The Nyquist frequency is the maximum frequency that a sampling system can reproduce without distortion. It is equal to half the sampling frequency. For a smartphone sampling at 44100 Hz, the Nyquist frequency is 22050 Hz.
Discover FizziQ
How to measure it in class
With the FizziQ app, it is possible to explore the Nyquist frequency and its effects.
Steps:
- Open FizziQ and note that the smartphone samples at 44100 Hz (Nyquist frequency = 22050 Hz)
- Use an external synthesizer or a frequency generator application
- Generate sounds of increasing frequency: 15000, 18000, 20000, 22000 Hz
- Observe with the frequency meter that measurements become imprecise near the limit
- Beyond 22 kHz, observe aliasing: a 23000 Hz sound appears as a 21100 Hz sound
Scientific activities on this topic
- Testing smartphone microphone limits
- Comparing human hearing and digital limits
- Studying the aliasing phenomenon
Learn more
Origin of the name:
Harry Nyquist, a Swedish-American engineer at Bell Labs, established the theoretical foundations of sampling in 1928. Claude Shannon formalized the theorem in 1949, hence the alternative name “Shannon-Nyquist theorem.”
Why this limit?
To reconstruct a sinusoid, at least two points per period are needed: one at the peak, one at the trough. With only two samples per period, we are at the Nyquist limit. Below this (fewer than 2 samples/period), reconstruction is impossible and produces “false” frequencies (aliasing).
Practical implications for FizziQ:
The smartphone microphone can theoretically capture sounds up to about 22 kHz. In practice, anti-aliasing filters and microphone characteristics often limit this to 18-20 kHz. Ultrasounds (> 20 kHz) cannot be analyzed directly.
Aliasing (spectral folding):
A frequency f higher than the Nyquist frequency fN appears as a “mirror” frequency f’ = |f - fs| where fs is the sampling frequency.
Formula
f_Nyquist = fs / 2
Shannon-Nyquist condition: fs > 2 x f_max
where:
- f_Nyquist: Nyquist frequency (Hz)
- fs: sampling frequency (Hz)
- f_max: maximum frequency of the signal to be digitized
Application examples
- CD audio (44100 Hz): Nyquist frequency = 22050 Hz, covering human hearing
- Telephone (8000 Hz): Nyquist frequency = 4000 Hz, sufficient for voice
- Ultrasonic dog whistles (> 20 kHz) cannot be analyzed by FizziQ
- A bat emitting at 50 kHz cannot be studied with a standard smartphone
FAQ
Q: Why doesn’t my smartphone capture ultrasounds? A: The standard sampling frequency (44100 Hz) limits capture to 22 kHz. Additionally, smartphone microphones are optimized for human voice (300-3400 Hz) and attenuate very high frequencies.
Q: What happens if I exceed the Nyquist frequency? A: The signal is “folded”: a frequency of 25000 Hz with sampling at 44100 Hz will appear as a 19100 Hz sound (44100 - 25000).
Q: Can this limit be bypassed? A: Yes, with specialized equipment. Some professional recorders sample at 192 kHz (Nyquist = 96 kHz). Dedicated ultrasonic sensors exist for bioacoustic studies.
Related concepts
Sampling - Aliasing - Sound digitization - Shannon theorem - Analog-to-digital converter