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The Observed Properties of Liquid Helium
at the Saturated Vapor Pressure

Chapter 3. First Sound Velocity

Adopted Database

Author(s)	Key #	Method	Range (K)	Uncertainty (%)
Van Itterbeek & Forrez	1	Resonance	2.5 T 4.24	< 0.26
Vignos and Fairbank	2	Pulse	2.5 T 4	< 0.3
Whitney and Chase	3	Pulse	0.15 T 1.8	0.1
Barmatz and Rudnick	4	Resonance	1.8 T 2.5	0.2
Heiserman et al.	5	Resonance	1.187 T 1.804	0.2
Tam and Ahlers	6	Resonance	1.5 T 2.16	0.1

Comments and Key to Authors

1) Ref. 10. Points above 2.5 K with errors less than 0.3%. Corrected to T₅₈ .
2) Ref. 20. Smoothed data.
3) Ref. 17. Values of the "reduced time delay", defined in terms of Whitney and Chase's value for u₁ at 0 K, u₁(0)=23830(13) cm/s, have been converted to velocities using our value of u1(0)=23821 cm/s obtained from an equation of state (Brooks (24)). This point was included in the data set. In the range 0.2 K < T < 1.1 K, the results are frequency dependent with variations as great as 20 cm/s between velocities measured at 1 MHz and 11.9 MHz.
4) Ref. 22. A constant 54 cm/s has been subtracted from the data to produce absolute agreement with the data of Tam and Ahlers. About 6 mK above T, the data show an anomaly in the temperature measurement due to the density maximum (change of sign of the expansion coefficient which affects the convective mechanism for thermal equilibrium).
5) Ref. 25. Simultaneously measured u₁, u₂, u₄.
6) Ref. 26. Simultaneously measured u₁, u₂, u₄.
7) References 27, 28 and 29 are more modern papers covering not only the velocity of sound, but also attenuation and dispersion, topics not contained in this compilation.

Table 3.1. Adopted database for first sound velocity of liquid ⁴He.

T90 (K)	u1 (m/s)	Key	T90	u1 (m/s)	Key
0.000000	2.3821E+2	3	1.869474	2.2973E+2	4
0.100365	2.3821E+2	3	1.877030	2.2953E+2	4
0.200706	2.3821E+2	3	1.895914	2.2911E+2	4
0.301026	2.3822E+2	3	1.904151	2.2893E+2	6
0.401326	2.3823E+2	3	1.904151	2.2895E+2	6
0.501608	2.3824E+2	3	1.912537	2.2869E+2	4
0.601874	2.3826E+2	3	1.930458	2.2823E+2	4
0.651991	2.3826E+2	3	1.946329	2.2780E+2	4
0.702125	2.3825E+2	3	1.954189	2.2750E+2	6
0.752245	2.3820E+2	3	1.954189	2.2749E+2	6
0.802362	2.3813E+2	3	1.961447	2.2738E+2	4
0.852476	2.3805E+2	3	1.974516	2.2699E+2	4
0.902586	2.3797E+2	3	1.986397	2.2665E+2	4
1.102955	2.3759E+2	3	1.998495	2.2627E+2	4
1.190093	2.3750E+2	5	2.004234	2.2597E+2	6
1.203267	2.3729E+2	3	2.009518	2.2588E+2	4
1.246176	2.3730E+2	5	2.022169	2.2535E+2	4
1.301319	2.3690E+2	5	2.035571	2.2490E+2	4
1.303324	2.3687E+2	3	2.047786	2.2446E+2	4
1.354445	2.3650E+2	5	2.054293	2.2420E+2	6
1.403515	2.3631E+2	3	2.054293	2.2420E+2	6
1.405517	2.3630E+2	5	2.056655	2.2412E+2	4
1.454557	2.3600E+2	5	2.063579	2.2382E+2	4
1.503598	2.3554E+2	3	2.072554	2.2353E+2	4
1.504599	2.3530E+2	5	2.079160	2.2320E+2	4
1.553637	2.3500E+2	5	2.084348	2.2294E+2	6
1.556640	2.3480E+2	6	2.086849	2.2285E+2	4
1.603690	2.3453E+2	3	2.095511	2.2249E+2	4
1.603690	2.3429E+2	6	2.103851	2.2214E+2	4
1.604692	2.3460E+2	5	2.104399	2.2209E+2	6
1.653779	2.3361E+2	6	2.104399	2.2205E+2	6
1.658789	2.3370E+2	5	2.111657	2.2176E+2	4
1.703882	2.3313E+2	3	2.114429	2.2158E+2	6
1.703882	2.3294E+2	6	2.119899	2.2133E+2	4
1.706888	2.3310E+2	5	2.124462	2.2108E+2	6
1.753981	2.3209E+2	6	2.126417	2.2088E+2	4
1.756986	2.3220E+2	5	2.133460	2.2061E+2	4
1.804065	2.3140E+2	3	2.134497	2.2057E+2	6
1.804065	2.3121E+2	6	2.136395	2.2039E+2	4
1.808071	2.3130E+2	5	2.141056	2.2018E+2	4
1.844214	2.3035E+2	4	2.144531	2.2006E+2	6
1.854119	2.3011E+2	6	2.145827	2.1995E+2	4
1.861054	2.2994E+2	4	2.149547	2.1973E+2	6

