Acoustic Metamaterials Quiz
Acoustic metamaterials overturn a premise that has organised acoustics since Newton: that a medium’s response to sound is fixed by its chemistry. By embedding sub-wavelength resonators inside a host fluid, engineers can prescribe effective mass density and bulk modulus independently — and even drive both negative across a designed band.
The result is not better absorption but a different regime of wave physics: refraction bends the wrong way, and evanescent fields grow rather than decay. This quiz tests the key ideas from Lesson 27:
- Effective medium theory and the deep-subwavelength condition
- Resonant unit cells and negative dynamic density
- Negative refraction, cloaking and transformation acoustics
- Phononic crystals, band gaps and superlensing
- Applications, challenges and future prospects
Work carefully with the physical picture and the algebraic condition together — that is exactly what the examination rewards.
Q1. An acoustic metamaterial is best described as:
A metamaterial is not a substance but a lattice of scatterers spaced far below the operating wavelength, so the array is sampled as a homogeneous medium with emergent constants.
Q2. At 1 kHz in air the wavelength is roughly 343 mm. A unit cell of 10 mm satisfies the deep-subwavelength condition by a factor of about:
The ratio is ##\dfrac{343\ \text{mm}}{10\ \text{mm}} = 34.3##, so the cell sits far inside the wavelength by a factor exceeding thirty, which legitimises homogenisation.
Q3. Below its resonance, a membrane-loaded cavity driven by pressure:
Below resonance the element moves in phase with the driving pressure and adds effective mass; above resonance it moves in antiphase and subtracts it. This sign reversal is the mechanism behind negative dynamic density.
Q4. The sign reversal of effective dynamic density in a resonant element occurs:
The effective density turns negative just above the resonance and returns to positive at higher frequencies, following the Lorentz form.
Q5. A cavity with a compliant wall is used in a metamaterial unit cell primarily to:
The compliant-walled cavity stores compression out of phase with the applied pressure, giving a negative effective bulk modulus over a narrow band. It is the second, independent dial controlling volumetric stiffness.
Q6. Why can a metamaterial designer obtain two independent dials, whereas nature provides only one?
In natural media, chemistry fixes ##\rho## and ##K## together. In a metamaterial, one resonator controls effective density and a second independent resonator controls volumetric stiffness, so the two can be tuned separately.
Q7. For a membrane of surface mass ##m_s##, tension ##T## and radius ##a##, the fundamental mode sits near:
The lesson gives the fundamental mode near ##f_0 = \dfrac{2.405}{2\pi a}\sqrt{T/m_s}##, and the effective density diverges as the drive approaches ##f_0## from below.
Q8. As the driving frequency approaches the membrane resonance ##f_0## from below, the effective density:
The divergence of the effective density as the drive approaches ##f_0## from below is the signature that a resonance, not a bulk property, is doing the work.
Q9. In a medium where both effective density and bulk modulus are negative, refraction:
When both parameters are driven negative across a designed band, the wave physics changes regime: refraction bends the wrong way and evanescent fields grow rather than decay.
Q10. In the negative-parameter regime of an acoustic metamaterial, evanescent fields:
The lesson states that in this different regime of wave physics, refraction bends the wrong way and evanescent fields grow rather than decay. This growth underlies superlensing.
Q11. The impedance used as the diagnostic language for engineered media in this lesson is:
Lesson 26 established ##Z = \rho c## and intensity transmission as the machinery governing reflection at boundaries; that machinery now diagnoses engineered media.
Q12. A phononic crystal differs from a resonant acoustic metamaterial chiefly in that its operating mechanism relies on:
Phononic crystals exploit periodic scattering and band gaps arising from the lattice periodicity, whereas resonant metamaterials exploit sub-wavelength resonators and effective-medium parameters.
Q13. Transformation acoustics is used in metamaterial design primarily to:
Transformation acoustics maps a coordinate transformation onto spatially varying effective material parameters, which is the design route to cloaking and wave guiding.
Q14. A key practical challenge in realising acoustic metamaterials for noise control is that:
The resonant mechanisms produce negative parameters over narrow bands, so broadband performance and fabrication at scale remain central challenges for noise-control applications.
Q15. Which statement best captures the lesson's framing of acoustic metamaterials for IIT JEE aspirants?
The lesson frames metamaterials as the transition from passive materials obeying tabulated constants to structured materials obeying geometry, sitting between ultrasound coupling (Lesson 26) and psychoacoustics (Lesson 28).