See Figure 1: One complete vibration or oscillation is called a cycle. The number of cycles per second is called the frequency (f); its unit is 1

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1 Waves and Sound Vibrations and Waves Waves are disturbances that transfer energy over a distance. Water waves, sound waves, waves in a rope, and earthquake waves all originate from objects that are vibrating. In each case, the vibrating source supplies the energy that is transferred through the medium as wave. When an object repeats a pattern of motion, we say the object exhibits periodic motion. The repeated pattern is called a cycle or a vibration. Three basic types of vibrations: () Transverse vibration occurs when an object vibrates perpendicular to its axis at the normal rest position. An example: A child swinging on a swing. Also, water wave, waves in a rope. () Longitudinal vibration occurs when an object vibrates parallel to its axis at the rest position. An example: coil spring supporting a vehicle. (3) Torsional vibration occurs when a string supporting an object is twisted, causing the object to turn or vibrate around and back. See Figure : One complete vibration or oscillation is called a cycle. The number of cycles per second is called the frequency (f); its unit is simply or s or hertz (Hz). The time required for one cycle is called the period (T). Thus f and T. When an s T f object vibrates, the distance from the equilibrium or rest position to maximum displacement is called the amplitude (A). Two identical pendulums are said to be in phase if they have the same period and pass through the rest position at the same time. They are said to be vibrating out of phase if they do not have the same period or if they have the same period but they do not pass through the rest position at the same time. The period of a pendulum is directly proportional to the square root of its length:. T l or f l In transverse waves, the high section of the wave is called a crest and the low section is called a trough. A wave consists of a single disturbance is called a pulse. A crest can be referred to as a positive pulse and a trough a negative pulse. The distance from the midpoint of one crest to the midpoint of the next crest is called the wavelength ( ). In longitudinal waves, the regions where the particles are closer together than normal are called compressions; the regions where they are farther apart are called rarefactions. Speed = Distance. Time T So the Universal Wave Equation: f applicable to all waves. The speed of a wave is unaffected by changes in the frequency or amplitude of the vibrating source. The factors affecting the speed of sound are: (i) producer of sound, (ii) medium, (iii) temperature, (iv) density. () Transverse Waves: Light; () Longitudinal Waves: Sound; (3) Complex Wave: Water; Waves that travel in the ground generated by earthquakes are of two main types: longitudinal P waves, (push-pull waves) and transverse S waves (side-by-side waves). S waves cannot travel through liquid matter, while P waves can travel through both molten and solid parts of the Earth s interior.

2 Transmission and Reflection () In fixed-end reflections, the pulse is inverted, i.e., a crest is reflected as a trough and a trough as a crest. () In free end reflections, there is no inversion. When waves travel in two media, at the boundary between the two media, the speed and wavelength change, and some reflection occurs. This is called partial reflection. For a wave (called the incident pulse) passing from a fast medium to a slow medium, the particles of the slower medium have greater inertia and the medium acts like a rigid obstacle (fixed-end), and the reflected wave is inverted but the transmitted wave is not inverted. When a wave travels from a slow medium to a fast medium, the fast medium acts like a free end reflection, and there is no inversion. When the reflected wave is inverted, it means the wave has undergone a phase shift of 800, that is, it is out of phase with the incident wave. Waves in Two Dimension Using a ripple tank, we can observe that light from a source above the tank passes through the water and illuminates a screen on the table below. The light is converged by wave crests and diverged by wave trough. Wavefront is the leading edge of a wave; wave ray is a straight line drawn perpendicular to a wavefront that indicates the direction of transmission. Straight waves can be reflected by a parabolic reflector to one point, called the focal point. Properties of Waves: Refraction and Diffraction A wave ray is a straight line drawn at right angles to the wavefront, indicating the direction of the wave motion. When waves are reflected from a solid obstacle, the angle of incidence is always equal to the angle of reflection. When a wave enters a medium in which it moves more slowly, its wavelength decreases, but frequency remains the same. When a water wave enters a slower medium at an angle, its direction of transmission changes; the wave has undergone refraction. When a wave passes by a barrier or through a small opening, it tends to diffract or change direction. Waves experience a large amount of diffraction when they pass through an opening which is smaller than the wavelength. Very little diffraction occurs when waves pass through an opening which is larger than the wavelength. There is no change in frequency or wavelength in diffraction. Diffraction is the bending (change of direction) of a wave in the same medium as it passes around an obstacle or through a narrow slit, causing the wave to spread. Refraction refers to the change in direction of a wave as it crosses the boundary between two media in which the wave travels at different speeds. The Cause of the Beauty of Sunset As light

