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I'm learning a bit about sound and was wondering:

If the speed of sound is determined by the amount of matter the source is surrounded with why doesn't it go through a wall?

Example:

Speed of sound is 343m/s

But in water, it moves at 1500 m/s, because of the increase of matter surrounding it. And since iron have more tightly packed matter it moves even faster, because it's moving the matter to move the vibrations.

If this is true, why doesn't the sound go through walls?

Is it because it loses its "strength" for the amount it travels?

Sound doesn't go through walls? Please tell my neighbor.

In electromagnetism, a medium has a property called an "impedance" which is related to the index of refraction and the speed of waves in the medium. At an interface between two media, the relative impedances determine how much of an incoming wave is transmitted or reflected, so that the entire power of the incoming wave goes somewhere. At an "impedance-matched" interface the reflection coefficient goes to zero. In signal cables and waveguides for electromagnetic waves this leads to people adding "terminating resistors" in various places, so that an incoming signal doesn't get reflected back from a cable junction. Conversely, at a junction with an impedance mis-match, the reflection coefficient is generally nonzero and not all of the power is transmitted.

You can do the same sort of analysis for sound waves moving from one medium to another. The reflection and transmission coefficients can depend on the frequency of the wave, as well, which is why my neighbor complains when I have my music turned up too loud: they can hear the low-frequency bass sounds just fine through the wall, but the high-frequency components (that they'd need to follow the lyrics) don't reach them.

Sound waves are just pressure oscillations; when they strike a surface they are either reflected, transmitted, or absorbed. When they're transmitted, you'll hear them on the other side.

According to Wikipedia, regarding acoustic absorption:

Deformation causes mechanical losses via conversion of part of the sound energy into heat, resulting in acoustic attenuation, mostly due to the wall's viscosity.

The fraction of sound absorbed is governed by the acoustic impedances of both media and is a function of frequency and the incident angle.

In general, soft, pliable, or porous materials (like cloths) serve as good acoustic insulators - absorbing most sound, whereas dense, hard, impenetrable materials (such as metals) reflect most.

So, walls will reflect the sound waves, as well as absorb them. The effectiveness of this depends on the material properties of the wall, as well as the frequency of the sound (low frequencies travel much easier through plywood, for instance).