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PHY
Article No. VK-PHY19

PHY19 Phase and Group Velocity

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

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Subject matter of the experiment

In the experiment, the phase and group velocity of an ultrasonic wave in water is investigated. The phase velocity is measured for several frequencies in dependence on the wavelength. The group velocity is determined by the measurement of the time of flight of a short ultrasonic pulse.

Keywords: Wavelength, frequency, phase velocity, time of flight, sound pulse, group velocity, frequency dependence, dispersion

Theoretical and practical aspects of the experiment

The term dispersion describes the dependence of a wave characteristic of the wavelength and/or frequency.
The characteristic/quantity investigated in the experiment is the phase velocity of an ultrasonic wave in water. For this, a hydrophone is moved along the sound axis of an ultrasonic probe. The hydrophone signal is set on an oscilloscope. By measuring the change in the probe-hydrophone distance and the respective number of phase runs at a fixed frequency f, it is possible to determine the wavelength ? and thus the phase velocity cP = λ · f. This measurement is carried out for several spacings and different frequencies.To determine the group velocity, the ultrasonic generator is operated in pulse mode so that short ultrasonic pulses are generated from the multifrequency probe. By measuring the time of flight t of an ultrasonic pulse for a certain distance s between ultrasonic probe and hydrophone it is possible to determine the group velocity cG = s / t.

Results

For the measurement result shown in the diagram, the phase velocity was determined at 6 different frequencies, each time for 5 different spacings between multifrequency probe and hydrophone. For water, in the investigated frequency range (5-10 MHz), no dependence of the phase velocity on the wavelength was found. A value of 1485 m/s was determined as the group velocity (time of flight of the sound pulse: 67.3 µs, probe-hydrophone spacing: 10 cm).

Phase velocity/wave length diagram

Phase velocity/wave length diagram

Equipment
Ord.no. Description
20100 cw generator SC600
10351 Hydrophone set with BNC plug
20139 Multifrequency probe
70200 Ultrasonic gel
Oscilloscope not included in delivery but used for the experiment
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