pHYSICS

Experiment 3

Aim of the Experiment

To find the adiabatic compressibility of a given liquid using an ultrasonic interferometer.

Principle

The schematic diagram of an ultrasonic interferometer is shown in the figure.

In an ultrasonic interferometer, the ultrasonic waves are produced by the piezoelectric method. In a fixed frequency variable path interferometer, the wavelength of the sound in an experimental liquid medium is measured, and from this one can calculate its velocity through that medium. The apparatus consists of an ultrasonic cell, which is a double walled brass cell with chromium plated surfaces having a capacity of 10ml. The double wall allows water circulation around the experimental medium to maintain it at a known constant temperature.

The micrometer scale is marked in units of 0.01mm and has an overall length of 25mm. Ultrasonic waves of known frequency are produced by a quartz crystal which is fixed at the bottom of the cell. There is a movable metallic plate parallel to the quartz plate, which reflects the waves. The waves interfere with their reflections, and if the separation between the plates is exactly an integer multiple of half-wavelengths of sound, standing waves are produced in the liquid medium. Under these circumstances, acoustic resonance occurs. The resonant waves are a maximum in amplitude, causing a corresponding maximum in the anode current of the piezoelectric generator.

The velocity of ultrasound is determined principally by the compressibility of the material of the medium. For a medium with high compressibility, the velocity will be less. Adiabatic compressibility of a fluid is a measure of the relative volume change of the fluid as a response to a pressure change. Compressibility is the reciprocal of bulk modulus, and is usually denoted by the Greek word beta (β).The adiabatic compressibility of the material of the sample can be calculated using the equation,

Where ρ is the density of the material of the medium and v is the velocity of the sound wave through that medium.

Materials required

Ultrasonic interferometer, sample liquids, high frequency generator etc.

Procedure

Procedure for performing the simulator:

• From the combo box Choose medium, select the desired experimental liquid.

• Using the slider Frequency of wave, set the frequency of the ultrasonic sound used. A lower frequency will give a longer wavelength, which is easier to measure accurately.

• Switch ON the frequency generator using the Power on button.

• Then adjust the GAIN and ADJ knobs such that the ADJ value is greater than GAIN value.

• At this micrometer setting the ammeter will show a maximum. Do not record the micrometer reading at this maximum. It could be inaccurate because the first maximum should be at zero and the micrometer cannot be set to zero.

• In the simulator, right and left arrows are provided to increase or decrease the micrometer distance. Increase the micrometer setting till the anode current in the ammeter shows a new maximum. (After the first few clicks, if you click and hold the arrow, the micrometer setting will increase continuously. A single click increases it by a small increment.) Note down the micrometer reading at the new maximum.

• Stop when you have recorded micrometer readings for 10 or more maxima.

• The distance between the adjacent maxima is calculated. From the equations, one can calculate the velocity of sound waves through the medium and also the adiabatic compressibility of the liquid can be calculated.

• A Show cross- section button is provided to see the cross section of the interferometer cell. The graph can be displayed using the button Show graph if needed.

• Show result button displays the result after doing the experiment.

Observations

Least count of the micrometer: …………..mm

Frequency of the ultrasound used (f): …………….Hz

n = ........... , D =...........mm.

v = ...... ms^-1.

Observation Table

Result

The adiabatic compressibility of the given liquid medium = ................................. m²N^-1.

Reference Material

1. Practical Physics. G. L. Squires. 4/e, 2001, Cambridge University Press.

2. Virtual Labs (https://vlab.amrita.edu/?sub=1&brch=280&sim=210&cnt=4)

Questions

1. What is frequency of Ultra sound?

2. What is ultrasonic interferometer.