# Acoustic Interferometry Pchem ‘Cloud’ Lab – Properties of Gases

An acoustic interferometer is an instrument, using interferometry, for measuring the physical characteristics of acoustic (soundwaves in liquids or gases. This is often a good instrument to begin a physical chemistry laboratory because the instrumentation is relatively simple to build (DIY), use remotely and redesign and repurpose for a lot of different physical chemistry measurements. This blog will provide a guide to setting up a simple acoustic interferometer for measuring the speed of sound of air or any gas that is contained within the acoustic interferometer tube (pchem ‘cloud’ lab YouTube Video is also publicly available). The speed of sound (c) is directly dependent on the thermodynamic properties of the medium it is traveling:

c = Sqrt(Ks / )

where Ks is the isentropic bulk modulus (or the modulus of bulk elasticity for gases) and  is the density. This can further be used with specific equations of state to make several thermodynamic property relationships (specifically the adiabatic index or ratio of specific heats – see references below). Hence, it is recommended that students first spend some time familiarizing themselves with basic physical chemistry background information and do some simulation and/or computational ‘experiments’ (e.g., molcalc.org, PHeT, ChemCompute) to become familiar with the molecular details and foundational principles. Specifically, it is good to interpret the adiabatic index in terms of the more intuitive concept of heat capacity and then try to understand the connection between heat capacity and the compressibility of a gas.

Computational Chemistry Component: Go to molcalc.org (or ChemCompute or download and install orca or gamess) and calculate the heat capacity of each of the following greenhouse gases.

### DIY Instrument

To get started with a basic DIY setup you need a speaker, microphone, tube/container and a way to send noise to the speaker and record from a microphone (basically, a computer, tablet or mobile phone with an attached speaker and mic). Below is a picture of a setup I made in 5 min. I found a clear tube (container of some old xmas candy) with end caps. I punched a hole in the two rubber end caps and inserted an earbud (cheap < \$10 set of 3.5mm jack earbuds) in one end-cap and a microphone (sony lav mic I had lying around as an extra microphone) in the other end-cap. I put the end-caps back on the tube and put the tube next to a 1 foot measurement stick (showing inches and mm). A picture is shown below:

This simple system doesn’t have a way to change the composition, temperature or pressure of the gas within the tube, but it’s a quick and easy DIY setup to get started. This simple system is perfect for testing out different speakers, microphones, tubes, end-caps, etc and making sure everything works for transmission of sound through the speaker and detection (recording) from the microphone. The most common app I use for handling sound transmission and recording is Audacity. I found it easy to use a pc, mac or raspberry pi computer and connect an earbud headset and/or microphone. I also tried using a tablet and even a cell phone with android and iOS. All where fairly easy to get working for a simple DIY acoustic interferometer setup. There are many options of available hardware combinations and software applications for anyone wanting to set this type of system up themselves. A compressed zip file of Audacity data collected for the system shown above is provided here:

Using the audacity data provided, you can download and analyze the acoustic interferometry data to determine the resonance mode frequencies. Making a plot of resonance mode (N) versus the resonant frequency should produce a linear area of points that can be fit. The slope is related to the length of the tube and the speed of sound of air (roughly 343 m/s). Hence, determine the exact length of the tube used for the measurement (you can see from the picture above that the approximate length is 10 inches).

A Google Spreadsheet has been created and made publicly available to show a summary of the information above and a sheet with basic data analysis and a calculation of the precise tube length. – A public shared link is provided here.

### Remote Acoustic Interferometer

There are lots of additions or improvements that can be made to this simple DIY acoustic interferometer to make it more user friendly, functional and most importantly allow for more accurate and precise measurements of a wider range of atomic and molecular systems and under a wider ranges of thermodynamic conditions (temperature, pressure, etc). There are 4 items that I personally consider most important (but please find your own most important aspects to optimize and modify for):

• Different Gases and/or Mixture of Gases. I want to start with a way to connect several common gas cylinders found in a typical modern chemistry lab and be able to purge the acoustic interferometer with various gases and then make measurements on the gases. This will primarily be used as a remote access (cloud) instrument lab. So, I want the gas selection and gas flow to be remotely accessible and controllable.
• I would like to be able to have the gases flow through a heat exchanger to allow for variable temperature of the sample (gas).
• I would like the system to be more ‘visual’ to operate. An example, is a Kundt’s tube which is often clear and filled with saw-dust or styrofoam balls and uses a large enough speaker that resonance frequencies can be seen.
• The remote access and control needs to be moved to a web interface for simplicity and better automation and general interfacing of the apparatus.

The first of these ideas has been implemented as part of ASU Online Pchem Lab for Spring 2022. The remotely accessible acoustic interferometer with gas control (and 4 gases connected to the system) is currently accessible through AnyDesk (VNC) (the AnyDesk ID and password are provided upon a request email sent to biopchem@gmail.com). A screenshot taken Jan 2022 is shown below.

Anyone and everyone is encouraged to access and collect data on this remotely accessible cloud instrument at ASU. The ‘unknown’ gas will be changed every week and I welcome anyone that is interested to remotely access the system and see if they can determine what the unknown gas of the week is!! The common starting point is to use the known gases to determine an accurate length of the acoustic interferometer tube. I am made a link to the biopchem public Google Sheet here for anyone wanting a starting point example. Also, some recently collected Audacity data from this remote instrument (which is on the ASU-Tempe Campus in PSH532, the physical chemistry laboratory) is provided below:

### Data and Error Analysis

A critical component to all physical chemistry labs is being able to analyze, visualize and/or plot and fit computational and experimental data. It is also a core component to be able to estimate or calculate associated error with all numerical values. While some links above provide some data analysis in Google Sheets, there is no associated error analysis. I am working on a colab notebook to better illustrate and provide an example of data and error analysis associated with this pchem cloud lab.