9 Optically Detecting Wavefronts and Wave Speeds in Water Using Refracto-Vibrometry 101 Fig. 9.4 Time of flight versus sample thickness for lead. Note that error bars are present in this data set, but they are small enough that they don’t show up relative to the data points. (a) Vibrometer measured data. (b) Transducer measured data Using the slope mof the data, and the speed of sound in water previously measured to be cWD1460˙10 m/s, the speed of longitudinal waves in lead, cPb, was found using Eq. 9.3. The speed of longitudinal waves cPb through lead as measured by the vibrometer was 2260˙20 m/s. The speed of sound through lead as measured by the ultrasound transducer was 2270˙30 m/s. These values are in agreement with each other within the bounds of their uncertainties. These values are slightly larger than accepted values for lead [15] which are 2160 m/s when annealed and 1960 m/s when rolled. It was not known what physical form the lead disks used for this experiment were. 9.4.3 Speed of Sound Measurement in Synthetic Bone A similar method was used to determine the speed of sound in a synthetic bone material immersed in water. Five different thicknesses of synthetic bone were cut. These thicknesses were used as samples in a speed of sound calculation, along with a trial containing no intervening sample. Both the vibrometer and transducer were placed above the sample so the ultrasound pulse would pass through the sample before being recorded. On the transmitted pulse, the time for the first main zero-cross was recorded for each instrument. Figure 9.5 graphs the resulting time values for each of the fabricated bone thicknesses. From the slope of the linear fit to this data, the speed of sound was found. For the data taken with the vibrometer the speed of sound through the bone sample is 1507˙11 m/s. From the transducer data the speed of sound through the bone samples comes out to be 1497˙13 m/s. There have been no published studies discussing the speed of sound in this synthetic bone media. However, the measured speed is roughly consistent with the 1500 m/s speed of waves in cancellous bone material [11].
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