Reflection of sound depends on frecuency?

[idmena]

Hi! I need some help understanding something related to sound.

I am currently studying a book called Sound Propagation. An Impedance Based Approach, by Yang-Hann Kim. There is a part where he talks about reflection and transmission of acoustic waves on a flat surface of discontinuity. He gets the coefficients for presure and velocity, and them combines them to get the power reflection and transmission, that is the one that would affect what we can hear. But I find it odd that his equations do not depend on frecuency, only in the characteristic impedance of the two media. In other words. The reflecion and transmission of power do not depend of the frecuency of the wave, all the components of the incoming signal are reflected and transmited by the same factor.

Later on he continues to talk about transmission loss at a partition. In that case he considers a thin wall, and takes into account the mass, the spring constant and the damping coefficient. In that case he doesn't even consider the characteristic impedance of the material that the wall is made of, and that equation does depend on the frecuency of the incident signal. He explained that when the incoming frecuency is much bigger than the resonant frecuency of the wall that's when the well known mass law applies, and continues to consider the other cases.

So tell me, how is this possible? When an acoustic waves enters a different medium all of it's components are reflected by the same factor? If so, how comes the transmission loss depends on the frecuency? The transmission loss is defined in terms of the transmission coeficient, which he stated before that depends only on the characteristic impedance of the media.

Attached are two pictures with the equations I mentioned. Sorry I don't know latex.

Thanks in advance

 

[pumila]

The reflection of a wave from a boundary where there is partial transmission and partial reflection is determined by the characteristic impedance of the wave in each media. Thus when dealing with reflection one starts by determining the impedance. The impedance will change with frequency (dispersion) and hence the reflection changes with frequency. The problem is important in acoustics where it is perfectly possible to have the same impedance (and hence no reflection at the boundary) for two different media and vastly different wave velocities; this does not happen with light waves so one can take short cuts in light waves that might lead one to think that reflection is a function of wave velocity, but light waves actually follow the same rules, but the properties of those media that transmit light waves are restricted, unlike acoustic media.

In your second paragraph, I have not seen the book, but it sounds like he is dealing with those components that are used to derive that characteristic impedance - deriving the characteristic impedance from first principles. So you see the same variation of characteristic impedance with frequency.