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The Observed Properties of Liquid Helium
at the Saturated Vapor Pressure

Chapter 4. Second Sound Velocity

Adopted Database

Author(s)	Key #	Method	Range (K)	Uncertainty (%)
Heiserman et al	1	Resonance	1.187 T 2.150	< 0.2
Greywall & Ahlers	2	Resonance	2.16 T 2.172	< 0.2
Tam & Ahlers	3	Resonance	0.15 T 2.16	< 0.2
Peshkov	4	Resonance	0.5 T 1.15	0.75
Wang et al.	5	Resonance	1.187 T 1.804	0.07
Lipa & Marek	6	Resonance	1.13 T 2.09	see comment 6

Comments and Key to Authors

1) Ref. 23. Points at 2.05 K and 2.15 K omitted as inconsistent with later measurements.
2) Ref. 19. Data above 2.145 K omitted in favor of data of Greywall and Ahlers.
3) Ref. 26.
4) Ref. 8. Data used only below 1.15 K, higher temperature data is inconsistent with later measurements.
5) Ref. 27.
6) Ref. 28. Consists of points normalized to measurements of Greywall and Ahlers at t=1-T/T =10^-3. Authors note that for t < 3x10^-6 tests of the calculation of superfluid density from second sound begin to deviate from the best fit function.
7) The velocities are listed in m/sec. Multiply by 100 to convert to cm/sec.

Table 4.1. Adopted database for second sound velocity in helium II.

T90 (K)	u2 (m/s)	Key	T90	u2 (m/s)	Key
0.551743	1.05000E+2	4	1.652076	2.03647E+1	5
0.601874	8.30000E+1	4	1.653078	2.03648E+1	5
0.651991	6.20000E+1	4	1.653779	2.04000E+1	1
0.702125	4.65000E+1	4	1.653779	2.03450E+1	3
0.752245	3.60000E+1	4	1.654080	2.03647E+1	5
0.802362	2.90000E+1	4	1.655082	2.03645E+1	5
0.852476	2.44000E+1	4	1.656084	2.03644E+1	5
0.902586	2.16000E+1	4	1.657086	2.03642E+1	5
0.952694	1.98000E+1	4	1.703882	2.03600E+1	2
1.002777	1.89000E+1	4	1.703882	2.02950E+1	3
1.052861	1.85000E+1	4	1.706888	2.03300E+1	1
1.102955	1.83300E+1	4	1.708993	2.03030E+1	5
1.122986	1.83000E+1	4	1.753981	2.01350E+1	3
1.137607	1.83754E+1	5	1.756986	2.01600E+1	1
1.137607	1.83742E+1	5	1.758690	2.01364E+1	5
1.83742E+1	1.83739E+1	5	1.804065	1.98900E+1	2
1.153029	1.83300E+1	4	1.804065	1.98450E+1	3
1.167152	1.84292E+1	5	1.808071	1.98800E+1	1
1.190093	1.84500E+1	1	1.808271	1.98395E+1	5
1.215134	1.85636E+1	5	1.808371	1.98381E+1	5
1.246176	1.87500E+1	1	1.854119	1.94200E+1	1
1.251399	1.87366E+1	5	1.854119	1.94000E+1	3
1.301319	1.90600E+1	1	1.857822	1.93832E+1	5
1.337208	1.92012E+1	5	1.904151	1.88000E+1	1
1.337409	1.91954E+1	5	1.904151	1.87800E+1	2
1.354445	1.93000E+1	1	1.904151	1.87550E+1	3
1.374079	1.93980E+1	5	1.904151	1.87620E+1	3
1.405517	1.95900E+1	1	1.907353	1.87314E+1	5
1.418729	1.96354E+1	5	1.954189	1.78400E+1	1
1.418829	1.96393E+1	5	1.954189	1.78640E+1	3
1.454558	1.98500E+1	1	1.954189	1.78700E+1	3
1.468770	1.98797E+1	5	1.957192	1.78245E+1	5
1.504599	2.01000E+1	1	1.976908	1.73749E+1	5
1.517108	2.00828E+1	5	2.004234	1.66800E+1	1
1.553637	2.02600E+1	1	2.004234	1.66380E+1	3
1.556640	2.02000E+1	3	2.006736	1.65832E+1	5
1.563245	2.02338E+1	5	2.026757	1.59588E+1	5
1.603690	2.03600E+1	1	2.036769	1.56137E+1	5
1.603690	2.03800E+1	2	2.046682	1.52424E+1	5
1.603690	2.03100E+1	3	2.054293	1.49260E+1	3
1.611903	2.03336E+1	5	2.054293	1.49350E+1	3
1.612103	2.03339E+1	5	2.056697	1.48429E+1	5
1.646264	2.03643E+1	5	2.066614	1.44125E+1	5
1.647266	2.03645E+1	5	2.076632	1.39451E+1	5
1.648168	2.03646E+1	5	2.084349	1.35550E+1	3
1.649170	2.03647E+1	5	2.086133	1.34778E+1	2
1.650172	2.03647E+1	5	2.086553	1.34370E+1	5

