Bruce Denardo

The force between two parallel rigid plates due to the radiation pressure of broadband noise: An acoustic Casimir effect

Theoretical and experimental results are presented for the force law between two rigid, parallel plates due to the radiation pressure of broadband acoustic noise. The noise is in the band of 5–15 kHz and has an intensity of 133 dB (re: 10−12 W/m2). Excellent quantitative agreement is shown between theory and experiment. These results constitute an acoustic analog for the Casimir effect, which is the force experienced by two closely spaced uncharged conducting plates due to the quantum electromagnetic zero-point field. In contrast to this case, however, band-limited noise can cause the force to be attractive or repulsive as a function of separation between the plates.

Experiments with electrical resistive networks

Theoretical problems involving equivalent resistances of large or infinite networks of resistors have received substantial attention. We consider two actual networks. In the first, the resistance is measured across one end of a ladder whose number of loops is incremented until the precision of the multimeter is exceeded. In the second, resistances are measured across nodes near the center of a 12 by 12 square grid of resistors. These experiments are useful in the introductory physics laboratory as interesting examples of equivalent resistance, and can be added to a standard Ohm’s law experiment. The square grid apparatus also can be employed for lecture demonstrations. In addition, this apparatus offers approximate experimental confirmation of complicated theoretical calculations for the equivalent resistance between two nonadjacent nodes of an infinite square grid. These experimental results are verified numerically.

A water wave analog of the Casimir effect

Two rigid plates are vertically suspended by thread such that they are parallel to and opposite each other. The plates are partially submerged in a dish of liquid that is attached to the top of a vertical shake table. When the shake table is driven with noise in a frequency band, random surface waves are parametrically excited, and the plates move toward each other. The reason for this attraction is that the waves carry momentum, and the wave motion between the plates is visibly reduced. The behavior is analogous to the Casimir effect, in which two conducting uncharged parallel plates attract each other due to the zero-point spectrum of electromagnetic radiation. The water wave analog can be readily demonstrated and offers a visual demonstration of a Casimir-type effect. Measurements of the force agree with the water wave theory even at large wave amplitudes, where the theory is expected to break down. The water wave analog applies to side-by-side ships in a rough sea and is distinct from the significant ...

Design and measurements of variably nonuniform acoustic resonators

We describe the design, construction, and acoustical measurements of resonators with nonuniform cross‐sectional areas that are easily altered to yield different resonance frequencies. These resonators are useful as educational demonstrations of symmetry breaking and of an effect of nonuniformity upon standing waves. Resonators that yield two, three, and four pitches are considered, where the relative frequencies are designed to correspond to musical intervals. Agreement is within 2% in all cases and 1% for most. The data reveal a breakdown of the theory, which is shown to be a result of additional kinetic energy, and thus effective inertia, near a discontinuity in cross‐sectional area. The data also reveal that it is more accurate accurate to employ the end correction of an infinite flange rather than that of a thin‐walled tube.

An acoustic radiometer

In contrast to Crookes’ radiometer, which rotates due to electromagnetic radiation, the analogous acoustic radiometer demonstrates radiation pressure. The apparatus consists of two panes attached to opposite ends of a horizontal arm that is pivoted at its center. One side of either pane is acoustically reflective and the other absorptive. The apparatus rotates when placed in an enclosure of high-intensity acoustic noise. Experimental values of the terminal angular velocity are in reasonable agreement with approximate theoretical predictions based on radiation pressure.

Quasi-nonpropagating wave sources in one dimension

When a medium is driven by a spatially extended wave source, it is possible that no waves emanate from the driven region and a standing wave occurs inside the region. This case is a nonpropagating wave source. We report numerical observations and theory in one dimension, where the realistic effects of weak dissipation and weak nonuniformity are included. Each of the effects causes a small amount of propagation to occur so that the source becomes quasi-nonpropagating. The amplitude of the outgoing wave compared to the amplitude of the standing wave is substantially reduced for a uniform source compared to a two-point source of the same length, which suggests that the more evenly a source is spread over a fixed length, the less is the relative propagation.

A rotating U‐tube experiment

A rotating U‐tube experiment is described in which the axis of rotation lies between a vertical arm and the axis of symmetry of the tube. As the rotational frequency is slowly varied, the equilibrium position of the liquid in the tube can abruptly change, resulting in a hysteresis loop. The effect is not due to friction, which causes a much smaller amount of hysteresis. The data agree well with the theory.

Parametric instability of two coupled nonlinear oscillators

One of the two normal modes of a system of two coupled nonlinear oscillators is subject to an instability. Several demonstration apparatus of weakly coupled oscillators that exhibit the instability are described. The effect is due to one normal mode parametrically driving the other, and occurs for the broad range of systems where the nonlinearity has a cubic contribution to the restoring force of each oscillator, which includes pendulums. The instability has an amplitude threshold that increases as the coupling is increased. A naive physical approach predicts that the mode opposite to that observed should be unstable. This is resolved by a weakly nonlinear analysis which reveals that the nonlinearity causes the linear frequency of a normal mode to depend upon the finite amplitude of the other mode. Numerical simulations confirm the theory, and extend the existence of the instability and the accuracy of the theoretical amplitude threshold beyond the regime of weak nonlinearity and weak coupling.

An acoustic Casimir effect

Theoretical and experimental results are presented for the force law between two rigid parallel plates due to the radiation pressure of broadband acoustic noise. The noise is in the band of 5 to 15 kHz and has an intensity of 133 dB (re: 10−12 W/m2). Good quantitative agreement is shown between theory and experiment. These results constitute an acoustic analog for the Casimir effect, which is the force experienced by two closely spaced uncharged conducting plates due to the quantum electromagnetic zero point field. In contrast to this case, however, band limited noise can cause the force to be attractive or repulsive as a function of the distance of separation of the plates. [Work sponsored by the Office of Naval Research.]

Investigation of parametric drive of a longitudinal gas filled resonance tube

High power drives for thermoacoustic refrigerators are being investigated by several groups. Theoretical calculations have been performed of the feasibility of parametrically driving a longitudinal resonance tube by uniformly modulating the temperature of the gas with a high‐power laser. Parametric drives are promising since the drive mechanism is distributed over the entire volume of gas and because the response may become large before saturation occurs. Although it is demonstrated that laser drive is not a practical means of high‐power drive for longitudinal resonators, much interesting physics has been considered in the analysis of the proposed system and is discussed.