A New Method in Applying the Universal Wave Equation to Measure the Speed of Sound in Water as a Function of Temperature with Low Frequency Ultrasound

Abstract

A new methodology was used to determine the speed of sound in water by using low frequency ultrasound over the temperature range 20 to 95° C. The initial procedure was developed based on finding the resonant locations over variable pathlengths in an acoustic tube and calculating their separation distances through the water, yielding the wavelength (λ) measurement. An in-house gain detector was employed to detect the resonant points, through detection of the amplitude voltage peaks in response to the displacement of the moving transmitter. The λ was calculated as 53 mm for water at 20° C with the fixed frequency of 28 kHz. As a result, using the universal wave equation, the speed of sound was estimated to be 1484 m/s with an accuracy of 99.89% compared to the references. The methodology was then followed through the second procedure to measure the sound speeds at temperatures higher than 20 °C, using coincidence frequency determination over different temperatures. In a fixed acoustic pathlength equal to the calculated λ at 20° C, the initial frequency, 28 kHz, was linearly swept to track the coincidence frequency corresponding to certain temperatures. The gain detector was used to obtain the coincidence frequencies, wherein the amplitude voltage peaks were recorded during the frequency adjustment. The simultaneous monitoring with an oscilloscope consolidated data when the phase differences between radiated and received waves were eliminated at the coincidence frequencies. The measured coincidence frequencies were then directly used to determine the speed of sound in water as function of temperature. The third order curve fitted to the results yielded an R² equal to 0.9856, representing excellent agreement with the reference data.