Wave frequency is a fundamental parameter governing wave behavior and its interaction with matter. Many physical laws, including Rayleigh's criterion and the Planck-Einstein relation, are frequency-dependent. Altering wave frequency offers the potential to overcome limitations imposed by these laws, impacting areas like imaging resolution, energy capacity, and wave propagation. Conventional materials, including metamaterials, possess time-invariant properties and cannot alter wave frequency. While nonlinear materials can generate higher harmonics, this requires high excitation levels. Active metamaterials offer more control but often come with added cost and complexity. This research explores a linear mechanism for time-base frequency conversion, independent of wave amplitude and without sensors, providing greater freedom in wave manipulation. Temporal modulation materials, which change local medium properties in a space-time sequence, have shown promise in breaking reciprocity linearly. Existing methods include moving medium (similar to the Doppler effect) and wave modulation. However, significant frequency shifts require extensive lengths or high speeds. This study introduces a linear temporal modulation device, the acoustic meta-layer (AML), to achieve frequency conversion with significantly higher efficiency than nonlinear methods. The AML is a programmable material enabling arbitrary frequency changes. Two key demonstrations are presented: audible sound conversion to infrasound and ultrasound, and the transformation of a monochromatic tone into white noise using a randomized MOSFET time sequence. These capabilities have broad implications for applications such as super-resolution imaging, energy flow control, and encrypted communication.

The paper reviews existing methods for wave frequency manipulation, highlighting the limitations of conventional materials and nonlinear techniques. It discusses the advantages of time-variant materials, emphasizing the need for a linear mechanism that is independent of wave amplitude and does not require sensors. The authors examine previous work on temporal modulation materials, distinguishing between moving medium and wave modulation approaches. Existing research on temporal materials and their applications in breaking reciprocity is summarized, noting the limitations related to achieving significant frequency shifts. The authors contrast their approach with existing amplitude modulation (AM) techniques and highlight the potential of pure temporal modulation materials for linear wave frequency alteration.

The study utilizes an acoustic meta-layer (AML) consisting of a suspended diaphragm from a moving-coil loudspeaker shunted by an analog circuit incorporating a MOSFET. The MOSFET, controlled by a predefined time sequence, switches the shunt circuit on and off, modulating the acoustic impedance. The acoustic impedance modulation is determined by the equation AZ = (BI)²Z⁻¹, where Z is the electrical impedance of the shunt circuit and BI is the force factor. The MOSFET state is described by a Heaviside step function, switching between a low resistance (4 mΩ) 'on' state and a high resistance (≈4400 Ω) 'off' state. The governing equation for the diaphragm's motion is a coupled electromechanical system described by equations (1) and (2) in the paper. Equation (1) describes the diaphragm's mechanical motion considering mass, damping, stiffness, and the electromagnetic force from the shunt circuit. Equation (2) describes the electrical dynamics of the shunt circuit, including the time-varying resistance of the MOSFET. These equations are solved using Fourier transforms and time-domain numerical methods (ODE45). The energy scattering efficiency from the source frequency to sidebands is calculated using equation (5). A dimensionless parameter, dm, representing the system mechanical loading, is used for parametric analysis. The acoustic impedance of the meta-layer is measured using an impedance tube to determine the modulation ratio. Experiments are conducted using an impedance tube with anechoic wedges to minimize reflections. Microphone pairs measure incident, reflected, and transmitted waves. The harmonic modulation experiments use a sinusoidal gating voltage to control the MOSFET. The random modulation experiments use a band-limited random voltage signal. Data analysis involves spectral decomposition of the measured sound pressure signals to quantify energy distribution in different frequency components.

The experimental results show a high acoustic impedance modulation ratio of up to 45, significantly exceeding that achieved by nonlinear techniques. In harmonic modulation experiments, the energy scattering efficiency reaches 46.8% with significant energy at the sum and difference frequencies of the source and modulation frequencies. Parametric analysis shows that energy scattering efficiency can be further increased by reducing system mechanical loading. The conversion of audible sound to infrasound (19 Hz) is experimentally demonstrated using modulation frequencies close to the source frequency. Numerical simulations predict the conversion of audible sound to ultrasound, though experimental verification is beyond the current capabilities of the research team. Random modulation experiments demonstrate the conversion of a monochromatic tone (135 Hz) to broadband noise, with approximately 43.4% of the transmitted energy in the noise component. The broadband noise has potential applications in encrypted communication due to its unpredictable time-domain behavior. The study shows the meta-layer is broadband effective for a range of frequencies (40 to 640 Hz), showcasing its versatility in noise control and wave manipulation applications.

The findings demonstrate a highly efficient linear mechanism for altering sound frequency, surpassing the capabilities of traditional nonlinear methods. The ability to convert sound to infrasound and ultrasound opens up possibilities for long-distance transmission and high-resolution imaging. The creation of broadband noise from a monochromatic signal has implications for secure communication and noise control. The high modulation ratio achieved, combined with the programmable nature of the AML, significantly expands the possibilities for wave manipulation. Future research could focus on scaling the device to higher frequencies to realize ultrasound applications. Further work is needed to optimize the design for specific applications and explore cascading multiple AML units for enhanced control and noise reduction.

This study introduces a novel linear method for controlling sound frequency using a time-varying acoustic meta-layer. The high efficiency and programmability of the AML offer significant advantages over existing techniques. The ability to convert audible sound to infrasound and ultrasound, as well as generate broadband noise, opens up various applications in communication, imaging, and noise control. Future research should focus on miniaturization for higher frequency applications and optimizing multiple-device configurations for enhanced control.

The experimental setup is limited by the impedance tube's capabilities, hindering the validation of ultrasound conversion. The theoretical model may not fully capture all aspects of the physical system, such as frequency-dependent properties of the diaphragm and electrical components. The random modulation experiments utilize a single AML unit; cascading multiple units could further enhance noise generation and encryption capabilities. Further research is needed to optimize the design and explore various configurations for specific applications.