A frequency meter is an instrument that measures the frequency of a periodic signal, that is, the number of repetitions of the pattern per second, expressed in hertz (Hz). For a sound, the frequency determines the perceived pitch: the higher it is, the higher the sound.
Discover FizziQ
How to measure it in class
On a smartphone, the frequency meter analyses the signal captured by the microphone: through a Fourier transform, FizziQ decomposes the sound into its frequency components and extracts the dominant frequency and the fundamental frequency. The instrument displays this frequency in real time.
Steps:
- Open FizziQ and select the Dominant frequency instrument among the microphone measurements: it is the app’s frequency meter, measuring from about 50 to 10,000 Hz.
- Strike a tuning fork or play a pure note from a generator app and read the displayed frequency.
- Check that a reference tuning fork indeed shows a value close to 440 Hz.
- Sing or whistle a sustained note and observe the stability of the frequency.
- Compare two notes (low then high) to relate perceived pitch and hertz value.
- Record the frequency over time to follow a glissando or the tuning of an instrument.
Scientific activities on this topic
- Tuning forks: pitch of A
- Chromatic scale and frequencies
- Doppler effect of a vehicle
- Air columns and pitch
Possible extensions with FizziQ: tuning a musical instrument, studying the Doppler effect of a moving source, or verifying the relation between the length of a string or a pipe and the emitted frequency. FizziQ’s sound synthesizer (Tools tab) generates a sound of chosen frequency, which allows testing the frequency meter with a known source.
Learn more: how it works
The microphone samples the acoustic pressure, typically 44,100 times per second. Over a window of these samples, the fast Fourier transform (FFT) algorithm computes the signal’s spectrum, that is, the distribution of the sound energy across frequencies. The frequency meter locates the main peak and derives the dominant frequency. Unlike the sound level, the frequency is measured accurately, to the nearest hertz, because it does not depend on the microphone’s amplitude calibration. Its limits come from the resolution of the analysis, tied to the duration of the analysed signal, and from ambient noise: a weak, brief sound or one buried in noise makes the measurement unstable, and a complex sound can make the device hesitate between the fundamental and a harmonic.
Orders of magnitude:
- Common sampling rate: 44,100 Hz.
- Audible range: 20 Hz (low) to 20,000 Hz (high).
- Measuring over a longer window improves resolution: a window of about 1 s gives a resolution close to 1 Hz.
- Reference tuning fork: 440 Hz (the concert A).
- Spoken voice: about 100 to 300 Hz; soprano singing voice: up to about 1,000 Hz.
Formula
The frequency is the inverse of the signal’s period T:
f = 1 / T, with f in hertz (Hz) and T in seconds (s).
Thus a sound of period T = 2.3 ms corresponds to f ≈ 440 Hz. Two sounds whose frequencies are in a ratio of 2 are one octave apart.
Application examples
- Tune a guitar, a violin or a piano by targeting the goal frequency of each note.
- Verify the frequency of a tuning fork or a sound generator.
- Measure the frequency of a sounding pipe and study its fundamental mode.
- Demonstrate the Doppler effect of a source approaching then moving away.
- Relate the perceived pitch of a note to its value in hertz.
- Study the relation between the length of a vibrating string and the emitted frequency.
FAQ
Q: Is the frequency measured by a smartphone accurate? A: Yes, to the nearest hertz for a pure, stable sound. The frequency does not depend on amplitude calibration, unlike the sound level: it is a time measurement, hence reliable.
Q: Why does the displayed value jump at times? A: A weak, brief sound or one masked by ambient noise produces a poorly marked spectrum. The algorithm then hesitates between several peaks, which makes the measurement fluctuate.
Q: Does the frequency meter give the fundamental or a harmonic? A: It locates the most energetic peak of the spectrum. For a complex sound, this peak is often the fundamental, but an intense harmonic can sometimes replace it and skew the reading.
Related concepts
Fundamental frequency - Dominant frequency - Spectral analysis - Pure tone - Sound synthesizer - Period - Microphone