# PROGRAM OF COMPLEX EXAM ON SPECIALITY

## when admitting to studying for educational and professional programs of master's degree in specialty 171 Electronics

#### FOREWORD

This program of professional integrated tests was created on the basis of the "Regulation on the admission to study for educational and professional training programs for a specialist, master's degree" (approved at the meeting of the Admissions Committee NTUU "KPI", Protocol No. 17 dated October 30, 2009) with the use of curricula the following normative vocational training disciplines:

#### List of disciplines

- Theoretical foundations of acoustics
- Physical acoustics
- Electroacoustic converters
- Applied acoustics
- Methods of acoustic signal processing

#### THEORETICAL BASES OF ACOUSTICS

- Equation of state and energy equation.
- The equation of continuity.
- Equation of motion (Euler's equation).
- Potential of velocity and its connection with the basic parameters of the ideal medium.
- Wave equation (Cartesian coordinate system - one-dimensional and three-dimensional cases).
- The general solution of the wave equation (Cartesian coordinates). Flat waves, the concept of a wave vector.
- The general solution of the wave equation (cylindrical coordinates). Cylindrical waves.
- The general solution of the wave equation (spherical coordinates). Spherical waves.
- Helmholtz equation.
- Common types of marginal conditions.
- Energy characteristics of sound waves (energy density).
- Energy characteristics of sound waves (density of power flux, law of conservation of sound energy).
- The normal fall of plane waves on the interface of the medium (problem statement, limiting conditions, solution).
- The normal fall of the plane waves on the interface of the medium (the case of reflection of the sound).
- The normal fall of the plane waves to the interface of the medium (the case of passing the sound).
- The inclination of plane waves to the interface of the interface (problem statement, limiting conditions, solution).
- Inclination of flat waves to the interface of the medium (the case of full penetration of the sound).
- Pressure, velocity, power in the waves, which have passed the boundary of the interface of the media with inclined incidence.
- Passage of a sound wave through a flat layer (an obstacle is another medium).
- The pulsating sphere (basic relations, solution for pressure and vibrational velocity).
- The pulsating sphere (basic relations, determination of specific impedance).
- Resistance to the radiation of the pulsating sphere.
- Synthesis pair (spatial characteristic when working in the zones of Fraunhofer and Fresnel).
- Non-phase pair (spatial characteristic when working in the zones of Fraunhofer and Fresnel).
- Oscillating sphere (basic relations, determination of specific impedance).
- Oscillating sphere (basic relations, solution for pressure and oscillatory velocity).
- The radiation resistance of the oscillating sphere.
- Radiation of sound by a cylinder (the solution of the Helmholtz equation in cylindrical coordinates).
- The main properties of the general solution of the Helmholtz equation for a radiating cylinder.
- Sound field of a pulsing cylindrical source (determination of pressure and oscillatory velocity).

#### PHYSICAL ACOUSTICS

- Hooke's Law.
- The derivation of the Lame equation. Wave equations.
- Nature of waves of type l and t (longitudinal and transverse). Polarization of waves.
- Waves in an elastic isotropic half-space. Mathematical formulation of the problem. Approximation in the formulation of the problem. Definition of PV harmonics.
- The field arising under the influence of PV-harmonics.
- Waves in an elastic isotropic half-space in the case (spatial period of influence).
- Surface Rayleigh wave.
- Ways of excitation of surface waves.
- The amplitudes of waves of type l and t, excited by the PV-harmonic in the thickness of the material. Spatial-frequency characteristics of the medium.
- Closer field of emitter of finite dimensions. Length of the searchlight zone.
- The field of elastic waves in the far range of the radiator of finite dimensions.
- Absorption of small amplitude waves in a visco-elastic medium.
- Solid environment. Symmetrical Waves of Lemba.
- Solid environment. Antisymmetric waves of Lemba.
- The equation of sound waves in a moving medium.
- Waves that arise in a moving medium under the action of space-time harmonics.
- Kirchhoff's theorem on the connection of field values in the volume and on its surface.
- An obstacle to small wave sizes, which differs from the medium only by the ability to shrink.
- Obstacle of small wave sizes, which differs from the medium only by density.
- An equation describing the propagation of waves in an inhomogeneous medium. Providing reasoning that allows us to provide a solution form, provided that the parameters of the medium change slowly.
- Substitution of the foreseen solution in the wave equation of an inhomogeneous medium and transformation of the latter into a system of equations.
- Equations of eikonal and transfer as a consequence of the wave equation.
- The concept of the front of the wave and beam. Derivation of the equation of rays from the eikonal equation.
- Waveguides Types of Limit Conditions.
- Normal waves. Their longitudinal and transverse structure. Phase propagation velocity for a layer with two soft boundaries.
- Mathematical nature of functions describing normal waves. Sturm-Liouville operator, its own functions and eigenvalues, their role in describing the structure of normal waves.
- The field of a point harmonic source in a plane waveguide (solution of the problem by a cross-sectional method).
- Application of the Kirchhoff formula for solving the wave reflection problem. Approximation of Kirchhoff.
- Reflection of a spherical wave from a solid disk when locating a locator on a disk axis. Fresnel Zone. Fresnel Zone Radius.
- Analysis of reflection of a spherical wave from a solid disk using the concept of Fresnel zones. Dependence of the amplitude of the reflected signal on the radius of the disk at a fixed distance.

