acoustics
I have gone through a lot of Google links before bothering you people. I wanted to know how megaphones work. I only got answers like they direct sound in one direction only (most probably in direction of audience).
Please elucidate, and also answer a question: Once the sound waves come out out of the mega phone won't they start expanding and moving in all directions?
What you did actually is the so-called horn loudspeaker. And what horns do is to narrow the propagation of sound produced by the loudspeaker. Conventional loudspeaker propagates a lot of sound up, down, left, right, etc. in relation to the axis of the cone. Horns concentrate the sound along the axis, which is therefore louder for the listener (if not located extremely to the side). That's why the police or other people who want to communicate in open space use such devices.
More technically (physically) speaking, given the displacement of the driver in your speaker (which does not change as you put the horn to it) the small cross-sectional area of the horn restricts the passage of air, which means increased air pressure in the direction of the listener as compared to your loudspeaker without the added horn, and increased pressure means increased sound volume.
As Carl Witthoft below suggested (thank you) another contributor to the higher efficiency of horn loudspeakers is the fact that they are better matching acoustical impedances of the source of the sound and the so-called load (air). The higher pressure increases the external impedance - which is naturally low due to low air density - to (better) match the impedance of the source. In (conventional) direct radiating loudspeakers this mismatch leads to a lot of energy being converted to heat within the driver instead of into the sound wave.
This has also some positive "side-effects". If designed and manufactured properly, i.e. when you are concerned mostly with the sound quality and not just with the loudness produced (which is not always the case, as you might have noticed with the police devices), horns contribute to better efficiency of the loudspeaker and lower distortion of sound. The loudspeaker's cone simply does not need to be displaced so much from rest position to produce the same volume as conventional speaker. Less displacement means less distortion of sound (and lower requirements concerning the amplifier), which can be demonstrated by the fact that good horns can produce total harmonic distortion 10 times lower than their conventional peers also considered good quality.
For quite some time horn loudspeakers were in retreat - they are big after all (especially if you want them to produce the whole spectrum of sound, including the bass, this way, as longer wave requires larger horn), which means their so-called WAF* (Wife Acceptance Factor) is rather low. Recently, however, they are coming back and are highly valued by many audiofiles, as the limitations of the smaller conventional loudspeakers became obvious. Also, more and more people are beginning to realize that the main culprit of poor sound quality is not the CD (turntable) or amplifier, but the loudspeakers.
*However, WAF can always be worked on, as can be seen - arguably - below. The real challenge is to match great sound with great visual design.
Pnoe Horns by Arcadian Audio
Klipsch Cornwall (bass unit is direct radiating, and not horn unfortunately)
To expand on Xcheckr's answer:
The full equation for a single-frequency traveling wave is $$f(x,t) = A \sin(2\pi ft - \frac{2\pi}{\lambda}x).$$ where $f$ is the frequency, $t$ is time, $\lambda$ is the wavelength, $A$ is the amplitude, and $x$ is position. This is often written as $$f(x,t) = A \sin(\omega t - kx)$$ with $\omega = 2\pi f$ and $k = \frac{2\pi}{\lambda}$. If you look at a single point in space (hold $x$ constant), you see that the signal oscillates up and down in time. If you freeze time, (hold $t$ constant), you see the signal oscillates up and down as you move along it in space. If you pick a point on the wave and follow it as time goes forward (hold $f$ constant and let $t$ increase), you have to move in the positive $x$ direction to keep up with the point on the wave.
This only describes a wave of a single frequency. In general, anything of the form $$f(x,t) = w(\omega t - kx),$$ where $w$ is any function, describes a traveling wave.
Sinusoids turn up very often because the vibrating sources of the disturbances that give rise to sound waves are often well-described by $$\frac{\partial^2 s}{\partial t^2} = -a^2 s.$$ In this case, $s$ is the distance from some equilibrium position and $a$ is some constant. This describes the motion of a mass on a spring, which is a good model for guitar strings, speaker cones, drum membranes, saxophone reeds, vocal cords, and on and on. The general solution to that equation is $$s(t) = A\cos(a t) + B\sin(a t).$$ In this equation, one can see that $a$ is the frequency $\omega$ in the traveling wave equations by setting $x$ to a constant value (since the source isn't moving (unless you want to consider Doppler effects)).
For objects more complicated than a mass on a spring, there are multiple $a$ values, so that object can vibrate at multiple frequencies at the same time (think harmonics on a guitar). Figuring out the contributions of each of these frequencies is the purpose of a Fourier transform.
Best Answer
I find the explanation given in the first paragraph of Wikipedia article is pretty good. Let me just elaborate some aspects to make it more clear.
Megaphone is simply an extension of your vocal tract. Therefore the acoustic impedance of the whole system rises so the pressure and volume flow variations at your vocal chords may grove. A trade-off is significant fatigue of vocal chords (well, conservation of energy...) and a bit unnatural sound of human voice. The extended vocal tract has modified radiation impedance and frequency response so the spectrum of the voice will be changed in a manner physiological waveguide wouldn't do.
A little off topic: there are therapeutic techniques based on this very phenomena. By extension of vocal tract by appropriate long narrow pipes you may let's say do some "vocal chords stretching and fitness".
You are right, according to Huygens principle sound is expanding (or tries to expand - don't forget the interferrence!) to all directions but there is no telling whether the intensity of the sound will be the same in all directions. The megaphone concetrates the intensity in its direction.
Don't forget the reflexion of the sound. In the room, usually just a smaller part of the sound is delivered to you by the direct field. The rest is sound reflected from the walls. Therefore you haven't to concentrate the sound energy, the room itself will partly do it for you by not letting the sound go towards infinity. But when you want to shout at a demonstration of unions somewhere outside, something should concertate the sound for you or it's just going to be wide-spread and therefore not loud. From the cone of the megaphone comes a narrow spherical wave with pronounced directivity and the diffraction is not so significant (see the GIFs here).