acousticswaves
If I put my hand over the speaker of my phone like in the picture, I can clearly hear my music amplified, why does this happen?
The only cause I can think about is the fact that all the intensity doesn't have to "expand" in all directions but only towards me, so the formula intensity = source_power / area is "applied" only after as a normal spherical surface
I also wanted to know why the sound seems a little higher (the frequency) if I do this to amplify my speakers
(I'm considering the speakers are emitting some kind of music or something nonperiodic, the situation gets a bit boring if you consider a uniform source)
It basically means Alice hears nothing. Atleast, not until Bob crosses (at which time your equation is no longer valid, the $-$ in the denominator becomes a $+$). She hears a sonic boom as Bob crosses her, and then hears two sounds at once. The first sound is whatever is being played by Bob after he crosses her, at a frequency $\frac{f}{3}$. The second, more interesting sound, is that whatever sounds were emitted by Bob are heard backwards, at a frequency $f$ (This comes from the $-f$ you derived). So, if Bob was playing Mozart's Symphony 23, and switched to Coldplay's Yellow when he passed Alice, Alice hears: boom; Yellow at one-third the pitch and simultaneously Symphony 23 playing backwards. Would probably sound horrible ;-)
Why is this?
Remember, Bob's speed is greater than the speed of sound. So, wavefronts emitted by Bob now are much closer to Alice than the wavefronts emitted in the past :
Here, the moving dot is Bob, and assume Alice to be another dot to the right of Bob in his path.
The edge of the cone that you see being formed is the "sonic boom". It's a region of a rapid rise and fall of pressure (extremely high pressure). Right after it passes, you see two kinds of wavefronts passing Alice. The first is the "left sides of the circular wavefronts". These have been emitted after Bob passed, and are playhed normally, with a third of the frequency (Yellow in my example). The other kind is the right side of the circular wavefronts emitted before Bob passed Alice. As you can see, these are heard top-down, i.e., the ones emitted last are detected first.
For comparison, here is the same diagram if the relative speed was $<v_0$:
To summarize, the negative frequency just means that the sounds emitted at that time are heard "backwards" at a later time--"reflected" at the point in time when Bob crosses Alice.
BONUS: http://what-if.xkcd.com/37/
It isn't possible to create an audio source in mid-air using the method you've described. This is because the two ultrasonic waves would create an audible source if the listener were standing at that spot, but those waves would continue to propagate in the same direction afterwards. You would need, as I point out below, some sort of medium which scattered the waves in all directions to make it seem as if the sound were coming from the point at which you interfered the two waves.
It is possible, however, to make the user percieve the sound as coming from a specific location, but it isn't as easy as the author makes it seem. I can think of two different ways. First of all, as described by @reirab, you can get audio frequencies by interfering two sound waves of high frequency. When they interfere they will generate a beat note which has the frequency of the difference between the two frequencies. I.E. if you send a sound beam with frequency $f_1=200\ \text{kHz}$ and another beam with $f_2=210\ \text{kHz}$, the frequency heard in the region where they combine will be $\Delta f-=f_2-f_1=10\ \text{kHz}$ which is in the audio band of humans.
There is an additional difficulty. You will need the sound to come out in a well-defined, narrow (collimated) beam, and this is not terribly easy to do. A typical speaker emits sound in all directions. There are many techniques for generating such beams, but one is to use a phased array.
How can you use this to make a person perceive the sound as coming from a specific point?
What does it mean to perceive sound as coming from a specific location? Our ears are just microphones with cones which accept sound mostly from one direction (excepting low frequencies). A large part of the way we determine where the sound came from is just the relative volume in our two ears. So, you could use the interference effect described above with beams which are narrow enough that you can target each ear. By using two separate sets of beams targeting each ear with different volumes, you could make the person perceive the sound as coming from a specific location; at least as well as a 3D movie makes a person perceive images in 3D.
The second method is to use the same interference effect, but this time combining the two beams at a point where a material scattered the sound waves in all directions. I'm going to be honest, I'm not sure how realistic such materials are, but lets assume they exist for now. If you did so, the two sound beams would be scattered with equal amplitude in all directions and the person you are trying to fool would percieve the sound as coming from this point. This method has the advantage of truly sounding to the person as if the sound came from that direction in all respects including reflections, phasing, etc.
In summary, the idea is definitely possible (maybe there are more ways than I've given), but it isn't as simple as the passage in the book makes it out to be.
Best Answer
There's no amplification - the total sound energy is the same.
What is happening is that your hand is reflecting more of the sound towards you.
The reason for the change in sound quality is most likely because your hands absorb some frequencies slightly more and reflect other frequencies better.