# (1 Hz = 1 cycle/s = 1 s-1) Amplitude: The maximum magnitude of displacement from equilibrium value is called the amplitude A of the wave.

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(1)2. Wave motion and Sound 2.1 Propagation of waves, longitudinal and transverse waves, mechanical and non- mechanical waves 2.2 sound waves, Architectural Acoustics, Classification of Sound 2.3 Loudness, Weber-Fechner law, Bel and Decibel 2.4 Absorption Coefficient, Reverberation, Sabine’s formula 2.5 Factors affecting acoustics of buildings and their remedies 2.6 Ultrasonic, properties, Production, piezoelectric and magnetostriction method, applications 2.7 Numerical.

(2) Wavelength: Wavelength is the distance between two identical adjacent points in a wave and it is typically measured between two easily identifiable points, such as two adjacent crests or troughs in a waveform. The SI unit of wavelength is meter.. Frequency: The frequency ( f ) is the number of cycles in a unit of time. It is always positive. The SI unit of frequency is the hertz (Hz). (1 Hz = 1 cycle/s = 1 s-1) Amplitude: The maximum magnitude of displacement from equilibrium value is called the amplitude A of the wave..

(3) Time period: The time period, (T) is the time for one cycle. It is always positive. The SI unit is the second. Vibration: One complete round trip is a complete vibration or cycle. Phases: Phase denotes the particular point in the cycle of a waveform, measured as an angle in degrees. Phase is a very important factor in the interaction of one wave with another, either acoustically or electronically. Relation between frequency and wavelength: The wave pattern travels with constant speed and advances a distance of one wavelength in a time interval of one period T. So the wave speed υ is given by υ = λ/T where ƒ = 1/T So that υ = f λ.

(4) WAVE CONCEPTS Mechanical waves are vibrational disturbances that travel through a material medium. e.g. include water waves, sound waves traveling in a medium such as air or water, waves along a string (as in a musical instrument) or along a steel beam, or seismic waves traveling through the Earth. Longitudinal waves are waves in which the motion of the individual particles of the medium is in a direction that is parallel to the direction of energy transport. e.g. sound wave The displacement of the medium is perpendicular to the direction of propagation of the wave is called transverse waves. e. g. a ripple on a pond, a wave on a string..

(5) The tuning fork is a common device for producing pure musical notes. A tuning fork consists of two metal prongs, or tines, that vibrate when struck. Their vibration disturbs the air near them. The molecules in an element of air in front of its movement are forced closer together than normal. Such a region of high molecular density and high air pressure is called a compression. Origin of sound: Sound waves are longitudinal waves traveling through a medium, such as air..

(6) Classification of Sound: Sound waves fall into three categories covering different ranges of frequencies. Audible waves are longitudinal waves that lie within the range of sensitivity of the human ear, approximately 20 to 20000 Hz.. Ultrasonic waves are longitudinal waves with frequencies above the audible range for humans and are produced by certain types of whistles. Animals such as dogs can hear the waves emitted by these whistles. Frequencies used for medical diagnostic ultrasound scans extend to 10 MHz and beyond. The ranges 20-100 kHz are commonly used for communication and navigation by bats, dolphins and some other species..

(7) Figure 1 Infrasonic waves are longitudinal waves with frequencies below the audible range. For example, some animals, such as whales, elephants and giraffes communicate using infrasound over long distances. Avalanches, volcanoes, earthquakes, ocean waves, water falls and meteors generate infrasonic waves. Some sources of man-made infrasound are nuclear and chemical explosions, engines, machinery and airplanes (Figure 1). Infrasonic waves propagate with very little attenuation and hence are capable of propagating over great distances..

(8) Classification of Audible Sound wave: Musical • The sound which produces pleasing effect on the ear is called musical sound. • Sounds of Sitar, Violin, Flute Properties of Musical Sound • Regular in Shape. • Have definite Periodicity. • They do not undergo a sudden change in amplitude.. Noise • The sound which produces a jarring effect on the ear and unpleasant to hear is called noise. • Sound of Road Traffic, Crackers, Aeroplane Properties of Noise • Irregular in Shape. • Do not have definite Periodicity. • They undergo a sudden change in amplitude..