3 3 waves encounter small particles suspended in air, the longer wavelengths of red and orange allow these waves to diffract around the particles and keep on going. The shorter wavelengths corresponding to blue tend to reflect off these particles. Since the sunlight that we observe at sunsets has traveled a long distance through air, we see the reds and oranges. Interference & Principle of Superposition () Constructive Interference occurs when pulses build each other up, resulting in a larger amplitude of supercrest or a supertrough. () Destructive Interference occurs when waves diminish one another and the amplitude of the resulting wave is less than it would have been for either of the interfering waves acting alone. If the two waves completely cancel each other out at a point, a node occurs at that point, where it seems there is no wave at all. Mechanical Resonance Every object has a natural frequency at which it will vibrate. The response of an object to a periodic force with the same frequency as the natural frequency of the object is called resonance. Resonance is the phenomenon that occurs when the frequency of forced vibrations on an object matches the object s natural frequency, producing a dramatic increase in amplitude. It is called mechanical resonance because there is physical contact between the periodic force and the vibrating object. When an object vibrates in resonance with another, it is called sympathetic vibration. Mechanical resonance must be taken into account when designing bridges, airplane propellers, helicopter rotor blades, turbines for steam generators and jet engines, plumbing systems, and many other types of equipment; otherwise a dangerous resonant condition may result. Examples of mechanical resonance: () Collapse of a footbridge near Manchester, England caused by Cavalry troops marching in rhythm in 83, () Collapse of the Tacoma Narrows Bridge in 940, (3) Rocking a car out of an ice rut, (4) Pushing a child on a swing, (5) Pendulum clocks, (6) A person walking with a bucket of water can cause the water swishing back and forth, (7) A truck drives down your street can cause windows of your house to rattle, (8) The low hum of large motors in a factory causes workers internal organs, like the heart, to vibrate, making the workers feel sick, (9) In hitting a ball using a baseball bat, you may feel the whole arm is jarred caused by the vibrating bat after impact with the ball, or you may experience a smooth, effortless hit (if the bat hits the ball at a node, point of destructive interference, the bat doesn t excite any resonance modes and hence doesn t vibrate, giving a smooth hit). At the so-called sweet spot, each resonance mode has a tiny amplitude, thus creating an effect similar to hitting the ball at a pure node.

4 4 (0) Radio and television provide another example of resonance involving sound waves. When you tune a radio or television, you are actually adjusting the frequency of vibration of particles in the electrical circuits of the receiver so that they resonance with the frequency of a particular signal from a radio or television station. FM radio and television signals are high frequency sound waves, and AM signals are low frequency sound waves (which diffract better and travel longer distance as to be seen later). See the following Figure:

5 5 Standing Waves A special Case of Interference in a one-dimensional medium when the interfering waves have the same amplitude, frequency, and wavelength and travel in opposite directions. In most cases of interference, the resultant displacement remains for only an instant, while standing wave interference remains relatively stationary. There is a point, or points, that remains at rest throughout the interference of the pulses. This point is called a node, or nodal point. The nodes are equidistant and that their spacing is equal to one-half of the wavelength (i.e. inter-nodal distance, d n ) of the interfering waves. Midway between the nodes are points where double crests and double troughs occur. These points are called antinodes. Each vibrating section between any two nodes is called a loop. Standing waves may be produced by means of a single source. For example, reflected waves will interfere with incident waves, producing standing waves. Since the incident waves and the reflected waves have the same source and cross the same medium with little loss in energy, they have the same frequency, wavelength, and amplitude. The distance between nodal points may be altered by changing the frequency of the source. However, for a given length of rope or of any other medium, only certain wavelengths are capable of maintaining the standing wave interference pattern because the reflecting ends must be nodes at a fixed end, or must be antinodes at a free end (Note that a wave reverses phase when it reflects at a fixed point and keeps the same phase when it reflects at a free point). This fact holds for all types of waves, longitudinal or transverse. Nodes and antinodes alternate every quarter wavelength. Standing waves are critical in the understanding of the production of musical sounds.

