# Homework Help: Sound amplification

1. Jun 17, 2010

### the_dialogue

1. The problem statement, all variables and given/known data

This is a problem I've been pondering, and I simply need some recommendations for texts to read on the topic.

Suppose you have an enclosed air chamber with an acoustic source on one end (e.g.). How can one predict the amplification, distortion, and dissipation of the sound that ends up on the other end of the chamber?

I am especially interested in what I think are likely basic mathematics that explain the amplification of the sound if the chamber is conical. This is akin to ear trumpets used for many years. Why does the sound get amplified? What are the relevant acoustic formulations?

2. General questions and Attempt

What text should I look into to help me understand this topic and answer these kinds of questions?

The only thing that I've heard, in a very unscientific way, is that sound is amplified by a factor equal to the Entry Cross section / Exit Cross section (so in a cone where the sound enters the larger end, the sound is amplified by some factor 'x'). But this alone is insufficient for my cause (i.e. I want some sort of mathematical basis for this kind of statement).

Thank you!

2. Jun 19, 2010

### RSW00001

I wouldn't call this amplification. To me that implies that you get out more energy than you put in, as would be the case with a powered audio amplifier. What you are doing is focusing (concentrating) the sound energy into a smaller space to make more efficient use of it.

3. Jun 19, 2010

### the_dialogue

Thanks so much for the response RSW!

But is "focusing" not a form of amplification?

Can someone offer a theoretical/objective answer?

4. Jun 20, 2010

### poor mystic

No, amplification is when more power comes out than went in. With an amplifier a whisper can fill a stadium, nobody wants to use ear-trumpets for this work.

5. Jun 20, 2010

### poor mystic

But the short, sweet and perfectly "scientific" answer is that a sound is a set of waves, which can be channeled in a cone so that the whole energy of a wave which enters a come can be compressed into a smaller tube. I think it is fair to say that the ratio of cross-sectional areas will be a fair indicator of the gain in energy intensity in the smaller part of the cone.

6. Jun 20, 2010

### the_dialogue

Thanks poormystic.

Is it reasonable to suggest that some kind of interference can happen depending on the geometry of the chamber? In other words, can we draw the analogy from light scattering in a conical mirror and apply it sound waves? I would think not, but nonetheless I seem to think some interference could result.

7. Jun 20, 2010

### poor mystic

Yes
in ordinary cases sound waves can be superposed, and it is reasonable (but very computation-intensive) to generate a model based on the reflection and addition of waves within the cone.

By reflection and superposition, all the energy of the wave becomes concentrated in a smaller area within the cone.

You can demonstrate the truth of additive superposition for yourself with a microphone and a pair of speakers which can be switched off or on to allow you to read the result of adding the waveforms in the air, or with a reflective wall of some kind that you can move around.. There are downloadable oscilloscopes which would make such an experiment a breeze.