Pure Tone

A pure tone is a sinusoidal signal of a single frequency, with no harmonic at all. It is an ideal case, almost absent from nature: the tuning fork is the real source that comes closest to it, along with a function generator or a synthesizer.

Discover FizziQ

How to measure it in class

FizziQ makes it possible both to generate a pure tone with the frequency synthesizer and to visualize its spectrum, which makes the difference between a pure tone and an ordinary sound visible.

Steps:

Open FizziQ’s frequency synthesizer and emit a sound at 440 Hz.
Display the oscillogram on a second device: the signal should appear as a regular sinusoid.
Switch to the frequency spectrum: a pure tone gives only one sharp peak, at 440 Hz.
Strike a tuning fork in front of the microphone and compare its spectrum to that of the synthesizer: the peak is single, but slightly wider.
Sing the same note or play a flute, then compare: several peaks appear, the sound is no longer pure.
Shorten the analysis duration to a few tens of milliseconds and observe that the peak widens, even though the emitted frequency has not changed.

Scientific activities on this topic

The following experiments and activities can be done with a smartphone or tablet to understand and experiment with the concepts of pure tone and complex sound:

Learn more

A pure tone is a sound characterized by a single fundamental frequency and no harmonic component. This means the sound is a simple sinusoidal wave, without any distortion or mixing of frequencies.

To produce a pure tone, you need a sound source that generates a single frequency at a constant amplitude. Here are some common methods for producing a pure tone:

Function generator: An electronic function generator is a device that can produce electrical signals in the form of sinusoidal waves. These signals can then be converted into audible sounds through a speaker.
Tuning fork: no common musical instrument produces a pure tone. The tuning fork is the only usual acoustic source that comes close to it: after a few tenths of a second, its secondary vibration modes have damped out and practically only the fundamental sinusoid remains. A flute, a violin string or an organ pipe, on the contrary, produce sounds rich in harmonics.
Audio software: Audio production software allows you to generate pure tones by creating sinusoidal waves with a specific frequency and amplitude.

Pure tones have several important applications:

Instrument calibration: Pure tones are used to tune and calibrate musical instruments and audio equipment. They serve as a reference to ensure that instruments are tuned precisely.
Acoustic analysis: Pure tones are useful in acoustic research and analysis to study the properties of sound waves and audio systems.
Tests and measurements: Pure tones are employed in various fields, such as audiology, architectural acoustics, and the audio industry, to perform precision tests and measurements.
Signal processing: In audio engineering, sound signals are often decomposed into their frequency components using a Fourier transform, and pure tones are used to represent these components.
Sound effects: In the film and audiovisual industry, pure tones can be used as components to create specific sound effects.

Formula

A pure tone is described by a sinusoidal function of time:

s(t) = A × sin(2π f t + φ)

where:

s(t): value of the signal (acoustic pressure) at time t (Pa)
A: amplitude of the signal, related to the perceived sound intensity (Pa)
f: single frequency of the sound, related to the perceived pitch (Hz)
t: time (s)
φ: initial phase (rad)

The period T of the signal is deduced from the frequency:

T = 1 / f

where:

T: period, duration of one complete cycle of the sinusoid (s)
f: frequency (Hz)

Application examples

An orchestra tuning fork vibrates at 440 Hz, that is, a period of 2.3 ms: it is the acoustic source closest to a pure tone.
FizziQ’s frequency synthesizer generates a pure tone of a chosen frequency, for example 1000 Hz, to test an audio chain.
An audiogram is performed with successive pure tones (250, 500, 1000, 2000, 4000, 8000 Hz) to measure the hearing threshold at each frequency.
The test signal of a television transmitter or the dial tone of a telephone are electronic pure tones.
A human whistle is very close to a pure tone: its spectrum is dominated by a single peak between 1000 and 3000 Hz.
The superposition of two pure tones of nearby frequencies, 440 Hz and 442 Hz, produces beats audible at 2 Hz.

FAQ

Q: Does a flute produce a pure tone? A: No. The flute has the reputation of a “pure” sound because its harmonics are few and weak, but its spectrum contains several. No traditional musical instrument produces a single sinusoid.

Q: Why is the peak of the spectrum never infinitely thin? A: A perfect pure tone would have to last indefinitely. Every real sound starts and stops, and this finite duration gives the spectrum a non-zero width. The shorter the analysis duration, the wider the measured peak.

Q: Is a pure tone pleasant to listen to? A: Not particularly. A sustained pure tone quickly seems artificial and tiring. It is precisely the harmonics of a complex sound that give instruments their richness.

Q: What is the difference between a pure tone and a musical note? A: A note designates a pitch, hence a fundamental frequency. An instrument playing that note emits a complex sound whose fundamental corresponds to the note, accompanied by harmonics.

Q: Can we hear the difference between a pure tone at 440 Hz and a tuning fork at 440 Hz? A: Yes, slightly. The tuning fork has a brief attack and a progressive decay, and its very first moments contain secondary components. Its pitch, however, is identical.

Complex Sound - Harmonic Sound - Timbre - Fundamental Frequency - Fourier Transform (FFT) - Pitch (Sound Height) - Acoustic Beat