Hofmann: the myth of the compact, powerful speaker with deep bass

Hofmann’s Law: The Non-Compressible Trade-Off of Audio

In many audio projects, the initial request looks like this:

• “We want a small enclosure.”

• “But with very deep low-frequency extension.”

• “And ideally good sensitivity.”

And every time, I have to say the same thing:

Physics does not allow that specification.

You can’t have all three.

That is exactly what Hofmann’s Law, also called The Iron Law in acoustics, states.

Why does this law exist?

Because a loudspeaker is not a miracle machine.
Its behavior depends on two very down-to-earth factors:

The air it needs to move (air volume)

To produce bass, you need to move a lot of air.
And in a small enclosure, the air is “stiffer,” the compliance is low.

The driver has to work harder → larger excursion → more distortion → lower efficiency.

The natural electroacoustic efficiency of a loudspeaker

A highly efficient speaker usually has:

• a strong motor (high BL)

• a light diaphragm

• a stiff suspension

Exactly the opposite of what you optimize for low-frequency extension.

So when you want a driver to reach deep bass in a very small enclosure, you’re fighting the physics of the transducer.

How has the industry “bridged the gap” (on the surface)?

Today, many products seem to defy Hofmann:

• small speakers that hit 40 Hz

• very compact soundbars

• portable speakers with “12h battery life + insane bass”

• large excursions with low distortion

• DSP that boosts bass without destroying the system

Except that behind the marketing magic, here’s what actually compensates:

• Aggressive DSP: LF boost, dynamic filtering, adaptive loudness

• Powerful class-D amps: Electricity is basically free; we put 200 W in a 3-liter box

• Modern long-excursion drivers: crazy Xmax, FEM-optimized motors, tough materials

• Smart limiting: prevents blowing the driver when pushed too hard

None of this removes Hofmann’s Law.
It simply pushes the limit further, at the cost of other compromises:

• more distortion

• reduced dynamic range

• higher group delay

• terrible efficiency

• bass that is “impressive but artificial”

The real question: what are you optimizing for?

Hofmann’s Law forces you to choose.
And that choice depends on the product, the use case, and the audience.

Case 1: compact / lifestyle speakers

Priority: size + bass extension
Sacrifice: sensitivity
Compensation: DSP + large amplifier

This is what 99% of connected speakers and Bluetooth speakers do.

Case 2: “old-school” Hi-Fi / high efficiency

Priority: sensitivity + dynamics
Sacrifice: enclosure volume
Result: 200-liter cabinets, but what a joy.

Case 3: monitoring / pro audio

Priority: bass extension + controlled dynamics
Accept: reasonable but not tiny volume
Optimize: alignment, group delay, power response

Case 4: IoT / embedded products

Priority: ultra-low volume
Sacrifice: sensitivity + bass extension
Compensation: intelligent voicing, psychoacoustics, DSP

If you don’t make a trade-off, you just break the constraints somewhere else

If you try to force all three, here’s what happens:

• The driver saturates → distortion

• DSP crushes the dynamics

• The amplifier overheats

• The real volume no longer matches the simulation

• Limiting kicks in constantly

• The system sounds loud but not good

And in the end, the client is disappointed not to have an alternative physics model inside their 30 cl plastic box.

So… how do you work intelligently with Hofmann’s Law?

Clearly define priorities at the start of the project

Not at the end.
Not after the industrial design.
From the concept phase onward.

Choose a driver aligned with the goals

This is where 70% of IoT projects fail.

Accept the trade-offs, but choose them yourself

• You can make it small and bassy.

• You can make it sensitive and bassy.

• You can make it small and sensitive.

• You cannot have all three.

Use DSP & class-D as intelligent crutches

Not as miracles that abolish physics.

Conclusion: Hofmann’s Law is not a wall, it’s a compass

If you design audio systems (speakers, IoT, embedded products), Hofmann’s Law shouldn’t be seen as a restriction.

It’s a decision tool.

It simply tells you:

• where you can go

• what you must accept

• what you need to stop promising

And above all:
it keeps you from fighting air with a screwdriver and a DSP.

At Soundfeel Lab, we help hardware, IoT, and audio teams design systems that respect, and intelligently leverage, the laws of physics.
If you have a project where bass, size, or efficiency is a challenge, we can talk.