6 6 Properties of Sound Waves Production and Transmission of Sound - Sounds are a form of energy produced by rapidly vibrating objects that travels as longitudinal waves containing regions of high and low pressure. Sound energy is extremely small compared to light energy. Sound energy dissipates to thermal energy while sound travels in air. For waves of higher frequency, the sound energy is transformed into thermal energy more rapidly than for waves of lower frequencies. So, sound of low frequencies will travel farther through air. We hear sounds because this energy stimulates the auditory nerve in the human ear. The ears of most young people respond to sound frequencies of between 6 Hz and 0,000 Hz. Frequencies of less than 6 Hz are referred to as infrasonic and those higher than 0,000 Hz are called ultrasonic. Sound requires a physical medium for its transmission. Sound travels as a series of compressions and rarefactions. Pitch is related to frequency: the higher the frequency, the higher the pitch. The Speed of Sound The speed of sound in air at 0 C is 33 m/s. The speed of sound increases when the temperature increases: T, v T. The speed of sound can be measured using echoes. The speed of sound changes if the medium changes. Factors affecting speed of sound: (i) producer of sound, (ii) medium, (iii) temperature, (iv) density. It should be noted that some of the benefits of the shorter travel time are negated by the greater rate of decrease in amplitude of the wave in the denser medium. This decrease means that the wave dies out faster when traveling through a solid than a gas. We hear thunder when the lightning is reasonably close, but we often fail to hear the thunder for distant lightning because of refraction. The sound travels slower at higher altitudes and bends away from the ground. The opposite often occurs on a cold day or at night when the layer of air near the ground is colder than the air above as in Figure 3. The Intensity of Sound is defined as the amount of sound energy passing each second through a unit area: Intensity = power of a sound watts W W. Sound audible to humans can vary from 0 - (the quietest whisper) to 0 (the level in area m m m painful to the ear) a difference of a factor of 03. One unit is used to measure the intensity level of sound is the bel (B), The W decibel (db) is more common than the bel: db 0 B. On the decibel scale, 0 db is the threshold of hearing ( 0 - ). The m scale is not linear, but is a logarithmic scale: The decibel unit of sound intensity is defined as 0 log I. In most cases, the I value for I is the threshold of hearing, an intensity of 0 - W. Every change of 0 units on the decibel scale represents a m tenfold effect on the intensity level. The loudness of the sounds humans perceive relates to the intensity of the sound. However, the two measures are not the same because the human ear does not respond to all frequencies equally. The average human ear is most sensitive to sound frequencies between about 000 Hz and 5000 Hz. Lower frequencies must have a higher sound level or intensity to be heard. The intensity of a sound received by the human ear depends on the power of the source and the distance from the source. Loudness and intensity are not the same thing; loudness is a measure of the response of the ear to the sound. The source of sound creates a sphere of sound moving away from it. The area of a sphere is A 4 r, I emitted from a single source at different distances is therefore given by: I (r ) I (r ) P P. The ratio of intensities A 4 r The human Ear magnifies and transforms sound into electrical nerve pulses. The range of hearing diminishes with age and/or with exposure to loud sounds. People in noisy locations should protect their hearing. Hearing loss can be improved by electronic devices, such as hearing aids. The Reflection of Sound Waves Sound waves obey the laws of reflection. Echoes are produced when sound is reflected by a hard surface, such as a wall or cliff. An echo can be heard distinctly only if the time interval between the original sound and the reflected sound is greater than 0.s. The distance between the observer and the reflecting surface must be greater than 7m for an echo to be heard. In large cathedral, echoes cause notes to gradually fade away as they reflect back and forth from wall to wall in a process called reverberation. Echolocation is used in sonar (an acronym for sound navigation and ranging) applications, including navigation and food collection by some animals, such as dolphins, Orcas whales, and bats. The sonar used by bats has a wavelength comparable to the size of their prey. The emitted pulses are 0.00 s in duration and are of a frequency too high for humans to hear. The location of the insect is determined by comparing the slight time difference for the returning signal to reach the bat s ears. The bat uses the Doppler effect, caused by the regular rhythm of the prey s wings, to determine whether the insect is traveling towards or away from it. It distinguishes edible prey from other objects by the apparent