Table 3.1. (Continued)

T90 (K)	u1 (m/s)	Key	T90	u1 (m/s)	Key
2.151463	2.1971E+2	4	2.177277	2.1807E+2	4
2.154563	2.1940E+2	6	2.177377	2.1810E+2	4
2.154563	2.1943E+2	6	2.177470	2.1815E+2	4
2.155158	2.1943E+2	4	2.177561	2.1821E+2	4
2.158715	2.1919E+2	6	2.177564	2.1817E+2	4
2.159827	2.1910E+2	4	2.177670	2.1820E+2	4
2.160600	2.1907E+2	6	2.177779	2.1823E+2	4
2.162195	2.1893E+2	6	2.177874	2.1825E+2	4
2.163759	2.1882E+2	6	2.177970	2.1827E+2	4
2.164925	2.1879E+2	4	2.178070	2.1828E+2	4
2.168944	2.1848E+2	4	2.178225	2.1831E+2	4
2.172074	2.1817E+2	4	2.178331	2.1833E+2	4
2.174028	2.1796E+2	4	2.179156	2.1845E+2	4
2.174796	2.1785E+2	4	2.182933	2.1882E+2	4
2.175628	2.1777E+2	4	2.186902	2.1900E+2	4
2.175886	2.1773E+2	4	2.206879	2.1955E+2	4
2.176097	2.1769E+2	4	2.211285	2.1966E+2	4
2.176207	2.1765E+2	4	2.218489	2.1978E+2	4
2.176278	2.1765E+2	4	2.226982	2.1996E+2	4
2.176439	2.1761E+2	4	2.233971	2.2010E+2	4
2.176557	2.1757E+2	4	2.244515	2.2025E+2	4
2.176655	2.1753E+2	4	2.254519	2.2042E+2	4
2.176742	2.1747E+2	4	2.264751	2.2054E+2	4
2.176760	2.1745E+2	4	2.277122	2.2071E+2	4
2.176772	2.1743E+2	4	2.292627	2.2092E+2	4
2.176786	2.1741E+2	4	2.302212	2.2105E+2	4
2.176791	2.1739E+2	4	2.314606	2.2115E+2	4
2.176796	2.1737E+2	4	2.327541	2.2129E+2	4
2.176802	2.1752E+2	4	2.344900	2.2142E+2	4
2.176804	2.1759E+2	4	2.363446	2.2159E+2	4
2.176808	2.1763E+2	4	2.405301	2.2178E+2	4
2.176817	2.1768E+2	4	2.462922	2.2173E+2	4
2.176825	2.1771E+2	4	2.505156	2.2200E+2	2
2.176834	2.1773E+2	4	2.576309	2.2170E+2	1
2.176842	2.1775E+2	4	2.577311	2.2200E+2	1
2.176855	2.1776E+2	4	2.660552	2.2170E+2	1
2.176867	2.1779E+2	4	2.678609	2.2130E+2	1
2.176876	2.1780E+2	4	2.956223	2.1820E+2	1
2.176883	2.1783E+2	4	3.006300	2.1800E+2	2
2.176916	2.1787E+2	4	3.050364	2.1680E+2	1
2.176936	2.1790E+2	4	3.377817	2.0990E+2	1
2.177020	2.1796E+2	4	3.506953	2.0700E+2	2
2.177114	2.1799E+2	4	4.007034	1.9000E+2	2
2.177171	2.1802E+2	4	4.248035	1.7950E+2	1

