Phase and Group Velocity

Investigation of the phase and group velocity of an ultrasonic wave in water

In the experiment, the phase and group velocity of an ultrasonic wave in water are investigated. The phase velocity is measured for several frequencies as a function of the wavelength. The group velocity is determined by measuring the transit time of a short ultrasonic pulse.

Keywords: wavelength, frequency, phase velocity, sound propagation time, sound impulse, group velocity, frequency dependence, dispersion

The term dispersion describes the dependence of a wave property on the wavelength or frequency. The property or quantity investigated in the experiment is the phase velocity of an ultrasonic wave in water. For this purpose, a hydrophone is moved along the sound axis of an ultrasonic probe. The hydrophone signal is fed to an oscilloscope. By measuring the change in the probe-hydrophone distance and the associated number of phase transitions at a fixed frequency f, the wavelength λ and thus the phase velocity c _P = λ • f can be determined. This measurement is carried out for several distances and different frequencies. To determine the group velocity, the ultrasonic generator is operated in pulse mode so that short ultrasonic pulses are generated by the multi-frequency probe. By measuring the transit time t of an ultrasonic pulse for a specific distance s between the ultrasonic probe and the hydrophone, the group velocity c _G = s / t can be determined.

Phase velocity-wavelength diagram

For the measurement result shown in the diagram, the phase velocity was determined at six different frequencies for five different distances between the multi-frequency probe and the hydrophone. For water, no dependence of the phase velocity on the wavelength was found in the frequency range examined (5-10 MHz). A value of 1485 m/s was determined as the group velocity (travel time of the sound pulse: 67.3 µs, distance between probe and hydrophone: 10 cm).

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