7 7 pitch changes in the sound generated by the prey s wings as the prey moves towards or away from the bat. Birds also use echolocation for navigation. Their clicks and pulses are low frequency compared to the high-frequency pulses of dolphins and bats, which makes them less effective. Its sounds are in the human hearing range and are emitted at a rate of 7.5 clicks in 0.3 s. Ultrasound (with frequencies higher than 0,000 Hz) has many medical applications, both for diagnosis and treatment (breaking up kidney stones). Diffraction and Refraction of Sound Waves Sound waves can be diffracted (that is why we can hear around corner) and refracted as in the warm air and cold air situation described in Figure 3 above. Diffraction is greater when the sound wavelengths (lower frequencies) are larger. The Interference of Sound Waves Sound waves interfere, producing areas of constructive and destructive interference with corresponding increase and decrease in sound intensity. The interference pattern between the two loudspeakers in phase is similar to the pattern that is observed in water waves between two point sources. If you walked across the area in front of these speakers, the sound intensity would fluctuate between loud and soft. Beat Frequency Consider a tuning fork that has one tine loaded with Plasticine or an elastic band wrapped around it. If this fork is struck at the same time as an unloaded, but otherwise identical, tuning fork, the observed sound will alternate between loud and soft, indicating alternative constructive and destructive interference. Such periodic changes in sound intensity are called beats. One beat is a full cycle of loudness variation from loud to soft and back to loud. In the interference between two sources with slightly frequencies, the wavelengths are not equal and hence the distances between successive compressions and rarefactions are not the same. At certain points, a compression from one source coincides with a rarefaction from the other, producing destructive interference and minimum sound intensity. When compression and compression coincide and rarefaction and rarefaction coincide, constructive interference results and maximum sound intensity occurs. The number of maximum intensity points that occur per second is called the beat frequency. To determine the beat frequency, the lower frequency is subtracted from the higher frequency. For example, if a tuning fork of 436 Hz is sounded with a 440 Hz tuning fork, the beat frequency is 4 Hz. In general, the beat frequency is equal to the difference in frequency between two sources: f beat f f. Piano tuners use beats to tune pianos. Herschel Tube a device that splits the sound waves from a single source into two paths of different lengths. The sound wav in the longer path lags behind the other wave. When it is finally reunited with its sister wave, they interfere according to the principle of superposition. If the longer section was longer than the other section, then every compression of one wave would meet a rarefaction of the other wave, resulting in total destructive interference and silence. The Doppler Effect and Supersonic Travel If you ve ever been to an automobile race, you probably noticed that when a racing car streaks past you, you can detect a change in frequency of the sound from the car. As the car approaches, the sound becomes higher in frequency. At the instant the car passes you, the frequency drops noticeably. The apparent changing frequency of sound in relation to an object s motion is called the Doppler effect, which occurs in subsonic conditions. When the source of sound moves toward you, the sound waves are closer together, so the wavelength is shorter ( v 0 t, where v0 is the speed of the object) and the frequency is higher. When it is moving away from you, the waves are farther apart, so the wavelength is longer ( v0t ) and the frequency is lower. Since each successive wave is produced in a time T, the period of the wave, we can write the equations as v 0 T, and f moving away from the observer, and ( v sound v sound v sound f v sound. ( v sound v0 ) is used if the source is ( v 0 T ) (v sound v 0 ) v0 ) is used if the source is moving toward the observer. The change in frequency

