shift is a multiple of **2π** (constructive feedback). The toy model injects a **test sine**; in practice the room, mic, and EQ set the spectrum.

Does moving the mic or turning down the volume help?

Yes: lowering **G** (gain, sensitivity, distance, orientation) or changing **D** and phase (latency, EQ, monitor equalization) can move the system out of the self-oscillation condition—basic concert feedback control.

Why use tanh instead of hard clipping?

**tanh** gives smooth saturation and bounded stable trajectories without harsh numerical issues; it qualitatively mimics how real amplifiers behave nonlinearly at large levels.

Does one discrete delay represent a real room?

Only **qualitatively**: reflections create a **distribution** of delays and frequency-dependent phases. A single **D** is the minimal model explaining why delayed feedback can go unstable.

Larsen Effect (Feedback Loop)

The Larsen effect (acoustic feedback) occurs when a microphone picks up a loudspeaker that is amplifying the same signal: the closed loop “microphone → amplifier → speaker → propagation → microphone” adds a delayed copy of the output to the input. If at some frequency the round-trip gain exceeds unity and the phase is an integer multiple of 2π (positive feedback), the amplitude grows exponentially until nonlinearity—amplifier saturation, supply limits, driver compression, or clipping—limits it. The simulator uses a discrete teaching model y[n] = tanh(G·y[n−D] + A sin(ωn)): G is effective loop gain, D is delay in samples (standing in for acoustic plus processing delay), and tanh provides soft limiting. It is not a substitute for measuring a venue’s transfer function, but it isolates how G, D, and saturation interact.

Who it's for: Students of acoustics, audio engineering, and control theory; instructors explaining instability conditions in feedback loops.

Key terms

Acoustic feedback
Delay
Loop gain
Self-oscillation
Saturation
Phase coherence
Whistle frequency

How it works

Microphone, amplifier, and loudspeaker in the same room form a loop: sound returns after a delay; if gain around the loop exceeds one at some frequency, level grows until something saturates — the Larsen effect.

Frequently asked questions

Why does the whistle pick a particular pitch?: Real loops have frequency-dependent gain and phase. The audible tone corresponds to a frequency where |G(ω)| is large and the total phase shift is a multiple of 2π (constructive feedback). The toy model injects a test sine; in practice the room, mic, and EQ set the spectrum.
Does moving the mic or turning down the volume help?: Yes: lowering G (gain, sensitivity, distance, orientation) or changing D and phase (latency, EQ, monitor equalization) can move the system out of the self-oscillation condition—basic concert feedback control.
Why use tanh instead of hard clipping?: tanh gives smooth saturation and bounded stable trajectories without harsh numerical issues; it qualitatively mimics how real amplifiers behave nonlinearly at large levels.
Does one discrete delay represent a real room?: Only qualitatively: reflections create a distribution of delays and frequency-dependent phases. A single D is the minimal model explaining why delayed feedback can go unstable.

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