Attenuation and dispersion of first sound near the superfluid transition of ${}^{3}{He}$ - ${}^{4}{He}$ mixtures

The attenuation

α

, the velocity

u

, and the dispersion

D = u (ω) - u (0)

of first sound have been determined in

{}^{3}{He}

{}^{4}{He}

mixtures (molar

{}^{3}{He}

concentrations

X_{3} = 0, 0.070, 0.194, 0.377, and 0.517

) at frequencies

2.3 \leq \frac{ω}{2 π} \leq 627

kHz, and in the temperature range 1 μK ≤

| T - T_{λ} |

≤ 10 mK. From the measured velocities we calculate the thermodynamic velocity

u (0)

, as well as

{(\frac{\partial S}{\partial P})}_{λ}

and

{(\frac{\partial V}{\partial P})}_{λ}

. The attenuation and the dispersion are considerably reduced when the

{}^{3}{He}

concentration is increased. They are interpreted as arising from a relaxation process occurring only below

T_{λ}

, and a fluctuation process occurring on both sides of the

λ

transition. Both contributions have about equal strength. The strength

A_{R}

of the relaxation process decreases nearly three orders of magnitude with increasing

X_{3}

in our concentration range. Using the obtained relaxation time

τ^{'} = τ^{'}_{0} t^{- x^{'}}

(with

t = \frac{| T - T_{λ} |}{T_{λ}}

), and published data for the correlation length

ξ^{'}

, and for the second-sound velocity

u_{2}

, we find

τ^{'} = \frac{ξ^{'}}{u_{2}}

for

T < T_{λ}

. The amplitude

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Attenuation and dispersion of first sound near the superfluid transition ofHe3-He4mixtures