8 8 and resulting change in wavelength is called the Doppler shift. (i) Astronomers use the Doppler effect of light waves to estimate the speed of distant stars and galaxies relative to that of our solar system. (ii) In police speed trap, radio waves are aimed at a car. The moving car then acts as a source of the reflected waves. By comparing the frequency of the original wave with that of the reflected wave, the speed of the car can be determined. (iii) Weather radar uses the Doppler effect to measure the wind velocities during storms. Radio waves reflected from raindrops that are moving toward the radar weather station will have their frequencies increased. The waves reflected from drops that are moving away from the station will have their frequencies decreased. In either case, the amount of the change in frequency depends on the horizontal speed of the drops, which in turn depends on the speed of the winds. Whenever the meteorologists see a reversal of wind direction over a short distance, that indicates a whirling pattern, which could become a tornado. Objects traveling at speeds less than the speed of sound in air have subsonic speeds. When the speed of an object equals the speed of sound in air at that location, the speed is called Mach. The Mach number of a source of sound is the ratio of the speed of the source to the speed of sound in air at that location. Thus, at 0 C near the surface of the earth, Mach is 33 m/s = 664 m/s. Speed greater than Mach are supersonic. When an airplane is traveling at subsonic speeds, the air molecules in front of the wing are pushed forward by the leading edge of the wing. As a result, a compression travels forward faster than the wing. The compression pushes other air molecules out of the way. Consequently, most of the air molecules are above or below the wing as it passes by. When an airplane is flying at the speed of sound, the compression cannot move faster than the wing, and the air molecules in front of the airplane pile up, producing an area of very dense air, or intense compression, called the sound barrier. The continual spillage of this compression above and below the wing forms a shock wave. To exceed the speed of sound, extra thrust is needed until the aircraft breaks through the sound barrier. The term sound barrier is used in aviation to describe the buildup of sound waves in front of a plane as it nears the speed of sound. At supersonic speeds, the spheres of sound waves are left behind the aircraft. These sound waves interfere with one another constructively, producing large compressions and rarefactions along the sides of an invisible double cone extending behind the airplane, from the front and from the rear. This intense acoustic pressure wave sweeps along the ground in a swatch having a width of about 5 times the altitude of the aircraft. This is usually referred to as a sonic boom (a phenomenon occurs in supersonic conditions), which is heard as two sharp cracks, like thunder. We don t hear a sonic boom from slower-than-sound or subsonic aircraft because the sound waves reaching our ears are perceived as one continuous tone. Only when the craft moves faster than sound do the waves overlap to reach the listener in a single burst as the shock wave. The sudden increase in pressure is much the same in effect as the sudden expansion of air produced by an explosion. While supersonic a aircraft generates a 3-dimensional shock wave, a speedboat knifing through the water similarly generates a -dimensional bowwave.

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10 Music, Musical Instruments, and Acoustics 0 A musical note originates from a source vibrating in a uniform manner with one or more constant frequencies. Music is the combination of musical notes. In contrast, noise originates from a source where the frequencies are constantly changing in a random manner. There are 3 main subjective characteristics of musical sounds: () pitch, () intensity or loudness, and (3) quality. As frequency increases, pitch increases, and wavelength decreases. In music, a pure note or tone is a sound where only one frequency is heard. Musical sounds usually consist of more than a single sound. Two or more sounds are harmonious if their frequencies are in a simple ratio. Harmonious pairs of sounds have high consonance; unpleasant pairs of sounds have high dissonance, or low consonance. Unison is a set of sounds of the same frequency. The interval between two musical notes that have frequencies in the ratio of two to one is called an octave, that is, an octave has sounds with double the frequency of the sounds in another frequency. For example, a 00-Hz sound is one octave above a 00-Hz sound. A musical scale is a set of pure tones with increasing or decreasing frequency. There are two common scales: () the scientific musical scale and () the musician s scale. On the scientific musical scale, the standard frequency is 56 Hz and is based on the number 8. The standard frequency can be multiplied by simple ratios to give the entire scale. Tuning forks in classrooms are often labeled with the frequencies of this scale. The notes G and C sound pleasant together because their frequencies are in the ratio 3 :. Another pleasant-sounding pair is B and E because the ratio of their frequencies 480 is 3 :. Because they are simple 30 ratios, we say the notes have high consonance. The musician s, or equitempered, scale has a standard frequency of 440 Hz, which is the frequency of the note A above middle C on the piano. An octave below has a frequency of 0 Hz and an octave above has a frequency of 880 Hz. The calculations for the frequencies of the musician s scale are based on two facts: () a note one octave above another is double the frequency of the other and () there are exactly equal intervals per octave. On a piano keyboard, for example, there are five black keys and eight white keys per octave 3 keys, frequency intervals. (Note that the 8th white key is the last note of the first octave and the first note of the next octave.) (A) Resonance in Vibrating Strings The vibrations of a string produce standing waves. Standing waves occur at specific frequencies, therefore a string vibrates at specific frequencies. The frequency of a vibrating string is determined by () its length ( f ), () tension ( f F ), (3) diameter ( f ), and (4) density ( f ). These factors must be taken into account l d D when designing stringed musical instruments such as the piano, guitar, and violin. The speed of a wave along a string under a given tension is constant. So f L is constant or f L f L Example: A guitar string produces an A note (0 Hz) when the vibrating segment is 63.0 cm long. How long should the segment be to produce a C note (30.8 Hz)? f L 0 Hz 63.0 cm 53.0 cm Solution: f L f L L f 30.8 Hz

