Put a phone in a mug and it gets louder and boxier. Slide it into a cardboard tube and a few notes jump out while the rest stay put. Stand it in a machined horn and a voice carries across the desk. All of these are sold or built as passive phone amplifiers, and none of them draws power. They work in different ways, and that decides what each one is good for.
The guides
Horn cutoff frequency: how the flare and the mouth set a horn’s lower limit
The cutoff formula, the mouth guideline and three flare profiles, worked through with numbers. They show why a horn small enough for a desk starts working only in the upper midrange.
Wood, plastic or aluminium: what the material changes in a passive phone amplifier
Horn theory assumes rigid walls, so a material matters only through how well it keeps the walls stiff, sealed and stable. Datasheet numbers for hardwood, printed plastic and machined aluminium.
Shapes that get called amplifiers
Every passive phone amplifier takes sound that would have spread out from the phone’s speaker slot and gives it a shape to travel through. What the shape does depends on whether it widens gradually, has fixed open ends or encloses a volume of air.
| Shape | Typical example | What sets its behaviour | Effect on the sound |
|---|---|---|---|
| Horn | A duct that widens from the speaker slot to a mouth | Flare rate and mouth size, which give a cutoff frequency | Raises output over a band above the cutoff and points it forward |
| Tube open at both ends | A cardboard roll or pipe with a slot for the phone | Length: resonances near c/2L and its multiples | Reinforces notes near the resonances, little in between |
| Cup or mug | A vessel closed at one end | Depth: resonances near c/4L and its odd multiples | A strong resonance at the lowest of these |
| Box with a small opening | A closed box with a hole or slot | Volume, opening area and neck length | One main peak at the Helmholtz frequency |
A tube that favours a few notes
Take a paper towel tube 25 cm long and 4 cm across, open at both ends, with a slot cut for the phone. A tube open at both ends resonates at c/2L and at whole multiples of that frequency. With c = 343 m/s and the bare length, the first resonance is 686 Hz.
The air just beyond each open end moves with the air in the tube. That adds about 0.6 times the radius at each end, so the effective length here is 27.4 cm. The resonances then fall near 626, 1,252 and 1,878 Hz. Notes close to those frequencies come out louder than the notes between them. Which of them you hear depends on where the slot is: a slot halfway along the tube excites the first and third strongly and the second hardly at all.
A cup is closed at the bottom, so it resonates at c/4L and only at odd multiples of it. A closed box with a small opening has one main resonance, at the Helmholtz frequency f = (c/2π) · √(S/(V·L)). Here S is the area of the opening, V the volume of the box and L the effective length of the neck. It is the note you hear when you blow across the top of a bottle.
None of these shapes is wrong. A resonator is quick to make and gives an audible lift at its own frequencies. It does not lift a band evenly, though, and its peaks move with every change of size.
What a horn does instead
A horn avoids a single strong resonance by changing its area gradually from the throat to the mouth. Above its cutoff frequency it lets the speaker drive the air more efficiently across a whole band, and it aims the result. The page on where passive gain comes from separates the two effects.
The catch is size. From a 20 mm² slot, an exponential horn with a cutoff of 500 Hz needs a mouth 218 mm across and a length of 411 mm. With a cutoff of 2 kHz it needs a 55 mm mouth and 65 mm of length. The guide to horn cutoff frequency works through the formula, the mouth guideline and the exponential, conical and tractrix profiles.
The throat matters as much as the flare. It has to sit close over the speaker slot, and the slot moves from one phone model to the next. The page on the Auricle Acoustic Waveguide shows how to find the slot on a phone in front of you.
Does the material matter?
Horn theory assumes rigid, smooth walls, so a material matters only as far as it keeps the walls that way. A 3 mm aluminium wall, a 5.3 mm maple wall along the grain and an 8.5 mm wall of solid printed PLA bend about equally. Wood also moves with humidity. Cut along the growth rings, a 10 mm slot in sugar maple can open or close by about 0.19 mm between a dry room and a humid one. Printed PLA softens near 59 °C. The guide to which material suits a passive amplifier sets out the data behind these figures.
Decisions in the order they come
Find the speaker slot
Locate the slot and decide how the throat will meet it. A gap of a few millimetres leaks sound, and a thick case widens it.
Decide what has to get louder
A horn with a mouth about 55 mm across helps from roughly 2 kHz upwards. A 1 kHz cutoff already needs a mouth twice as wide. Bass stays out of reach at desk size.
Choose a horn or a resonator
A resonator lifts one note or a few and is quick to build. A horn lifts a band above its cutoff and needs a calculated flare.
Set the cutoff, then the mouth and the length
Derive the flare constant and the mouth from the cutoff, then check whether the length fits. If it does not, fold the path or accept a higher cutoff.
Choose the material
Size the walls for stiffness, close the inside surface and allow for humidity in wood or heat in printed plastic.
Measure bare against amplified
Measure the phone on its own and in the amplifier at the same distance and volume. The procedure is on the page about measuring passive gain.
Common questions
Do passive phone amplifiers really make a phone louder?
Yes, within limits. They add no energy. A horn wastes less of what the phone’s speaker already produces and points it at the listener. The Braeburn record states up to 8 dB for its cradles. To know what a particular design adds, measure it as a pair of readings, bare and amplified.
Why does my tube amplifier make some notes stand out?
A tube resonates at frequencies set by its length. Take a 25 cm tube, 4 cm across and open at both ends. Its first resonances sit near 626 and 1,252 Hz, so notes close to those come out louder than the rest. Changing the length moves the peaks. A horn with a gradual flare avoids a single dominant peak.
Will a passive amplifier work with any phone?
Only if its throat lines up with that phone’s speaker slot. Slots sit in different places from model to model, and the Braeburn record lists a separate body for each phone generation. A thick case pushes the phone away from the throat and lets sound escape through the gap.
Does a passive amplifier drain the battery?
No. It has no electronics, and the phone’s own amplifier works just as hard with or without it. What changes is how much of the sound reaches the listener. With the amplifier in place the volume can come down a step, which keeps the phone’s output stage away from the compression it shows near maximum.
Sources
- J. Wolfe, “Open vs Closed pipes (Flutes vs Clarinets)”, University of New South Wales. Resonances of open and closed pipes, the end correction of about 0.6 times the radius.
- J. Wolfe, “Helmholtz Resonance”, University of New South Wales. The resonance of a volume with a neck.
- B. Kolbrek, “Horn Theory: An Introduction, Part 1”, audioXpress. Horn types, cutoff and the assumptions behind horn theory.