Microphone

A microphone is a transducer that converts the pressure variations of a sound wave into an electrical signal. It therefore measures a pressure, not a sound level: the decibels are computed afterwards by the software. Smartphones use MEMS microphones.

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How to measure it in class

FizziQ gives access to the microphone signal in several forms: oscillogram, sound level in decibels, dominant frequency and spectrogram. It is the same pressure signal, presented in four different ways.

Steps:

• Open FizziQ and select the oscillogram, then whistle or make a tuning fork vibrate in front of the microphone to see the sinusoid appear.
• Measure the period of the signal by locating two consecutive zero crossings in the same direction, then deduce the frequency.
• Switch to the frequency spectrum and compare a tuning fork (a single line) with a voice or an instrument (fundamental and harmonics).
• Select the sound level and note the value in decibels in the silence of the room, then at one meter from a source, keeping in mind that the microphone is not calibrated in absolute terms.
• Locate where the microphone is on the device and point it toward the source: moving it a few centimeters or placing a finger on it changes the measurement markedly.

Scientific activities on this topic

Several experiments that can be carried out with a smartphone’s microphone make it possible to study sound and the propagation of sound waves.

• Cardiac auscultation by mic - Build a stethoscope and record heartbeats to count their frequency.
• Speed of sound: two stopwatches - Measure the speed of sound in air from the delay between two sound detections.
• Reaction time by stopwatch - Use a sound signal to trigger the measurement and evaluate a reaction time.

Learn more

A transducer, not a sound level meter

The microphone transforms a mechanical quantity, the acoustic pressure, into an electrical quantity, a voltage. Nothing else. The sound level in decibels is the result of a calculation done afterwards: the software takes the RMS value of the signal over a time window and compares it to a reference pressure. Confusing the two leads to the classic error of believing that the sensor “measures decibels”.

The MEMS microphones of smartphones

A MEMS microphone is a miniature capacitor: a mobile silicon membrane of a few hundred micrometers, facing a fixed perforated plate. The acoustic pressure deforms the membrane, the gap between the two plates varies, so the capacitance varies, so the voltage across the terminals varies. An integrated preamplifier delivers the signal. These sensors are very reproducible and very small, which explains their widespread use, but their bandwidth is limited at the low end of the spectrum.

Directivity

A microphone does not pick up sound the same way in all directions. An omnidirectional mic responds almost equally in all directions, a cardioid mic favors the front and attenuates the rear. The MEMS mics of smartphones are close to omnidirectional, but the phone’s body acts as a screen and introduces a de facto directivity. Turning the phone over during a measurement can change the recorded level by several decibels.

A smartphone microphone is not calibrated in absolute terms

No manufacturer guarantees the correspondence between the displayed number and the actual level in decibels SPL. Moreover, operating systems often apply automatic gain and filtering intended for voice, which compress loud levels and boost weak ones. The pedagogical consequence is clear: level differences between two situations are usable, absolute values are not without calibration against a sound level meter.

Orders of magnitude

Hearing threshold at 1 kHz: pressure of 2 × 10⁻⁵ Pa, that is 0 dB by definition. Ordinary conversation: about 0.02 Pa, that is 60 dB. Pain threshold: about 20 Pa, that is 120 dB. Atmospheric pressure is 10⁵ Pa: a sound wave is therefore only a tiny modulation of the ambient pressure. Typical sensitivity of a MEMS mic: of the order of a few millivolts per pascal. Sampling frequency of a smartphone: 44.1 kHz, which allows analyzing frequencies up to about 22 kHz.

Formula

The sensitivity of the microphone relates the delivered voltage to the received acoustic pressure:

U = S × p

where:

• U: voltage delivered by the microphone (V)
• S: sensitivity of the microphone (V/Pa)
• p: acoustic pressure, pressure deviation from ambient pressure (Pa)

The sound level is then computed by the software from the RMS pressure:

L = 20 × log(p_eff / p₀)

where:

• L: sound pressure level (dB)
• p_eff: RMS value of the acoustic pressure (Pa)
• p₀: reference pressure, 2 × 10⁻⁵ Pa

The frequency is deduced from the period read on the oscillogram:

f = 1 / T

where:

• f: frequency of the sound (Hz)
• T: period of the signal (s)

For the measurement of the speed of sound by two separate detections:

v = d / Δt

where:

• v: speed of sound in air, about 340 m/s at 20 °C (m/s)
• d: distance between the two detection points (m)
• Δt: delay between the two detections (s)

Application examples

• Measure the frequency of a tuning fork: the oscillogram gives a period of about 2.3 ms, that is a frequency of 440 Hz.

• Compare the spectra of a flute and a guitar playing the same note: same fundamental, harmonics of different amplitudes, which defines the timbre.

• Measure the speed of sound by placing two detections 10 m apart: the expected delay is about 29 ms at 20 °C.

• Check the decrease of sound level with distance: in free field, doubling the distance to the source loses about 6 dB.

• Record heartbeats through a cardboard tube and count the heart rate on the recording.

• Observe the beats between two sounds of neighboring frequencies, for example 440 and 443 Hz: the envelope of the signal repeats three times per second.

FAQ

Q: Does the microphone measure decibels? A: No. It delivers a voltage proportional to the acoustic pressure. The level in decibels is computed afterwards by the software, from the RMS value of the signal compared to a reference pressure of 2 × 10⁻⁵ Pa.

Q: Why do two smartphones not display the same sound level? A: Because smartphone microphones are not calibrated in absolute terms and each system applies its own signal processing. Differences between two measurements made with the same device remain reliable, however.

Q: Should the phone be pointed toward the source? A: Yes, and the same orientation must be kept throughout the series of measurements. The body acts as a screen and the recorded level can vary by several decibels depending on the face presented to the source.

Q: What is the highest frequency measurable with a smartphone? A: About 22 kHz. Sampling is done at 44.1 kHz and the Shannon criterion means that only frequencies below half this value can be reproduced.

Q: Can a very weak or very loud sound be measured? A: With difficulty at both extremes. A very weak sound drowns in the sensor’s own noise, and a very loud sound saturates the input: the oscillogram is then clipped and the displayed level underestimated. In that case, the phone must be moved away from the source.

Related concepts

Sound Level - Decibel - Frequency - Spectral Analysis - Timbre