Table 4.1. (Continued)

T90 (K)	u2 (m/s)	Key	T90	u2 (m/s)	Key
1.651174	2.03647E+1	5	2.096678	1.28791E+1	5
2.096777	1.28865E+1	2	2.169878	4.95010E+0	2
2.104399	1.24120E+1	3	2.170387	4.79702E+0	6
2.104399	1.24070E+1	3	2.170722	4.69640E+0	2
2.106209	1.23112E+1	2	2.171109	4.57153E+0	6
2.114429	1.17390E+1	3	2.171274	4.51860E+0	2
2.114572	1.17519E+1	2	2.171601	4.40753E+0	6
2.121978	1.12045E+1	2	2.172127	4.28890E+0	2
2.124462	1.09980E+1	3	2.172516	4.14923E+0	6
2.128512	1.06792E+1	2	2.172678	4.08362E+0	6
2.134262	1.01738E+1	2	2.172714	4.06910E+0	2
2.134497	1.01330E+1	3	2.173031	3.94628E+0	6
2.143812	9.21890E+0	2	2.173227	3.86140E+0	2
2.144531	9.15200E+0	3	2.173323	3.81918E+0	6
2.147768	8.77150E+0	2	2.173667	3.66760E+0	2
2.149547	8.53300E+0	3	2.173702	3.65415E+0	6
2.151231	8.34400E+0	2	2.174015	3.50552E+0	6
2.154307	7.93250E+0	2	2.174071	3.47580E+0	2
2.154563	7.87300E+0	3	2.174404	3.30200E+0	2
2.154563	7.88500E+0	3	2.174434	3.29027E+0	6
2.157027	7.53700E+0	2	2.174695	3.14020E+0	2
2.158715	7.24200E+0	3	2.174712	3.13242E+0	6
2.159393	7.16540E+0	2	2.174894	3.02889E+0	6
2.160303	7.02130E+0	6	2.174954	2.98440E+0	2
2.160601	6.92000E+0	3	2.175059	2.92025E+0	6
2.160728	6.94955E+0	6	2.175174	2.84060E+0	2
2.161555	6.80603E+0	6	2.175303	2.75214E+0	6
2.161688	6.77390E+0	2	2.175395	2.68280E+0	2
2.162195	6.63700E+0	3	2.175417	2.67168E+0	6
2.162543	6.62154E+0	6	2.175579	2.54290E+0	2
2.162797	6.57542E+0	6	2.175637	2.50102E+0	6
2.163463	6.44730E+0	6	2.175726	2.42110E+0	2
2.163548	6.42830E+0	2	2.175757	2.39647E+0	6
2.163759	6.34400E+0	3	2.175873	2.28530E+0	2
2.164086	6.32429E+0	6	2.175873	2.29089E+0	6
2.164086	6.32941E+0	6	2.175965	2.19915E+0	6
2.164859	6.16542E+0	6	2.175982	2.17940E+0	2
2.165154	6.10070E+0	2	2.176020	2.14431E+0	6
2.165684	5.99373E+0	6	2.176052	2.11151E+0	6
2.166426	5.82716E+0	6	2.176092	2.06150E+0	2
2.166576	5.79100E+0	2	2.176134	2.01360E+0	2
2.167091	5.67341E+0	6	2.176173	1.97109E+0	6
2.167334	5.61191E+0	6	2.176176	1.96400E+0	2
2.167822	5.49940E+0	2	2.176282	1.83476E+0	6
2.168334	5.37105E+0	6	2.176309	1.79320E+0	2
2.168924	5.21570E+0	2	2.176312	1.79069E+0	6
2.169001	5.19167E+0	6	2.176370	1.70920E+0	6

