First off, much of this answer is based on the amazingly helpful University of New South Wales website on acoustic impedance. This is a topic I'm very interested in and this is a great opportunity to reduce the complex topic of impedance down for my own learning purposes as well as to provide an answer.

You ask,

does that mean that high frequency sound waves have a lower acoustic impedance than low frequencies (hence why high frequencies are reflected and more than low frequencies?)

Actually, specific acoustic impedance, $z$, is a property of the *medium*, not of the waves themselves.

It has both a real part, **resistance** $r(\omega)$ and an imaginary part, **reactance** $x(\omega)$:

$$z(\omega) = r(\omega) + i \space x(\omega)$$

Where $\omega$ is the angular frequency, $2 \pi f$.

Reactance has a positive and a negative part: **compliance (capacative) reactance** $x_C(\omega)$, and **inertive (inductive) reactance** $x_L(\omega)$:

$$x(\omega) = x_L(\omega) - x_C(\omega)$$

Without going into exhaustive detail, I want to point out the relevant fact that inertiance, associated with the density of the medium, *is proportional* to frequency:

$$x_L(\omega) \propto \omega$$

While compliance, associated with the elasticity of the medium, *is inversely proportional* to frequency:

$$x_C(\omega) \propto \frac{1}{\omega}$$

In other words,

- denser media are more likely to impede high-frequency waves
- more elastic media are more likely to impede high-frequency waves

In the example of your concrete wall - a dense, inelastic media relative to air - we might expect more of an impedance missmatch (between the two media) for higher-frequency energy than for the lower frequency energy. This would result in the higher frequency energy being reflected more.

*Amplitude* coefficients are complex. The reflection and transmission coefficients must account for both amplitude change and phase change. In order to account for both of these, complex coefficients are required. These are the most general, and are needed for a complete description.

In some special (and simple) cases, the phase shift is $0^\circ$ or $180^\circ$, and the coefficient may be expressed as a positive real or negative real. An example would be an ideal mirror.

There might be times when all that is needed is the amplitude is needed, so the phase can be dropped. (I'm not sure when one would use such a thing.)

If one is interested in *intensity* or *power* coefficients, the appropriate coefficient is the modulus of the amplitude coefficient, and hence is a positive definite number.

**Edit** In the last paragraph I really should say *the square* of the modulus

## Best Answer

The frequency can change upon reflection; see e.g. Doppler Radar. And if the reflecting object is not infinitely heavy, have a look here