#### ELECTROACOUSTIC CONVERTERS

- Classification of converters, their brief characterization according to classification characteristics.
- Simple mechanical oscillator. Free fluctuations. Forced fluctuations. The energy of oscillations. Resistance to losses. Frequency dependencies of power and phase.
- The method of energy equivalents for systems with distributed parameters.
- Rod vibrational systems. Equation of motion and its solution. Input mechanical impedance. Free bar. Rod with fixed end.
- Composite two-section rod. Nodal (neutral) section. Mechanical stresses. Mechanical Q-factor.
- Two initial positions regarding the study of energy conversion systems. Electromechanical acoustic system.
- Equation of electromechanical transformation.
- Radiation and reception modes of electromechanical transducers and their characteristics: impedance, power, kp, sensitivity.
- Energy coefficient of electromechanical coupling.
- Longitudinal oscillations of the piezoceramic rod. Transverse and longitudinal piezoelectric effect.
- Equation of motion of a piezoceramic rod with transverse piezoelectric effect. Impedance and resonance frequencies of free rods.
- Longitudinal oscillations of the piezoceramic plate in thickness.
- Piezoelectric rod as an oscillator. Coefficient of electromechanical transformation. The ratio between the electrical and electromechanical capacities of the converter.
- Piezoelectric rod as a system with many degrees of freedom. Energy method. Lagrange equation. Types of acting in the transformation of energies. Expressions for each of the acting energies. Relationships that follow from the balance of active energies.
- Piezoelectric rod emitter: emitter with overlays of different thicknesses; one-sided emitter with one loaded pad; quarter wave radiator; Emitter with loaded overlay; half-wave emitter.
- Piezoelectric cylindrical converters. Positive qualities and disadvantages. Settlement model.
- Motion equation, impedance and resonance frequencies of the unloaded ring. Electromechanical diagram of loaded ring. Estimated ratios in radiation mode.
- Settlement ratios in reception mode. Calculations of a partitioned cylindrical converter. The design of a cylindrical converter.
- Plate transducers that work on bending oscillations. Positive qualities and disadvantages. Principle of action
- Resonance frequencies of plate transducers. Circular converters. Rectangular converters.
- Spherical, arched and longitudinal-bending piezoelectric converters.
- Constraints that need to be considered when designing and operating converters.
- Effect of Cavitation on EAP.
- Mechanical strength of EAP.
- Electrical strength of EAP.
- EAP maximum power.
- Features of the choice of type of converters.
- Features of the choice of the form of converters.
- Features of the choice of converter sizes.
- Selection of active material of converters.