Table 4.1. (Continued)

T90 (K)	u2 (m/s)	Key	T90	u2 (m/s)	Key
2.169524	5.05328E+0	6	2.176405	1.64980E+0	2
2.169730	4.99384E+0	6	2.176416	1.63489E+0	6
2.176478	1.52760E+0	2	2.176798	2.36555E-1	6
2.176492	1.50471E+0	6	2.176798	2.31385E-1	6
2.176495	1.49907E+0	6	2.176798	2.31731E-1	6
2.176521	1.44833E+0	6	2.176798	2.25518E-1	6
2.176533	1.42230E+0	2	2.176798	2.28820E-1	6
2.176576	1.33353E+0	6	2.176798	2.22728E-1	6
2.176576	1.33060E+0	2	2.176798	2.26967E-1	6
2.176587	1.30893E+0	6	2.176798	2.23868E-1	6
2.176590	1.29971E+0	6	2.176798	2.23047E-1	6
2.176610	1.24990E+0	2	2.176798	2.19049E-1	6
2.176614	1.24231E+0	6	2.176798	2.20092E-1	6
2.176625	1.21207E+0	6	2.176798	2.21236E-1	6
2.176637	1.17840E+0	2	2.176798	2.18135E-1	6
2.176641	1.17056E+0	6	2.176798	2.17216E-1	6
2.176649	1.14596E+0	6	2.176798	2.17216E-1	6
2.176650	1.14391E+0	6	2.176798	2.17216E-1	6
2.176660	1.11521E+0	6	2.176798	2.17216E-1	6
2.176660	1.11828E+0	6	2.176798	2.15304E-1	6
2.176660	1.11490E+0	2	2.176798	2.14397E-1	6
2.176672	1.07626E+0	6	2.176798	2.13386E-1	6
2.176678	1.05750E+0	2	2.176798	2.13386E-1	6
2.176693	1.00600E+0	2	2.176798	2.12502E-1	6
2.176697	9.94256E-1	6	2.176798	2.12502E-1	6
2.176706	9.59200E-1	2	2.176798	2.10558E-1	6
2.176710	9.43007E-1	6	2.176798	2.08686E-1	6
2.176717	9.16500E-1	2	2.176798	2.07804E-1	6
2.176726	8.77500E-1	2	2.176798	2.07852E-1	6
2.176729	8.62034E-1	6	2.176798	2.07852E-1	6
2.176733	8.41800E-1	2	2.176798	2.05951E-1	6
2.176737	8.25000E-1	2	2.176798	2.05093E-1	6
2.176743	7.97461E-1	6	2.176799	1.97314E-1	6
2.176744	7.93200E-1	2	2.176799	1.94212E-1	6
2.176754	7.39040E-1	6	2.176799	1.94212E-1	6
2.176764	6.69348E-1	6	2.176799	1.95274E-1	6
2.176764	6.71398E-1	6	2.176799	1.92427E-1	6
2.176775	5.89418E-1	6	2.176799	1.91700E-1	6
2.176777	5.65851E-1	6	2.176799	1.91700E-1	6
2.176785	4.83908E-1	6	2.176799	1.88324E-1	6
2.176788	4.51148E-1	6	2.176799	1.87355E-1	6
2.176792	3.82645E-1	6	2.176799	1.87355E-1	6
2.176795	3.24563E-1	6	2.176799	1.88426E-1	6
2.176797	2.72095E-1	6	2.176799	1.84011E-1	6
2.176797	2.66044E-1	6	2.176799	1.80988E-1	6
2.176797	2.61090E-1	6	2.176799	2.02214E-1	6
2.176797	2.48180E-1	6	2.176799	2.02434E-1	6

Table 4.1. (Continued)