(9) Characteristics of Musical Sound / Quality of Musical Sound. Pitch Related To Frequency Of Sound. Loudness Related To Intensity Of Sound. Timbre Related To Quality Of Sound.

(10) Pitch and frequency: • The pitch is defined as the characteristic of sound by which a particular sound appears to be grave or shrill. • The pitch of a musical note is that characteristic which distinguishes two sounds produced by two different frequencies even though the intensity of both may be the same. • The sensation of a frequency is commonly referred to as the pitch of a sound. A high pitch sound corresponds to a high frequency sound wave and a low pitch sound corresponds to a low frequency sound wave..

(11) • In a common technique of acoustic measurement, acoustic signals are sampled in time and then presented in more meaningful forms such as time frequency plots. This method is used to analyze sound and better understand the acoustic phenomenon. • If the greater the frequency, higher is the pitch. A pitch of higher frequency is termed shrill. • The pitch of sound of men is low and hence their voice is grave while the pitch of sound of women and children is high and hence their voice appears shrill. • The pitch of buzzing of a mosquito is higher than that of a roaring of a lion but the loudness of roaring of a lion is much higher than that of buzzing of a mosquito..

(12) Loudness : • Loudness is the characteristic of sound due to which a particular sound senses to be feeble or loud. • Loudness is the rate of flow of energy to the ear. or • Loudness is a degree of sensation produced on ear. • Thus, loudness varies from one listener to another. Loudness depends upon intensity and also upon the sensitiveness of the ear. • This is applicable to all sounds whether classified as musical or noisy. There is clear distinction between the intensity and loudness. • The relation of loudness and intensity is ∝ og = og (1) where K is a constant. • The unit of loudness is decibel (dB)..

(13) Weber-Fechner law “The loudness is directly proportional to the logarithm of intensity” This statement is called Weber-Fechner law. From Eqn. (1) ,. = where. (2). is called sensitiveness of ear. Therefore, sensitiveness. decreases with increase in intensity. Loudness is physiological Quantity..

(14) Intensity (I): Intensity of sound wave at a point is defined as the amount of energy (E) flowing per unit area in unit time when the surface is held normal to the direction of propagation of sound wave. or We define the intensity I as the rate at which energy E flows through a unit area A perpendicular to the direction of travel of the wave. or The intensity of sound is the quantity of sound energy crossing unit area surrounding a point in unit time, the area being taken normal to the direction of propagation of sound..

(15) =. =. =. The unit of intensity is W/m2. For a point source, energy spreads out in all directions (Area of a sphere A = 4πr2 ) The range of audible intensities is from 10-12 to 10 W.m-2. The use of a logarithmic scale compresses the range of numbers required to describe this wide range of intensities. Unlike the expression for the energy density of a sound wave, the expression for the intensity is different for different types of sound field. For any free progressive wave. =. !.

(16) ENERGY DENSITY A sound wave contains kinetic energy, as a consequence of the particle velocity, and potential energy as a result of the sound pressure. This energy propagates with the speed of sound. The sound wave, therefore, transfers mechanical energy. The amount of energy per unit volume of a sound wave is measured by a quantity known as the energy density. For a plane sound wave the energy density, E, per unit volume is defined by. =. "# \$%&. ' ( #. ∵!=. .+ ", '. where P rms = mean square sound pressure (Pa) ρ = density of air (kg m-3 ) v = speed of sound (m s-1) E = energy density (W s m- 3 ) ( = 101 kPa, ρ = 1.16 kg/m3@ 30 oC and 1.22 kg/m3 @ 15 oC).

(17) Intensity Level (IL): The minimum sound intensity which a human ear can sense is called the threshold intensity. Its value is 10-12 W/m2. If the intensity is less than this value then our ear cannot hear the sound. This minimum sound intensity is also known as zero or standard intensity. The intensity of a sound is measured with reference to standard intensity. The human ear subjectively judges the relative loudness of two sounds by the ratio of their intensities, which is a logarithmic behaviour. The intensity level or relative intensity of a sound is defined as the logarithmic ratio of intensity I of a sound to the standard intensity I0.. =. log.

