Phase and Group Velocity Apparatus

Precision apparatus uses sound waves to clearly illustrate the often poorly understood phase and group velocity concepts

Any wave system displays two different propagation velocities, depending on what is being measured. The phase velocity refers to the propagation of an endless stream of similar waves, while the group velocity refers to the propagation of a wave packet or pulse. The group velocity may be higher or lower than the phase velocity, depending on the wave system. The distinction is important for transmitting digital information in pulses. The apparatus is easily understood. It consists of a frame carrying a fixed ultrasonic transmitter and a movable receiver. The transmitter and receiver are immersed in a trough of liquid. Three troughs are supplied for testing different liquids. Distilled water, salt water, and denatured alcohol are suitable examples. A precision lead screw and scale provide for accurate positioning of the receiver. A control unit supplies an frequency-adjustable ultrasonic sine wave signal between 500kHz and 900kHz or a series of 3μs pulses. The signals are displayed on a user-supplied dual channel oscilloscope. The phase velocity measurement using the continuous signal can be made in two different ways. Viewing the transmitted and received signals simultaneously, the position of the receiver cal be adjusted until the signals are in phase, then moved until they are in phase again. The difference in position is the wavelength of the known frequency waves. Alternatively, these positions can be found using the Lissajous figure method. The group velocity measurement is made using the pulse transmission. Viewing the transmitted pulse and the received signals simultaneously allows the time for the pulse to travel between the two sensors of known separation to be measured directly.