Uncertainty analysis
According to the ISO guidelines the expanded relative uncertainty of the ultrasonic velocity DUc/Uc, can be expressed as
The time delay was measured with a picoseconds resolution. However, due to extra systematic errors, such as diffraction contribution, etc., the resulting relative standard uncertainty DUtd=Utd for the TOF delay td was estimated as: DUtd=Utd ¼ 0:1%. Similarly, the relative standard uncertainty of the path L (resulting from calibration measurements in water) was estimated as: DUL/ UL¼0.1%. Consequently, the expanded relative uncertainty for the sound speed in liquid equals 0.3% at a 95% confidence level.