Analysis of First,Second, and Fourth Sound Modes in a Helium 4 Superfluid

Christopher Spencer
UCLA Physics and Astronomy
Professor Gary Williams
11 June 2014

Abstract

First,second,and fourth sound were successfully found and plotted. Graphs show a lack of steepness in decay as sound modes approach \(T_{\lambda}\), this could be due to refilling liquid helium later than recommended leaving less medium for the sound modes to propogate through. Scattering factor,n, was found to be n=1.239 ± .007 and porosity,P, was found to be 0.46 ± 0.02 close to the theoretical value of \(\approx 40 \%\) porosity.

Introduction

Acoustics can be used to further investigate properties of material. For example the acoustics of sending sound waves in a cyldrical and rectangular geometry can be used to see if and how the speed of sound changes in air. In the same way, the properties of a liquid can investigated using acoustics. In quantum fluids, apparent attenuation and dispersion of sound occurs.Helium 4 is a bose liquid that exhibits these superfluid properties, which supports wave motions we can measure. In this experiment we want to investage sound modes in a superfluid helium 4 liquid called 1st,2nd, and 4th sound.

Theory

In this lab, the acoustic effects of superfluid helium 4 are measured. What is meant by saying superfluid is that a phase transition occurs in which a portion of the fluid is able to flow without friction or zero viscosity [1]. The superfluid component of liquid helium can then lead to new sound modes, ones that are investigated in this lab. The superfluid transition of helium 4 has a characteristic transition temperature called \(T_{\lambda}=2.172 K\) at saturated vapor pressure. The phase diagram of helium 4,shown in figure 1, and it shows that