(18) Let I and I0 represent intensities of two sounds of a particular frequency; L and L0 be their corresponding measures of loudness. Then, according to Weber-Fechner law, = =. log. (1). log. (2). Therefore, the intensity level or relative intensity is = − = log − log − log = log =. log. ,. (3). The intensity level would be expressed in Bel. This unit was named in recognition of Alexander Graham Bell..

(19) In the Eq. (1), we increase the intensity 10 times, i.e. I = 10 I0 corresponds to 1 bel. Therefore, bel is the intensity level of a sound whose intensity is 10 times the standard intensity. Bel is a large unit. Hence, another unit known as decibel (dB) is more often used. 1 1 01 = 3 10 To express the intensity level in dB (decibel) multiply the logarithm of the ratio by 10. Thus, = 10 log (unit in dB) ,.

(20) Intensity of various sound:.

(21) Hertz and Decibels The relationship between Hertz and decibels allows a listener to measure the frequency and perceived loudness of any sound. The frequency or amount of air pressure change vibration is measured in Hertz. The resulting change in air pressure created through the vibrating object is measured in decibels. Decibels, in effect, measure the loudness of a sound and Hertz measures the frequency of the sound..

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(23) Decibels, Phons and Sones A pure tone having an intensity level of 20 dB and a frequency of 1000 Hz would be clearly audible whereas a tone having the same intensity but a frequency of 100 Hz would not be heard at all as it lies well below the threshold of hearing. The unit phon is used to indicate an individual’s perception of loudness. By definition, 1 phon is equivalent to 1 deciBel at 1000 Hz (1 kHz). The sone scale is based on the observation that a 10 phon increase in a sound level is most often perceived as a doubling of loudness. According to the sone scale, a 1 sone sound is defined as a sound whose loudness is equal to 40 phons..

(24) Why is reverberation time important? The reverberation time of a room describes how long a sound “lingers” or “persists” after the source has stopped emitting it. This quality is also described a room using subjective terms such as “active”, or “live”, or “echoey”. In technical terms, the reverberation time measures rate of energy loss of a steady state sound field once the source has been shut off..

(25) Reverberation : • When a source creates a sound wave in a room or auditorium, observers hear not only the sound wave propagating directly from the source but also the myriad reflections from the walls, floor, and ceiling. These latter form the reflected wave, or reverberant sound. • Reverberation is the persistence or prolongation of sound in a hall even though the sound source is stopped. or • The phenomenon of retention of audible sound, after its production is stopped, over a short period of time is known as reverberation..

(26) • After the source ceases (stops), the reverberant sound can be heard for some time as it grows softer. The time required, after the sound source ceases, for the absolute intensity to drop by a factor of 106 or equivalently, the time for the intensity level to drop by 60 decibels is defined as the reverberation time (RT, sometimes referred to as RT60). • The reverberation time is the time taken by the sound wave to fall below the minimum audibility level after the source is stopped. Or • Time taken by sound to reduce its intensity up to one millionth of its original intensity after the source is cutoff is known as Reverberation time..

(27) • The reverberation time is a measure of how fast the sound dies away in a given room. • The size of the room and the choice of materials determine the reverberation time. • Once we know the sound absorption coefficient of a material and how much of it there is in a room, we can calculate the total absorption in the room. The unit of measurement is the metric sabine (m2 sabine). • Once we know the size of the room and the total absorption, using Sabine’s equation we can calculate the reverberation time, even before the room is built..

(28) If Reverberation Time is too low: (Dead space) Sound disappear quickly and become inaudible. If Reverberation Time is too high: (Boomy space) Sound exist for a long period of time-an overlapping of successive sounds cannot hear the information clearly. For the good audibility, Reverberation time should be kept at an optimum value..

