# Effects of Acoustic Impedance

1. May 30, 2012

### troglodrew

I am working on an animal vocalization study and I need a clarification about acoustic impedance. All of the sources I have gone to are a bit too technical for me, so if you would be so kind to answer my question I would be very grateful!

My question is this:
What happens to a sound in high impedance environments versus low impedance environments? For example, if a bird is utilizing the same call in a high elevation forest (with low impedance) will that sound degrade faster than it would in a low elevation (high impedance) forest?

I know other factors are at play (humidity, temperature, attenuation) - however, in a perfect scenario, if other factors were the same, what specifically happens to a sound wave in high versus low acoustic impedance environments? To add to this, what would be the discernible difference to the human ear.

Thank you so much. I really appreciate your help!

2. May 30, 2012

### DragonPetter

Acoustic impedance will determine the speed of sound in that acoustic medium.

Acoustic impedance is also important to consider when you have a mis-match of impedance at some boundary. Consider a wall that has a different acoustic impedance than the air surrounding it. When a sound wave is in one medium and incident on a new one with different impedance, you will get:

1. reflections
2. refraction

You can use snell's law just like in optics to calculate these things.

If you replace the wall with more air, but air that is slightly different in impedance, you will also have some energy reflects, and some refracted, although the effect will be very small if they have closely matched impedances.

There are also other calculations you can make regarding the reflection coefficient and the boundary conditions that acoustic impedance is a factor in if you look at Zoeppritz equations, it tells you the angle and phase that your reflections will have.

Last edited: May 30, 2012
3. May 30, 2012

### DragonPetter

Elevation can definitely play a role. Temperature and humidity directly affect the acoustic impedance. If you are familiar with temperature gradients, you can see that there will also be an acoustic impedance gradient between sea level and high in the atmosphere. So, if a bird chirps in the sky, the sound may bend in a direction to some degree.

The distance the sound travels should not depend that greatly on the acoustic impedance directly unless it just rained or you're comparing winter and summer, since it is probably mostly the same, but humidity may play a factor. The amount of energy transferred from the bird's voicebox thing to the air depends on the acoustic impedance, but that shouldn't change so much. However, sound intensity will reduce over distance by something you can't escape really - called spreading loss - that is dependent on geometry, and then there are other losses where the acoustic energy is absorbed, which is what humidity in the air might do to certain frequencies (just like salt in the water can absorb certain frequencies and lower the intensity of the sound over distance), but this effect would not be directly related to acoustic impedance.

I'm not sure about how strong the effects are in air, but in water the sound will bend up or down depending on the temperature/salinity gradients. This is an effect of refraction. You could also have channels (say hypothetically between 300 feet and 500 feet the air has a much different temperature/humidity than the air above or below that region), in the acoustic medium that cause sound to bounce up and down between a horizontal column at a given elevation. Channeling can greatly increase the range of an acoustic signal since it alters the geometry that determines spreading loss, but this depends on the wavelengths/frequencies that the sound has. This all depends on the frequency of the sound used also. Again, it may not be significant in air, I've never studied that and I'm applying underwater acoustics to your question, so its hypothetical.

Last edited: May 30, 2012
4. May 30, 2012

### troglodrew

Thank you so much for your reply. This is very helpful. Can you tell me what the discernible difference in sound would be in a high impedance medium versus a low impedance medium?
Would the bird require more energy to transmit a call in a low impedance medium? If so, then I would assume, lower frequencies would benefit the bird in lower impedance environments?
Thanks again!!

5. May 30, 2012

### DragonPetter

The differences in impedance can have subtle effects, so you may not see much difference. I think you may be jumping to inaccurate conclusions.

To answer your question as direct as possible, I will simplify it like this. Consider two cases, a homogenous, infinite volume of air with a higher acoustic impedance and one with a lower acoustic impedance, and a bird flying in each volume:

The main discernible effect would be the speed that the sound travels through the medium, and this just says you will have time delay A in one volume, and time delay B in another before it reaches an ear. It will travel the same distance at the same intensity in both, just one gets to the distance faster.

The only difference in energy required to transmit a call (which will say how loud the sound is at a given distance) with the same intensity would be the difference in mismatches of impedance between the bird's voicebox, the ear listening, and the two different cases of air impedances. This would probably be negligible, but I'm not sure. The reason I say it is negligible is because in the real world, all the other factors I described in the other post have a bigger impact.

Also, you should not tie the ideas of low impedance to low frequency. They are not directly related to each other and do not go hand-in-hand. When I said things depend on frequency, I am alluding to other discussions that would only complicate things, but I hint at it to be more accurate.

6. May 30, 2012

### troglodrew

Thank you. You have cleared a lot up.

7. May 30, 2012

### DragonPetter

Also, if you look up/research the mathematical relations for:

- Acoustic impedance
- speed of sound in a medium
- Spreading loss (this is not just specific to sound, but other energy radiation like light too)
- Sound absorption (also referred to as sound attenuation)
- Refraction
- Reflection

You will get a good understanding of how all the information is related.

travel time dependency: You will see the speed of sound depends on the acoustic impedance of the medium it travels through. This is about the most direct "conclusion" or fact you can come to when you consider a homogenous acoustic impedance.

distance dependency: When the sound transitions between air of 2 different acoustic impedances, this is when you have to consider refraction and reflection that can affect the intensity of the sound. Note that it is a difference and transition in acoustic impedance more so than acoustic impedance itself that is causing this behavior. You will see the distance a sound can travel while having a certain volume is dependent on things we call losses. There are spreading losses and absorption losses to name a few. Neither are directly dependent on a homogenous acoustic impedance. They are dependent on the geometry the sound travels, e.g. a open volume in a sphere (all directions), a pipe/channel (confined to travel in a certain direction). The sound energy has to spread out over the surface area it travels through, so a pipe would keep the sound focused over a greater distance. The sound absorption factor can be ultimately dependent on impedance mismatching on the very small scale, but this is actually complex, non-linear, and negligible when we abstract the concept as an "absorption loss" and use empirical data to calculate this. For our purpose, we consider the air as a single acoustic impedance, not the acoustic impedance between different molecules/gases in the air that actually can absorb the energy. This is why absorption loss is not defined by acoustic impedance, but by temperature/humidity/pressure factors that tell us how much energy will be absorbed. We are looking at the big picture of sound transmission here, not how sound is actually absorbed in losses.

Last edited: May 30, 2012
8. May 30, 2012

### troglodrew

This is great. Thank you so much for your help. I was on a bit of an off-ramp there.