Table 3.2. Knots and coefficients for the spline fit of first sound velocity of liquid ₄He.

Knots	Coefficients
K(1) = 0.000000	C(1) = 2.382100E+2
K(2) = 0.000000	C(2) = 2.382041E+2
K(3) = 0.000000	C(3) = 2.382203E+2
K(4) = 0.000000	C(4) = 2.382958E+2
K(5) = 0.5.016077	C(5) = 2.375414E+2
K(6) = 0.7021246	C(6) = 2.364020E+2
K(7) = 1.002777	C(7) = 2.270033E+2
K(8) = 1.804065	C(8) = 2.221461E+2
K(9) = 2.004234	C(9) = 2.187201E+2
K(10) = 2.154563	C(10) = 2.180010E+2
K(11) = 2.169604	C(11) = 2.176634E+2
K(12) = 2.175800	C(12) = 2.175663E+2
K(13) = 2.176300	C(13) = 2.174367E+2
K(14) = 2.176750	C(14) = 2.173641E+2
K(15) = 2.176797	C(15) = 2.175712E+2
K(16) = 2.176797	C(16) = 2.176713E+2
K(17) = 2.176797	C(17) = 2.178168E+2
K(18) = 2.176810	C(18) = 2.179702E+2
K(19) = 2.176830	C(19) = 2.181464E+2
K(20) = 2.176950	C(20) = 2.187212E+2
K(21) = 2.177300	C(21) = 2.193106E+2
K(22) = 2.178000	C(22) = 2.216496E+2
K(23) = 2.184625	C(23) = 2.238243E+2
K(24) = 2.224629	C(24) = 2.056185E+2
K(25) = 2.505156	C(25) = 1.795017E+2
K(26) - K(29) = 4.248035

Figure 3.1. The recommended values for the first sound velocity of liquid 4He as a function of temperature at saturated vapor pressure.

Figure 3.2. Detail of the recommended values for the first sound velocity of liquid 4He about the lambda transition.

Figure 3.3. The fractional deviation of the adopted database from the recommended values of the velocity of first sound in liquid 4He expressed in percent.

Figure 3.4. The fractional deviation of the adopted database from the recommended values of the velocity of first sound in liquid 4He expressed in percent for T< T.

Figure 3.5. The fractional deviation of the adopted database from the recommended values of the velocity of first sound in liquid 4He expressed in percent for T < T

Table 3.3. Recommended values of first sound velocity in liquid ⁴He.

