I have found that if a cup with my hand with my thumb on my index finger, and all the fingers progressively more greatly clenched into a cone shape, a lot like the shape of when holding waffle cone, and a put my mouth against the ring formed by my index finger and thumb and speak into my hand, my voice gets deeper and louder, though muffled of course. I found that other hand configurations offer even greater changes, offer even greater changes. All involve basically forming a cup with ones, and the most effective involve two hands. One in particular actually makes my throat hurt while speaking. It involves putting the four fingers of my left hand over the pinky and next finger in of my right, with the thumb laying across the first three fingers (also right hand, which, along with the pinky, are in the 'saddle' between my thumb and index finger of my right, with the left hand thumb on the meaty padding where the thumb meets the palm, and speaking in the ring formed.
Any ideas on the cause of this phenomena? Especially why my voice would sound deeper, though they are probably related.

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Sound is the vibration of air. Just as the sub woofer box adds resonance to your sound systems bass notes. So can your hands. A cupped hand behind your ear will reflect more sound into your ear. Have a look at a cat. A audio amplification by building a sound shell with your hands is all you are doing....The apparent deeper tone is just the audio note being redirected... and what has this to do with astronomy?

Er. . . nothing. But it is physics related. *grins sheepeshly*. Sorry, didn't realise the questions were astronomy only. My bad. ANd I know that the sound IS deeper, because I recorded some of the sound with a head set mic poked through my fingers. Could you explain further, and would you like me to upload some?

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All I can add is.. That the higher toned notes of your voice are absorbed by the hands... The lower tones ( frequency ) are reflected. Sound engineering.

Your mouth is a resonant cavity modified by coupling it with another cavity. Ever notice the bass in a car sounds different(louder) with the windows cracked open?
Cupping your hands does not result in a new resonator, per say. The wavelength of bass notes is much too long for standing waves to be a factor.

"louder, though muffled?"

The uneven surface of one's fingers and hand tend to scatter higher frequencies while allowing lower frequencies to pass with less interference.

The pitch (deepness) of your voice remains the same. It's the predominently higher-pitched timbre that is muted, thus giving the impression that your voice is deeper.

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I am Mugs, of the Alien clan of Usa, Nordamerica, a Terran, of Sol. A human.

Whoever says "perception is reality" is daft. It's merely an abstraction, and often not a very good one.

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Everything I need to know I learned through Googling.