why it screams

mri · part four · the noise

This is the part of an MRI everybody has personally experienced and nobody explains. The scanner does not hum or whir — it hammers, at a pitch that changes when the sequence changes, loudly enough that you are given ear protection before they will run it. All of that is a direct consequence of parts one to three: the sound is the pulse sequence, made audible by the same field that makes the images possible.

1 · A hundred kilograms per metre of wire

Part two needs gradients: coils that make the field vary across the bore, switched on and off thousands of times a second. Those coils sit inside B₀, carrying hundreds of amps. A wire carrying current I across a field B feels a force per unit length of exactly

F / L = B · I

which is not a small number in a magnet this strong. Every metre of gradient winding is being shoved sideways, and then shoved back, at kilohertz rates. The former flexes; the flexing pushes air; that is the noise. There is no acoustic design problem here that is separable from the imaging — the force is the same B₀ that gives you the signal, times the same gradient current that gives you the resolution.

the force on one metre of winding

gradient current 300 A B₀ 3.0 T

force per metre—

…as a weight—

reversing at—

…

2 · You hear the corners

The force follows the current, so the coil's displacement follows the gradient waveform. But what radiates sound is not displacement — it is the acceleration of the radiating surface. Differentiate a trapezoid twice and the ramps vanish: what is left is a pair of impulses at each corner, where the slew rate changes. That is why an EPI train clatters rather than hums, and why a faster gradient is a louder one — halve the ramp time to double the slew rate, and you double the size of every kick.

gradient current, and what the coil radiates

top: G(t), the readout train · bottom: d²G/dt², the acoustic drive

echo spacing 500 µs ramp time 100 µs amplitude 20 mT/m

slew rate—

k-space per lobe—

current period—

…

Push the ramp slider fast enough and the readout above will tell you that you have left the range any real scanner can operate in — and the limit is not the amplifier. A changing magnetic field induces an electric field in the patient, and past a threshold that field stimulates peripheral nerves: a tingling or tapping sensation, well before anything is dangerous, but firmly a limit. Clinical systems run around 200 T/m/s for that reason, not because faster switching is unbuildable. The quietest sequence and the fastest sequence are pulling on the same rope, and a third rope is tied to the patient's nerves.

3 · The sound is a comb locked to the sequence

Because the drive repeats exactly every two lobes, the spectrum is not noise — it is a harmonic comb, every line sitting on a multiple of 1/(2·esp). The engine's test asserts that better than 90% of the acoustic energy lands on those lines. Halve the echo spacing and the whole comb goes up an octave. When a radiographer changes the sequence and the scanner starts making a different noise, you are hearing the timing change.

The loudest line is usually not the fundamental: the second derivative weights every harmonic by ω², pushing the peak up the comb until the ramps' own roll-off takes over.

listen to it · headphones down first, this is a scanner

acoustic spectrum · comb lines marked at multiples of 1/(2·esp)

synthesised from the waveform above — nothing here is a recording

former resonance 1000 Hz its Q 6

comb spacing—

loudest line—

that is harmonic—

…

What is physics here and what is a model. The waveform, the Lorentz force, the second-derivative relationship and the resulting comb are computed exactly and checked by tests. The step from force to sound is a single damped resonator standing in for the coil former's mechanical response — a real former has many modes and a measured transfer function. The timing structure is the physics; the timbre is a model. This will not sound like your scanner, and moving the resonance slider is changing an assumption, not a measurement.

4 · How loud is loud

Decibels compress so aggressively that the numbers stop meaning anything. EPI reaches 110–120 dB against an occupational exposure limit of 85 dB, and that gap is not "a bit louder":

sound pressure level, and what the ratios actually are

source	SPL	pressure	× energy vs 85 dB

A scanner running EPI at 120 dB is delivering — times the acoustic energy of the 85 dB limit. This is why ear protection is not a courtesy, and why the quietest useful thing a sequence designer can do is lengthen a ramp — at the cost of the speed that made the sequence worth running.

Where this stops. The acoustic output of a real gradient set is dominated by the mechanical resonances of the former and the bore liner, which are measured rather than derived, and by radiation efficiency that depends on geometry — none of which is modelled here. Serious quieting work happens in three places this page does not go: gradient coil design that balances the Lorentz forces so they cancel, damping and vacuum-mounting the former, and sequence design that avoids exciting resonances. Motovilova and Winkler's review is the way in to all three — and the fourth option, not switching the gradient at all, is Weiger's zero-echo-time imaging below.

Where this comes from

Motovilova E & Winkler SA (2022). Overview of methods for noise and heat reduction in MRI gradient coils. Front Phys 10:907619. Open access, and the source of every decibel figure on this page: EPI at 110–120 dB, the NIOSH 85 dB limit, average SPLs of 97.6 dB (head) and 90.5 dB (body) gradient coils, and 0–3 kHz as the band covering most sequences. Also the survey of what can be done about it.
Mansfield P (1977). Multi-planar image formation using NMR spin echoes. J Phys C 10:L55–L58. EPI: the boustrophedon readout train whose alternation sets the comb spacing. The loudest sequence in the clinic is the same one that made functional imaging possible.
Twieg DB (1983). The k-trajectory formulation of the NMR imaging process. Med Phys 10:610–621. Why the lobe area is not free: Δk = γ̄·∫G dt, so the k-space a readout must traverse fixes the area, and only the trade between amplitude and duration is available.
Schaefer DJ, Bourland JD & Nyenhuis JA (2000). Review of patient safety in time-varying gradient fields. J Magn Reson Imaging 12:20–29. Why gradient slew rates stop where they do: a changing field induces an electric field in the patient, and past a threshold it stimulates peripheral nerves. The ceiling on speed — and so the floor under the noise — is physiological.
Weiger M, Brunner DO, Dietrich BE, Müller CF & Pruessmann KP (2013). ZTE imaging in humans. Magn Reson Med 70:328–332. The other end of this page: if the noise comes from switching the gradient, do not switch it. Zero-echo-time imaging keeps the gradient on and steps it in tiny increments between excitations, and the result is near-silent — a scan you can hold a conversation through. The trade is everything else about the sequence.
Roemer PB et al. (1990). The NMR phased array. Magn Reson Med 16:192–225. Not about noise — but the reason part one's arrays let you undersample, which shortens the echo train, which is one of the few ways to be both fast and quiet.

The Lorentz force, the slew rate, the lobe area and its k-space extent, the harmonic comb and the decibel ratios are each checked against a closed form or an analytic Fourier series: the spectrum path is validated against a square wave's odd harmonics, and the comb test asserts that >90% of the acoustic energy sits on multiples of the sequence clock. cd sci/engine-rs && cargo test --release — 45 known-answer tests.

engine: rust → wasm · no dependencies · 45 tests · one · two · three · sci