Sound synthesizer: generating a frequency with a smartphone

A sound synthesizer is a tool that generates a sound signal of chosen frequency and amplitude, the opposite of measuring instruments, which analyse an existing sound. On a smartphone, it turns the loudspeaker into a reference sound source: the emitted frequency is known exactly, which makes it possible to test measuring instruments and to set up quantitative acoustics experiments.

Discover FizziQ

How to use it in class

In FizziQ, the synthesizer lives in the Tools tab. It generates sine waves, that is, pure tones, with a frequency adjustable from 20 to 20,000 Hz, and can superimpose up to three simultaneous voices to study chords and beats.

Steps:

Open FizziQ, Tools tab, then the sound synthesizer. Set the frequency to 440 Hz and listen to the reference A.
On a second device, measure this sound with the frequency measurement and check the displayed value.
Sweep slowly from 20 Hz to 15,000 Hz and find each person’s hearing limits: they vary strongly with age.
Superimpose two very close voices, for example 440 and 442 Hz, and listen to the beat: the intensity pulses at 2 Hz.
Superimpose two frequencies in a simple ratio (440 and 880 Hz, one octave) then in an arbitrary ratio, and compare the feeling of consonance and dissonance.

Scientific activities on this topic

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A reference source, within the limits of the loudspeaker

The synthesizer computes a sinusoid digitally and sends it to the loudspeaker. The emitted frequency is very exact, because it relies on the device’s clock. The actual amplitude, however, depends on the loudspeaker: the miniature speakers of smartphones reproduce low frequencies poorly, and the emitted sound level drops sharply below about 200 Hz. A loudspeaker pushed too hard also adds harmonics: the sound is then no longer rigorously pure. For fine experiments, keep a moderate volume and mid-range frequencies.

Two sources are better than one

Many experiments use two devices: one emits with the synthesizer, the other measures with the sound level meter, the frequency measurement or the spectrum analyser. You can thus verify a frequency, find the resonance of a tube or a bottle, create beats between two phones, or vary the source-receiver distance to study the decrease of the sound level.

Orders of magnitude: audible range: 20 Hz to 20,000 Hz, the upper limit falling towards 15,000 Hz or less with age; reference A: 440 Hz; beats that are audible and easy to count: below 10 Hz of difference between the two voices; faithful reproduction by a smartphone loudspeaker: about 200 Hz to 15,000 Hz.

Formula

The superposition of two pure tones with close frequencies f₁ and f₂ produces a beat whose frequency is:

f_beat = |f₁ - f₂|

Where:

f₁, f₂: frequencies of the two voices (Hz)
f_beat: number of intensity pulses per second (Hz)

The resulting sound is perceived at the average frequency (f₁ + f₂)/2, modulated in intensity at the beat frequency.

Application examples

Verify the accuracy of the frequency measurement with a known emitted frequency.
Tune a musical instrument by listening to the beats with the reference note.
Find the resonance frequency of a tube, a bottle or a guitar body.
Measure the hearing thresholds of a group and plot their distribution by age.
Create standing wave patterns on the surface of a liquid placed on a speaker.
Illustrate consonance and dissonance by superimposing frequencies in simple or arbitrary ratios.

FAQ

Q: Is the generated sound really at the displayed frequency? A: Yes, very nearly: the frequency is produced digitally from the device’s clock, far more stable than the rest of the chain. It is the amplitude, dependent on the loudspeaker, that is poorly controlled, not the frequency.

Q: Why are low frequencies barely audible? A: The tiny loudspeaker of a smartphone cannot move enough air to reproduce bass. Below about 200 Hz, the emitted level drops sharply; below 50 Hz, it becomes practically inaudible on most devices.

Q: Can beats be created with a single phone? A: Yes: FizziQ’s synthesizer superimposes up to three voices. By setting two voices a few hertz apart, you hear the beat directly, without a second device.

Pure tone - Acoustic beat - Fundamental frequency - Pitch - Spectral analysis - Amplitude - Resonance frequency

Sound synthesizer