T90	(K)	T90 (K)	u1 (m/s)
0.0000	2.382E+2	2.1765	2.176E+2
0.0500	2.382E+2	2.1766	2.176E+2
0.1000	2.382E+2	2.1767	2.175E+2
0.1500	2.382E+2	2.1768	2.175E+2
0.2000	2.382E+2	2.1769	2.178E+2
0.2500	2.382E+2	2.1770	2.179E+2
0.3000	2.382E+2	2.1800	2.186E+2
0.3500	2.382E+2	2.2000	2.194E+2
0.4000	2.382E+2	2.2500	2.203E+2
0.4500	2.382E+2	2.3000	2.210E+2
0.5000	2.382E+2	2.3500	2.215E+2
0.5500	2.383E+2	2.4000	2.218E+2
0.6000	2.383E+2	2.4500	2.219E+2
0.6500	2.383E+2	2.5000	2.219E+2
0.7000	2.382E+2	2.5500	2.218E+2
0.7500	2.382E+2	2.6000	2.217E+2
0.8000	2.381E+2	2.6500	2.214E+2
0.8500	2.381E+2	2.7000	2.211E+2
0.9000	2.380E+2	2.7500	2.208E+2
0.9500	2.379E+2	2.8000	2.203E+2
1.0000	2.378E+2	2.8500	2.198E+2
1.0500	2.377E+2	2.9000	2.192E+2
1.1000	2.376E+2	2.9500	2.186E+2
1.1500	2.375E+2	3.0000	2.178E+2
1.2000	2.373E+2	3.0500	2.171E+2
1.2500	2.371E+2	3.1000	2.162E+2
1.3000	2.369E+2	3.1500	2.153E+2
1.3500	2.367E+2	3.2000	2.143E+2
1.4000	2.363E+2	3.2500	2.132E+2
1.4500	2.360E+2	3.3000	2.121E+2
1.5000	2.355E+2	3.3500	2.109E+2
1.5500	2.350E+2	3.4000	2.097E+2
1.6000	2.345E+2	3.4500	2.084E+2
1.6500	2.338E+2	3.5000	2.070E+2
1.7000	2.331E+2	3.5500	2.056E+2
1.7500	2.322E+2	3.6000	2.041E+2
1.8000	2.313E+2	3.6500	2.025E+2
1.8500	2.302E+2	3.7000	2.009E+2
1.9000	2.290E+2	3.7500	1.992E+2
1.9500	2.277E+2	3.8000	1.975E+2
2.0000	2.262E+2	3.8500	1.957E+2
2.0500	2.244E+2	3.9000	1.939E+2
2.1000	2.223E+2	3.9500	1.920E+2
2.1500	2.197E+2	4.0000	1.900E+2
2.1760	2.177E+2	4.0500	1.880E+2
2.1761	2.177E+2	4.1000	1.859E+2
2.1762	2.177E+2	4.1500	1.838E+2
2.1763	2.176E+2	4.2000	1.816E+2
2.1764	2.176E+2

