How does an acoustic megaphone work?
May 30, 2017 8:14 AM   Subscribe

How does an acoustic (unpowered) megaphone (or gramophone horn) amplify sound? I know that it directs sound, and catches the sound that would go in less useful directions, but I am led to believe that it also actually amplifies sound by the principle of acoustic impedance matching. The problem is, I don't understand this concept.

This video comes tantalizingly close to making me understand it.

Every other source I see only talks about directing the sound, but these aren't scholarly or technical sources that I'm finding, so I don't necessarily trust them. And when I specifically try looking for sources that mention impedance matching, all I can find is things about electrical impedance.

So, can someone help me understand how this acoustic impedance matching works? Also, can we use this knowledge to answer these further questions?
1. What is the maximum size that a megaphone can be and still be useful?
2. How much amplification would we get from that biggest megaphone?
posted by Galaxor Nebulon to Science & Nature (8 answers total) 6 users marked this as a favorite
It's a similar reason why speaker cones are cone shaped. You make the transition between the source and the medium the sound is going into more gradual to better match the impedance between the two.

Impedance mismatch happens when something travels from a medium with some impedance to a medium with a different impedance. Whenever this happens, power is lost. Every medium has some characteristic impedance. This impedance depends on the inherent resistive properties of the medium, mass, and stiffness. The size and shape of the medium contributes to these impedance characteristics. If you want don't want to lose power, you want to match impedances.

This is a useful concept in all sorts of systems. It's the same reason that if you want to maximize power you match impedances between, say, your headphones and your music player. Also the reason we have middle ear bones - you lose a lot of power going from sound in air to sound in fluid. Also why they put a bunch of gel on your skin if you've ever had electrophysiology or ultrasound performed.

In the case of the megaphone - When you move sound from your throat to the open air, you have a big impedance mismatch because the size and shape and other qualities of these two cavities is drastically different. When you speak into the air, much sound is reflected back at you because of this impedance mismatch. Gradually changing the cross section of the cavity - like you do with a megaphone - helps to match the impedance between your throat and the air and makes the transfer of power more efficient - less is reflected back.

The megaphone does provide some directionality, as you mentioned, improving the signal-to-noise ratio at a listener directly in front of it. Also, because of the resonant characteristics of the megaphone, you'll get a boost in the high frequencies, which typically helps make things clearer as that's where most consonants are (same reason why people cup their ears to hear better - you boost high frequencies doing this and get about a 5 dB gain).

The questions about the theoretical limits are tough. I guess technically a megaphone with a cross section gradation approaching whatever size and shape of the air you're putting the signal into would be expected to do better, but I don't know if the returns would be diminishing or not or what other issues you'd get. As far as what the output would be - I don't know. I guess you'd have to build this and measure the transfer function or something.
posted by Lutoslawski at 8:46 AM on May 30, 2017 [4 favorites]

Very cool question! I thought I knew the answer, but as I looked in to it, I'm less sure, because the detailed physics and math of nonlinear acoustics of the vocal apparatus is really hard stuff™. Here goes:

It's amplification compared to not using a megaphone, it's not amplifying the actual power coming off your vocal chords. Asking for the loudest acoustic megaphone is like asking for the loudest trumpet: it depends on who's lungs it's linked to. That said, we can ask what the ideal shape of a megaphone is for maximizing power transmission: that probably depends on what frequency bands you want to maximize transmission of, because the megaphone is also acting as a filter, boosting some components more than others.

Electrical impedence is basically the same thing as acoustic impedance, at least as far as the math goes. In both cases, the idea is to use impedance matching to maximize power transfer. That is, the megaphone doesn't give any more power to your vocal apparatus, but it does transfer more power to the air, because the shape is designed to make a smoother transition between the vocal chords and the air of the outer world. That is, it reduce ts the amount of power lost to reflection and absorption.

I don't know how much math you want to get in to but wikipedia has a nice lay summary: " If the acoustic impedance of the two media are very different most sound energy will be reflected (or absorbed), rather than transferred across the border. ... Horns are used like transformers, matching the impedance of the transducer to the impedance of the air. This principle is used in both horn loudspeakers and musical instruments. ... Sound, coupling with air, from a loudspeaker is related to the ratio of the diameter of the speaker to the wavelength of the sound being reproduced. " More here.

If you want the gory math, see WP's Acoustic Impedance. If, like a lot of us, your mechanical intuition is better than your electrical or acoustic intuition, check out the Impedance Analogy.

I haven't worked it all out in my head yet, but we should probably be able to use the impedance analogy to construct a mechanical model of what a megaphone is doing with its impedance matching. If anyone can help with that I'd appreciate it. It might be something as simple as a lever.

Finally, here's a scholarly article Transmissions of Lung Sounds that has a nice overview of the general biophysics as well as a section on impedance.
posted by SaltySalticid at 8:51 AM on May 30, 2017 [1 favorite]

One other thought about high frequencies - it might also be, in conjunction with the resonant properties of the megaphone, that you get more high frequency boost since high frequencies are mass controlled, rather than stiffness, and most of the impedance matching you're doing with the megaphone would be mass matching. Not totally sure, but seems reasonable.
posted by Lutoslawski at 8:57 AM on May 30, 2017

Ok, how about this. We can safely ignore the electrical amplification of e.g. loudspeakers, and still gain an understanding from horn design. That is, a horn on a loudspeaker is doing the same thing to the vibrations of the driver as a fully acoustic megaphone is to doing to your voice. Horns are horns, from an acoustic point of view, no matter what's driving them. Here's a technical but fairly accessible introduction to horn theory, it covers the properties of many horn shapes, including parabolic, exponential, tractrix. Also has lots of cool graphs. Most "good" megaphones and speaker horns I see seem to be exponential or traxtrix, only novelty/promotional megaphones seem to be conical these days.
posted by SaltySalticid at 9:06 AM on May 30, 2017

Thanks, I'm gonna read all that stuff! Meanwhile, a question: The energy that's lost to a bad impedance match: Where does that go? It's reflected back, you say? Does it, like, cause my throat to heat up or something?
posted by Galaxor Nebulon at 9:43 AM on May 30, 2017

Aha, I found the answer to my latest clarifying question in the article that SaltySalticid posted:

"The result [of the impedance mismatch] is that most of the energy put into
a direct radiating loudspeaker will not reach the air, but will be converted to
heat in the voice coil and mechanical resistances in the unit."
posted by Galaxor Nebulon at 9:57 AM on May 30, 2017

And, singing techniques include shaping the vocal tract for better impedance matching between the innards and the outards.
posted by JimN2TAW at 1:27 PM on May 30, 2017 [1 favorite]

If the wind is blowing at 8mph, I do not move at 8mph. Is that because the wind is low-impedance and my body is high-impedance? Is a sail an impedance-matching device? If I jump in a river with an 8mph current, I'll move at much closer to 8mph. Is that because the water is higher-impedance, and better matched to the impedance of my body?
posted by Galaxor Nebulon at 11:26 AM on May 31, 2017

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