T90 (K)	u2 (m/s)	Key	T90	u2 (m/s)	Key
2.176798	2.42206E-1	6	2.176799	2.01435E-1	6
2.176798	2.36261E-1	6	2.176799	2.01435E-1	6
2.176798	2.35518E-1	6	2.176799	2.02490E-1	6
2.176799	1.99587E-1	6	2.176799	1.76016E-1	6
2.176799	1.98775E-1	6	2.176799	1.72643E-1	6
2.176799	1.99832E-1	6	2.176799	1.73834E-1	6
2.176799	1.94911E-1	6	2.176799	1.69586E-1	6
2.176799	1.95192E-1	6	2.176799	1.70702E-1	6
2.176799	1.78538E-1	6	2.176799	1.67700E-1	6
2.176799	1.78538E-1	6	2.176799	1.67819E-1	6
2.176799	1.77168E-1	6	2.176800	0.00000	0
2.176799	1.77211E-1	6

Table 4.2. Knots and coefficients for the spline fit for the velocity of second sound. The spline returns the velocity in m/s.

Knots	Coefficients
K(1) = 0.5517426	C(1)=1.050000E+02
K(2) = 0.5517426	C(2)=9.287425E+01
K(3) = 0.5517426	C(3)=4.973642E+01
K(4) = 0.5517426	C(4)=2.712778E+01
K(5) = 0.6419700	C(5)=1.931258E+01
K(6) = 0.8062300	C(6)=1.795336E+01
K(7) = 0.9297000	C(7)=1.923863E+01
K(8) = 1.069640	C(8)=2.115625E+01
K(9) = 1.285500	C(9)=1.921708E+01
K(10) = 1.720200	C(10)=1.575245E+01
K(11) = 1.940430	C(11)=1.192157E+01
K(12) = 2.068850	C(12)=8.953388E+00
K(13) = 2.126220	C(13)=6.771458E+00
K(14) = 2.153079	C(14)=5.506380E+00
K(15) = 2.164207	C(15)=4.456879E+00
K(16) = 2.169182	C(16)=3.840343E+00
K(17) = 2.170551	C(17)=2.542421E+00
K(18) = 2.174832	C(18)=1.957438E+00
K(19) = 2.175738	C(19)=1.427086E+00
K(20) = 2.176319	C(20)=1.001273E+00
K(21) = 2.176600	C(21)=6.743104E-01
K(22) = 2.176735	C(22)=4.565972E-01
K(23) = 2.176780	C(23)=3.519492E-01
K(24) = 2.176787	C(24)=2.088277E-01
K(25) = 2.176797	C(25)=1.059874E-01
K(26) - K(29)	C(26)=0.000000E+00
= 2.176800

Figure 4.1. The recommended values for the velocity of second sound in helium II as a function of temperature at saturated vapor pressure.

Figure 4.2. Detail of the recommended values for the second sound velocity in helium II about the lambda transition.

Figure 4.3. The fractional deviation of values of the adopted data base from the recommended values for the velocity of second sound in helium II expressed in percent.

Table 4.3. Recommended values of second sound velocity in helium II.

T90 (K)	u2 (m/s)	T90 (K)	u2 (m/s)
0.6000	8.385E+1	1.6500	2.037E+1
0.6500	6.273E+1	1.7000	2.033E+1
0.7000	4.707E+1	1.7500	2.018E+1
0.7500	3.635E+1	1.8000	1.990E+1
0.8000	2.928E+1	1.8500	1.946E+1
0.8500	2.461E+1	1.9000	1.883E+1
0.9000	2.166E+1	1.9500	1.796E+1
0.9500	1.990E+1	2.0000	1.678E+1
1.0000	1.893E+1	2.0500	1.511E+1
1.0500	1.849E+1	2.1000	1.269E+1
1.1000	1.835E+1	2.1500	8.492E+0
1.1500	1.837E+1	2.1760	2.164E+0
1.2000	1.851E+1	2.1761	2.055E+0
1.2500	1.874E+1	2.1762	1.937E+0
1.3000	1.900E+1	2.1763	1.806E+0
1.3500	1.928E+1	2.1764	1.660E+0
1.4000	1.956E+1	2.1765	1.489E+0
1.4500	1.981E+1	2.1766	1.275E+0
1.5000	2.003E+1	2.1767	9.809E-1
1.5500	2.021E+1	2.1768	0.000E+0
1.6000	2.033E+1

