Gravity Waves - Phase Velocity of Nonlinear Traveling Gravity Waves скачать в хорошем качестве

Gravity Waves - Phase Velocity of Nonlinear Traveling Gravity Waves

Gravity Waves - Phase Velocity of Nonlinear Traveling Gravity Waves Hello. I'm Prof. Denardo. I'm here in the Lecture Demonstrations Laboratory in the Physics Department at the Naval Postgraduate School. I would like to show you a demonstration that we do in our nonlinear oscillations and waves course. A pure-frequency traveling wave in a system moves with some speed, called the phase velocity. However, this speed can depend upon amplitude. This demonstration involves the speed of gravity waves, which are waves on the surface of liquid, where gravity supplies the restoring force. Here is a channel of liquid with a wave maker at one end. The liquid is ethyl alcohol with flourescein, which is a dye. The wave maker is a wedge attached to a loudspeaker, which is driven at 6 Hz. We use a function generator and an amplifier. Right now, low-amplitude waves are being generated. A homemade wave height probe is here. These are two bare wires, and the ac resistance is detected across the wires. The resistance decreases as the level of the liquid increases, and we utilize this to transduce the wave. Here is the signal on an oscilloscope. The top trace is the wave, and the bottom trace is the signal from the function generator to the amplifier. The scope is triggering off the drive. I've positioned the probe such that the two traces are in phase. The channel is long enough so that the amplitude of the reflected wave is negligible at the probe. Now we're ready for the demonstration. Note that the waves are sinusoidal. I'm now slowly turning up the amplifier, and the amplitude of the waves is increasing. Note that the wave and the drive remain in phase. But at greater and greater drive amplitudes, we see that the wave is more and more ahead of the drive. The crest is arriving at an earlier time, so the wave is traveling faster. You can also see some distortion of the wave. That is, the wave is no longer sinusoidal at higher amplitudes. This is due to two effects: the nonlinearity of the waves and nonsinusoidal motion of the driver. However, this distortion of the driver cannot itself cause the waves to change their speed. That effect is coming from nonlinear nature of the waves.