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My daughter and I did a project and made this:

http://osxdaily.com/2014/07/28/diy-iphone-speakers-paper-towel-roll-plastic-cups/

We hypothesized that the sound was "amplified" because it directed the sound toward the front. We tested this by turning around the "speaker" and we found that indeed it was louder in front, but it was also louder in back than when the iphone is out of the speaker.

We then hypothesized it had something to do with the sound vibrations in the cardboard, but when holding the iphone speaker to the cardboard directly (without putting it into the "speaker", it didn't make any difference.

Can someone explain why this appears to "amplify" the sound, and what effects we are experiencing with this?

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Quite an interesting project indeed.

The paper towel roll and cups are are working as an acoustic megaphone, also called (in ancient times) speaking trumpet.

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Directional focus of the radiating sound waves is part of the way the megaphone works, but that's not all, as, as you have noticed, there is also amplification in other directions, not just the front of the cone (and the other project without paper cups also works to some extent).

That is due to an acoustic phenomenon called acoustic impedance matching. Acoustic impedance is often compared to electrical impedance, and much like in electrical circuits, circuit stages (e.g. amplifier and speaker) work better when their impedance is similar (or "matched"), also in acoustic systems sound energy is transmitted more efficiently when the vibrating body has an acoustic impedance closer to that of the propagation medium.

By adding mass to the vibrating body that's producing the sound, the megaphone approaches more closely the acoustic impedance of air, and thus the energy produced by the emitting device (the vocal chords in the case of a speaking trumpet, or the iphone speaker in the case of your daughter's project) is transmitted more efficiently to the air.

Note that yes, the megaphone device must vibrate for this to work, but the vibration is transmitted by the air vibrating inside the tube (much like the the vibration of air inside a brass instrument), not by direct contact between the speaker and the tube. The same principle was at work too in the primitive gramophones or phonographs. The stylus induced vibration to a diaphragm which produced faintly audible sound; it was this sound that was amplified by the characteristic horn.

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I think that in the case of your project the paper roll provides the vibrating mass and the plastic cups some directional focus, as their mass is very little and the way they are tied to the roll is anyway very loose to receive vibration from the roll.

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  • Wow! What a great answer. Thank you so much. My daughter and I will study megaphones now to understand this phenomena better. And I think we will experiment with this effect (maybe try a metal pipe instead of a cardboard tube for more mass).
    – richard
    Commented Jul 10, 2016 at 1:18
  • The key here is "matching" the right impedance, not the larger the mass the better. Too much mass and the speaker will not have enough power to excite it. And there are other factors involved like density and elasticity of the materials. But experimenting is excellent, of course, trying find what materials work best and why will surely be fun and educational.
    – José David
    Commented Jul 10, 2016 at 12:17
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Pitch content that roughly matches the resonance tendencies of the shape will also get a boost relative to the other frequency content. The resonance frequencies of the tube are probably very limited, hence the sound will continue to be unbalanced in terms of EQ. The flare of the old phonographs have a wider range of resonant frequencies.

The vibrations of the cardboard itself are probably represent a loss of energy at the tube openings. If the tube were metal there would be more energy flaring from the openings relative to the weaker, more flexible cardboard. I doubt the tube material itself functions like a violin body, or at least, if it does, it is no where near as efficient as a violin body.

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  • Good points Phil, cardboard is almost for sure not the best material, just the most readily available for a home project. As I said in my comment above I'm concerned that a metal pipe may be to heavy (the human voice is generally more powerful than a tiny iPhone speaker) but perhaps a small metal tube gives better results than a large cardboard one.
    – José David
    Commented Jul 11, 2016 at 10:07
  • About the violin, in that case the sound is transmitted to the body of the instrument through the wooden bridge (by means of direct physical contact) not through air. The violin body then vibrates in a specific way due to the way it is built (the upper board is kept in permament tension by the shape of body). The f holes add specific resonances too. In the case of the megaphone the vibration is transmitted to the body through air, so the principles at work are indeed different.
    – José David
    Commented Jul 11, 2016 at 10:19

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