# Is there a math formula to calculate difference of dB of sound, in different pure transmitting mediums?

Is there a math formula to calculate the difference of dB of sound, in different pure transmitting mediums?

For example, based on a measurable decibel level, with a known frequency, a known atomic weight of say, oxygen or hydrogen, a known volume of transmitting medium.

Two unlabeled boxes the same size, one with oxygen the other hydrogen, I send a sound wave through each box, measure the dB and then be able to tell which box has Oxygen from the resulting dB level. Is there a formula? PS With a formula I may be able to predict what the dB level may be.

• I hope member Theo will try to answer this. – Mark DeGregg Feb 22 '17 at 18:32

## 1 Answer

The level of the sound after passing through the box will depend on the attenuation coefficient of the gas and the length of the path through the gas. The attenuation coefficient for the gas depends on the pressure too. I think that attenuation for hydrogen is lower than for oxygen at the same pressure but I was not able to find actual data yet.

However I suggest to measure the difference in the speed of sound rather than attenuation. The speed of sound in hydrogen is about 4 times larger than in oxygen (at the same temperature). Using an ultrasound transducer you can just send a short pulse through the box and receive the echo from the opposite wall. The time of flight of the acoustic pulse will give you the speed of sound. I assume you can measure the dimensions of the box.

The difference in attenuation may be too small to measure accurately.