(29) Sabine’s Formula for Reverberation Time • Sabine recognized that the reverberation time of an auditorium is related to the volume of the auditorium and to the ability of the walls, ceiling, floor, and contents of the room to absorb sound. • The reverberation time in a room can be calculated as 4 =. 0.167 7. • Reverberation time in sec, T • Volume of the room in m3, V • Total sound absorption of surfaces, A.

(30) • The total sound absorption is depending upon an absorbing material of area S and absorption coefficient a. • If there is more than one type of absorbing material in the room or auditorium, the absorption coefficient are different for different material. • The Total Absorption is = 8 +. 8 +. =< 8. : 8:. +⋯.

(31) Absorption coefficient • Sound absorption measures the amount of sound energy absorbed by a material and is one of the most important performance considerations in the acoustic design of a room. • The selection quantity and positioning of sound absorbing materials are key factors in achieving the correct reverberation time for the rooms intended use. • “The sound absorption coefficient (a) of a material is defined as the ratio of sound energy absorbed by the surface to the total sound energy incident on it.” Or • “The sound absorption coefficient of a material describes its ability to absorb sound and is measured over a number of specific frequencies.”.

(32) • The result is expressed as a number between 0 and 1 where 0 is total reflection and 1 is total absorption. • If the coefficient is multiplied by 100, it provides the percentage of incident sound that is absorbed. Sound energy absorbed by the surface a = The total sound energy incident on it • Sabine chose 1 m2 of an open window as the standard unit of absorption. Since all sound energy falling on it and it passes through without any reflection. They can be said to be completely absorbed. • “The sound absorption coefficient (a) of a material is reciprocal of the area of material which absorbs same amount of sound energy which has been absorbed by 1 m2 of an open window area.”.

(33) • For Example, If a sound absorbing material of 5 m2 absorbs the same amount of sound energy as absorbed by 1 m2 of open window, then the absorption coefficient of the material is given = 0.20. The surface absorbs 20 percent of the sound by = striking it. • The unit of absorption coefficient is sabine and is also called O.W. U. (Open Window Unit) Absorption coefficients of common materials at several frequency (hertz) material. 125. 250. 500. 1,000. 2,000. 4,000. concrete. 0.01. 0.01. 0.02. 0.02. 0.02. 0.03. plasterboard. 0.20. 0.15. 0.10. 0.08. 0.04. 0.02. acoustic board 0.25. 0.45. 0.80. 0.90. 0.90. 0.90. curtains. 0.12. 0.25. 0.35. 0.40. 0.45. 0.05.

(34) Ultrasonic – production and its application The ultrasonic generators can be divided into two groups (1) Mechanical generators (e.g. Galton’s whistle, siren etc.) (2) Electrical generators: (a) Magnetostriction Oscillator: (b) Piezoelectric Oscillator Magnetostriction oscillator: Principle: Magnetostriction effect When a ferromagnetic rod like iron or nickel is placed in a magnetic field parallel to its length, the rod experiences a small change in its length. This is called magnetostriction effect..

(35) The change in length (increase or decrease) produced in the rod depends upon the strength of the magnetic field, the nature of the materials and is dependent of the direction of the magnetic field applied. L1. L2. c. b. e. Fig. 1. Experimental arrangement of the Magnetostriction oscillator.

(36) Experimental Arrangement: A bar of a ferromagnetic material (nickel, iron) is held at middle by means of a clamp C. Two coils L1 and L2 are connected (wound) to the ends of the rod. The coil L2 which forms an inductance is connected in parallel with a variable capacitor C. The combination of L2 and C form a resonant tank circuit. The tank circuit provides the oscillations and determines the frequency of the circuit. The other inductance coil L1 forms the feedback loop..

(37) Working: Initially, direct current is passed to magnetize the rod, so that it is ready to undergo the magnetostriction effect. Now when the circuit is switched ON, the capacitor C charges and discharges through the inductance coil L2. When the rod is placed inside a magnetic coil carrying current, the rod suffers a change in length. That is, the rod vibrates with a particular frequency. The amplitude of vibration is usually small, but if the frequency coincides with the natural frequency of the rod, the amplitude of vibration increases due to resonance..