#### APPLIED ACOUSTICS

- Condenser microphones pressure, pressure gradient. Directional characteristic control.
- Acoustic sensitivity of microphones pressure and pressure gradient.
- Main acoustic characteristics of microphones. Microphone sensitivity.
- Acoustic systems. Sound speakers.
- Loudspeaker speakers. Acoustic field in a horn.
- Calculation of the external design of the loudspeaker (shield, open box, closed box, box with a phase-inverter).
- Input resistance of the loudspeaker. Speaker impedance.
- The structure and principle of the electrodynamic diffuser loudspeaker.
- Classification and basic characteristics of the loudspeakers.
- Resistance to radiation. Dependence on external design (piston in the screen, without screen, half-pixel).
- Method of electromechanical and electroacoustic analogies.
- HH round flat converter.
- HN rectangular pistons.
- HH of a linear equidistant group of point sources (transceivers) of sound.
- Coefficient of axial concentration of emitters and transceivers of sound.
- Characteristics of the direction (HH) of emitters and transceivers of sound. Numerical characteristics of HH.
- Soundproofing of premises.
- Acoustic sound absorbing materials.
- Qualitative analysis of acoustics of a room with the help of geometric theory.
- Basic acoustic requirements for designing premises of different purposes.
- Standard Reverberation Time. Acoustic attitude. Effective reverberation time.
- Basic acoustic characteristics of the room within the framework of statistical theory.
- Sources of formation of consonant sounds. Acoustic characteristics of the consonants.
- Phonation Acoustic characteristics of vowel sounds.
- Acoustic model of the vocal tract.
- Integral sound localization. Stereo sound transmission methods.
- Harmonic and melodic tone height. Sound tone
- Loudness Volume of complex sounds.
- Volume level. Curves of equal volume.
- Theory of hearing and the mechanism of sound perception.

#### METHODS OF ACOUSTIC SIGNAL PROCESSING

- Non-recursive filters. The equation of filtration (symmetric and asymmetric forms). Filter order. Impulse and frequency characteristics of a non-recursive filter.
- Calculation of non-recursive low-frequency filters by the method of inverse Fourier transformation. Gibbs phenomenon. Window Functions.
- Calculation of non-recursive RF, strip and filter filters.
- Recursive filters. Algorithm of recursive filtration. Impulse and frequency characteristics of the recursive filter.
- Calculation of recursive filters by frequency conversion.
- Kaiser's window and the calculation of non-recursive filters by the Kaiser method.
- Non-recursive differentiating filter.
- Recursive Integrating Filter.
- Optimal (according to Chebyshev) non-recursive filters.
- Hilbert transformation and its basic properties.
- Calculation of Hilbert transform using Fourier transform.
- Hilbert discrete transformation.
- Four Forms of Fourier Transform.
- Digital filtering using a discrete Fourier transform.
- Window Functions in Discrete Fourier Transform.
- Interpolation using Fourier transformation and adding zeros.
- Fast Fourier Transform. The mechanism of winning in the number of arithmetic operations.
- Estimation of the probability density of stationary. the process by the method of the hydrostagram.
- Spot evaluation of the MAP expectation and its quality.
- Spot evaluation of the dispersion of the SSP and its quality.
- Interval estimation of MTP expectation.
- Interval estimation of dispersion of SSP.
- Evaluating the spectrum of SSP. Raw and modified periodograms.
- Estimation of the correlation function of the MTS. Assessment forms.
- Mathematical expectation and variance of the estimates of the correlation function of the MTS.
- Wiener-Khinchin theorem. Two-sided and one-sided power spectra.
- Correlation function and power spectrum of the harmonic process with a random initial phase.
- Correlation function and spectrum of white noise power with spectrum bounded by frequency.
- The mechanism of detecting a harmonic signal on the background of noise by means of correlation processing.
- Evaluating the spectrum of SSP. Estimates of Bartlett and Welch.

### Evaluation structure

The exam consists of a written work. Written work lasts 150 minutes and contains five tasks.

**Criteria for assessing the performance of the entrance examination tasks:**

The maximum number of points is 100, respectively, the scale of evaluation of the general results:

Total points |
Traditional score |
Numerical equivalent of score |

95-100 | Excellent | 5 |

85-94 | Good | 4,5 |

75-84 | 4 | |

65-74 | Satisfactory | 3,5 |

60-64 | 3 |

The scale of evaluation of the results of each of the five tasks. The number of points is 20.

**Scale of the results of the tasks execution**

The assessment of the written response is determined by the compliance with the main and additional criteria. The maximum number is 20 points for each of the five assignments. An evaluation of the written response is carried out on the following scale:

19 … 20 | Full answer. The Applicant has demonstrated the possession of the material in full |

17 … 18 | True but incomplete answer |

15 … 16 | The answer contains minor errors |

12 … 14 | The answer contains substantial but non-principled errors |

1…11 | The answer contains fundamental errors |

0 | No answer |

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Зав.каф. АиАЕ, д.т.н., проф. | В. С. Дидковский | |

Проф.каф. АиАЕ, д.т.н., проф. | С. А. Найда |