Chronological Bibliography for First Sound Velocity

1	J. C. Findlay, A. Pitt, H. Grayson-Smith, and J. O. Wilhelm, "The Velocity of Sound in Liquid Helium," Phys. Rev. 54, 506-509 (1938).
2	J C Findlay, A. Pitt, H. Grayson-Smith, and J. O. Wilhelm, “Velocity of Sound in Liquid Helium Under Pressure,” Phys. Rev. 56, 122-123 (1939).
3	V. P. Peshkov, “Experimental Determination of the Fourth Sound Velocity in Helium II,” J. Phys. USSR 10, 389-398 (1946).
4	J. R. Pellam and C. F. Squire, “Ultrasonic Velocity and Absorption in Liquid Helium,” Phys. Rev. 72, 1245-1252 (1947).
5	K. R. Atkins and C. E. Chase, “The Velocity of First Sound in Liquid Helium,” Proc. Phys. Soc. Lond. A64, 826-833 (1951).
6	R. D. Maurer and M. A. Herlin, “Pressure Dependence of Second Sound Velocity in Liquid Helium II,” Phys. Rev. 81, 444-447 (1951).
7	K. R. Atkins and R. A. Stasior, “First Sound in Liquid Helium at High Pressures,” Can. J. Phys. 31, 1156-1164 (1953).
8	C. E. Chase, “Ultrasonic Measurements in Liquid Helium,” Proc. Roy. Soc. Lond. A220, 116-132 (1953).
9	G. J. Van den Berg, A. Van Itterbeek, and W. Limburg, “Apparatus to Measure the Velocity of Sound Down to Liquid Helium Temperatures with the Optical Method,” Physica 20, 307-310 (1954).
10	A. Van Itterbeek and G. Forrez, “First Sound Measurements in Liquid Helium,” Physica 20, 133-138 (1954).
11	C. E. Chase and M. A. Herlin, “Ultrasonic Propagation in Magnetically Cooled Helium,” Phys. Rev. 97, 1447-1452 (1955).
12	G. J. Van den Berg, A. Van Itterbeek, G. M. V. Van Aardenne, and J. H. J. Herfkens, “Determination of the Velocity of Ultrasonic Waves in Liquid Helium by the Optical Method,” Physica 97, 860-866 (1955).
13	A. Van Itterbeek, G. Forrez, and M. Teirlinck, “Measurements on the Velocity of Ultrasonic Waves in Helium at 1 Degree K with Different Frequencies,” Physica 23, 63-64 (1957).
14	A. Van Itterbeek, G. Forrez, and M. Teirlinck, “Measurements on the Velocity of Ultrasonic Waves in Liquid Helium,” Physica 23, 905-906 (1957).
15	C. E. Chase, “Propagation of Ordinary Sound in Liquid Helium Near the Lambda Point,” Phys. Fluids 1, 193-200 (1958).
16	H. L. Laquer, S. G. Sydoriak, and T. R. Roberts, “Sound Velocity and Adiabatic Compressibility of Liquid 3He,” Phys. Rev. 113, 417-422 (1959).
17	W. M. Whitney and C. E. Chase, “Velocity of Sound in Liquid Helium at Low Temperatures,” Phys. Rev. Lett. 9, 243-245 (1962).
18	B. E. Keen, P. W. Matthews, and J. Wilks, “The Acoustic Impedance of Liquid 3He,” Proc. Roy. Soc. Lond. A284, 125-136 (1965).
19	I. Rudnick and K. A. Shapiro, “Velocity of Sound in Liquid Helium at its Lambda Point,” Phys. Rev. Lett. 15, 386-389 (1965).
20	J. H. Vignos and H. A. Fairbank, “Sound Measurements in Liquid and Solid 3He, 4He, and 3He-4He Mixtures,” Phys. Rev. 147, 185-197 (1966).
21	W. M. Whitney and C. E. Chase, “Ultrasonic Velocity and Dispersion in Liquid Helium II from 0.15 to 1.8 Degrees K,” Phys. Rev. 158, 200-214 (1967).
22	M. Barmatz and I. Rudnick, “Velocity and Attenuation of First Sound Near the Lambda Point of Helium,” Phys. Rev. 170, 224-238 (1968).
23	B. M. Abraham, H. Eckstein, J. B. Ketterson, M. Kuchnir, and P. R. Roach, “Velocity of Sound, Density, and Gruneisen Constant in Liquid 4He,” Phys. Rev. A 1, 250-257 (1970).
24	J. S. Brooks, “The Properties of Superfluid Helium Below 1.6 Degrees Kelvin,” Ph.D. Thesis, University of Oregon, 1973 (unpublished).
25	J. Heiserman, J. P. Hulin, J. Maynard, and I. Rudnick, “Precision Sound-Velocity Measurements in Helium II,” Phys. Rev. B 14, 3862-3867 (1976).
26	W. Y. Tam and G. Ahlers, “Superfluid Fraction of 4He from 1.5K to T Lambda (P) and from Vapor Pressure to the Melting Curve,” J. Low Temp. Phys. 66, 173-190 (1987)
27	C. Buchal and F. Pobell, “Attenuation and dispersion of first sound near the superfluid transition of 3He-4He mixtures” Phys. Rev. B14,1103-1122 (1976).
28	R. Carey, Ch. Buchal and F. Pobell “Attenuation and dispersion of first sound near the superfluid transition of pressurized 4He”. Phys. Rev. B16, 3133-3147 (1977).
29	D. B. Roe, H. Meyer and A. Ikushima, “Sound Propagation in 3He-4He Mixtures Near the Superfluid Transition” J. Low Temp. Phys. 32, 67-99 (1978).