(38) The vibrations of frequency f1 is given by > =. 1. @ 2? This produces longitudinal vibrations in the rod. As the rod elongates and contracts along its length, the vibrations set up an emf in L1. This emf is fed to the base of a transistor T, which positively feeds the amplified emf back to the coil L2 through the tank circuit. This feedback overcomes the loss of energy in the tank circuit and the oscillations are maintained in the tank circuit. The variable capacitor is now adjusted so that the frequency of the oscillatory circuit is same as that of the natural frequency of the rod..

(39) The vibration of the rod attains a maximum when it is set to resonance. The milliammeter shows a maximum current when resonance is achieved. The resonant vibrating frequency f2 is given by the physical dimensions and material of the rod 1 > = 2 where l is the length of the rod; E, the modulus of elasticity of the rod; and ρ is the density of the rod. Under resonance, the frequencies are > =>.

(40) Advantages (Merits): • Construction of the circuit is simple. • The cost of the oscillator is low. • At low ultrasonic frequencies, large power output is possible without the risk of any damage to the oscillatory circuit. Limitations (Demerits): • It cannot generate ultrasonic frequency above 3000 kHz. • The frequency of oscillations depends on operating temperature. At higher temperatures the output from the oscillator will not be very stable..

(41) Piezoelectric Oscillator: If mechanical pressure is applied to one pair of opposite faces of certain crystals like quartz, equal and opposite electrical charges appear across its other faces. This is called as piezoelectric effect. The converse of piezoelectric effect is also true. If an electric field is applied to one pair of faces, the corresponding changes in the dimensions of the other pair of faces of the crystal are produced. This is known as inverse piezoelectric effect or electrostriction..

(42) uartz crystal. 3. Fig. 1 Circuit diagram of the Piezoelectric oscillator. 2. 2. Experimental Arrangement: The circuit consists of a transformer connected to a quartz crystal in the secondary coil and a frequency generating circuit connected to its primary coil. The frequency is generated by a tank circuit consisting of a variable capacitor C2 and the primary coil L2..

(43) The inductor L2 of the tank circuit is inductively connected to the secondary coil of the transformer L3. A quartz crystal is connected at one of the terminals of the secondary coil, whose other end is inductively coupled to the inductor coil L1 in the primary coil. The coil L1 is connected to the base of the transistor T that is connected in the common-emitter configuration. The collector of the transistor is positively coupled to the tank circuit..

(44) Working: When the circuit is switched ON, current starts to flow in the tank circuit. The oscillating frequency generated by the tank circuit is given by > =. 1. 2? @ These oscillations are mutually fed into the secondary coil of the transformer through L3. The crystal now starts vibrating under inverse piezoelectric effect. This causes a back emf to be generated across L1. This emf is amplified by the transformer and fed back into the tank circuit, where the oscillations get sustained. Now the value of the variable capacitor is adjusted so that the quartz crystal starts to vibrate in resonance with its natural frequency..

(45) At this point, the current in the circuit reaches a maximum. Since there is the presence of continuous emf across the crystal, it produces ultrasonic waves continuously. The natural frequency of the vibrating crystal is given by. > =. 2. where P is the integer with values of 1, 2, 3,... for fundamental mode; t is the thickness of the crystal; E is the modulus of elasticity of the crystal; and ρ is the density of the crystal. Under the condition of resonance, > =>.

(46) Advantages: • Ultrasonic frequencies as high as 500 MHz can be obtained with this arrangement. • The output of this oscillator is very high. • It is not affected by temperature and humidity. Disadvantages: • The cost of piezoelectric quartz is very high • The cutting and shaping of quartz crystal are very tedious..

(47) Application of Ultrasound: An ultrasound-based diagnostic imaging technique used to visualize subcutaneous body structures including tendons, muscles, joints, vessels and internal organs for possible pathology or lesions. Obstetric sonography is commonly used during pregnancy. Ultrasound uses in the diagnosis and therapeutic procedure as interventional procedures. Ultrasound uses in the navigation purpose as Sound navigation and Ranging (SONAR)..

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