Chronological Bibliography for Second Sound Velocity

1	V. P. Peshkov, “Determination of the Velocity of Propagation of the Second Sound in Helium II,” Sov. Phys. USSR 10, 389-398 (1946).
2	V. P. Peshkov, “Velocity of Second Sound From 1.3 to 1.03 K,” JETP USSR 18, 950-951 (1948).
3	R. D. Maurer and M. A. Herlin, “Second Sound Velocity in Helium II,” Phys. Rev. 76, 948-950 (1949).
4	J. R. Pellam and R. B. Scott, “Second Sound Velocity in Paramagnetically Cooled Liquid Helium II,” Phys. Rev. 76, 869-870 (1949).
5	R. D. Maurer and M. A. Herlin, “Pressure Dependence of Second Sound Velocity in Liquid Helium II,” Phys. Rev. 81, 444-447 (1951).
6	D. De Klerk, R. P. Hudson, and J. R. Pellam, “Second Sound Propagation Below 1 Degree K,” Phys. Rev. 93, 28-37 (1954).
7	P. J. Bendt, R. D. Cowan, and J. L. Yarnell, “Excitations in Liquid Helium: Thermodynamic Calculations,” Phys. Rev. 113, 1386-1395 (1959).
8	V. P. Peshkov, “Second Sound in Helium II,” Sov. Phys. JETP 11, 580-584 (1960).
9	D. L. Johnson and M. J. Crooks, “Second Sound Velocities in Helium II Near T Lambda,” Phys. Lett. A 27, 688-689 (1968).
10	C. J. Pearce, J. A. Lipa, and M. J. Buckingham, “Velocity of Sound Near the Lambda Point of Helium,” Phys. Rev. Lett. 20, 1471-1473 (1968).
11	J. A. Tyson and D. H. Douglass Jr., “Critical-Region Second-Sound Velocity in Helium II,” Phys. Rev. Lett. 21, 1308-1310 (1968).
12	D. L. Johnson and M. J. Crooks, “Second-Sound Velocities, Superfluid Hydrodynamics, and Scaling Laws in Helium II,” Phys. Rev. 185, 253-257 (1969).
13	R. Williams, S. E. A. Beaver, J. C. Fraser, R. S. Kagiwada, and I. Rudnick, “The Velocity of Second Sound Near T Lambda,” Phys. Lett. A 29, 279-280 (1969).
14	M. Kriss and I. Rudnick, “Size Effects in Helium II as Measured by Fourth Sound,” J. Low Temp. Phys. 3, 339-357 (1970).
15	R. A. Sherlock and D. O. Edwards, “Oscillating Superleak Second Sound,” Rev. Sci. Instr. 41, 1603-1609 (1970).
16	D. S. Greywall and G. Ahlers, “Second Sound Velocity, Scaling, and Universality in Helium II Near the Superfluid Transition,” Phys. Rev. Lett. 28, 1251-1254 (1972).
17	G. Terui and A. Ikushima, “Superfluid Density Near the Lambda Point of 4He Under Pressure,” Phys. Lett. A 39, 161-162 (1972).
18	G. Winterling, F. S. Holmes, and T. J. Greytak, “Brillouin Light Scattering from Superfluid Helium Under Pressure,” in 13th Conference on Low Temperature Physics, edited by K. D. Timmerhaus, W. J. O'Sullivan, and E. F. Hammel (New York: Plenum Press, 1972), pp. 537-541.
19	D. S. Greywall and G. Ahlers, “Second Sound Velocity and Superfluid Density in 4He Under Pressure Near T Lambda,” Phys. Rev. A 7, 2145-2162 (1973).
20	A. Ikushima and G. Terui, “Superfluid Density Near the Lambda Point of 4He Under Pressure,” J. Low Temp. Phys. 10, 397-405 (1973).
21	W. F. Vinen, C. J. Palin, and J. M. Vaughan, “The Scattering of Light by Liquid 4He Close to the Lambda Line,” in 13th International Conference on Low Temperature Physics, edited by K. D. Timmerhaus, W. J. O'Sullivan, and E. F. Hammel (New York: Plenum Press, 1973), pp. 524-531.
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