11 Modes of Vibration Quality of Sound In its simplest, or fundamental mode of vibration, the string vibrates in one loop or segment. This produces its lowest frequency, called the fundamental frequency ( f 0 ). If L represents the length of the string, then v v one loop has the length of L. So L 0, 0 L, f 0. If the string vibrates in more than one loop, the resulting 0 L modes of vibration are called overtones. Since the string can only vibrate in certain patterns and always with nodes at each end, the frequencies of the overtones are simple, whole-numbered multiples of the fundamental frequency called harmonics, such as f 0, 3 f 0, 4 f 0, and so on. Thus, the fundamental frequency in musical terms ( f 0 ) is called the first harmonic in scientific terms, f 0 (the first overtone) is the nd harmonic, 3 f 0 (the nd overtone) the 3rd harmonic, etc. In this way the string can vibrate at, or resonate with, different frequencies. These special frequencies are called resonant frequencies. The quality of a musical note depends on the number and relative intensity of the overtones it produces along with the fundamental. A pure note has no overtone. A rich note contains several overtones in addition to the fundamental frequency. It is the element of quality that enable us to distinguish between notes of the same frequency and intensity coming from different sources; e.g. we can easily distinguish between middle C on the piano, on the violin, and in the human voice. (B) Resonance in Air Columns for the understanding of the working of wind instruments: Sound waves from one source can cause an identical source to vibrate in resonance. 3 5 () Closed Air Columns Resonance occurs at lengths of,,, and so on of the original sound wave. The corresponding series of fundamental and overtone frequencies are: f 0, 3 f 0, 5 f 0, 7 f 0, 9 f 0. 3 () Open Air Columns Resonance occurs at lengths of,,,, and so on. The corresponding series fundamental and overtone frequencies are: f 0, f 0, 3 f 0, 4 f 0, 5 f 0.

12 The shortest column length is known as the first resonant length. Notice that once the first resonant length is determined, the others can be calculated by simply adding of the sound wave each time. Musical Instruments: Most instruments consist of () a vibrating source and () a structure called the soundbox to enhance the sound through mechanical and acoustical resonance. () Stringed Instruments consist of a vibrating string and resonating soundboard, or hollow box. (i) Plucking, like banjo, guitar, mandolin, ukulele, harp: (When a guitar string is plucked, the energy of vibration is transferred from the string to the saddle and bridge. The bridge in turn transmits the energy to the soundbox. The soundbox consists of an enclosed air space, sides, a back plate, and a top surface-called the soundboard. Because the soundboard has a larger vibrating surface than the string, it translates its vibrations more effectively into compressions and rarefactions of air to produce sound of a higher intensity. However care must be taken to avoid strong resonance so that no notes will be amplified far beyond others.) (ii) Bowing, like violin: (iii) Striking, like piano: () Wind Instruments (trumpet, clarinet, tuba, flute, and oboe) contain either open or closed air columns of vibrating air; the initial vibration is created by a reed or by the player s lips. Basically there are 4 mechanisms for forcing air molecules to vibrate. (i) In air reed instruments (ii) In single-membrane reed instruments (iii) In double-membrane reed instruments (iv) Lip reed instruments

13 3 (3) Percussion Instruments (drums, cymbals) involve striking one object against the other. (i) Single definite pitch instruments (ii) Multiple definite pitch instruments (iii) Variable pitch instruments The Human Voice as a Musical Instrument In the human voice, air from the lungs causes the vocal chords to vibrate, initiating a sound. The throat, mouth, and nasal cavity create a resonant chamber that affects the quality of the resulting sound. Electrical Instruments are made of three main parts (i) a source of sound, (ii) a microphone, and (iii) a loudspeaker. The microphone changes the sound energy into electrical energy, which after amplification causes vibrations in a loudspeaker. These vibrations reproduce the original sound with an amplified loudness. A single loudspeaker does not have the same frequency range as our ears, so a set of two or three must be used to give both quality and frequency range. Digital sound recording is a method of storing sound as a series of binary numbers, not as waves. An Electronic Instrument consists of 4 main parts (i) an oscillator creates the vibrations, (ii) the filter circuit selects the frequencies that are sent to the mixing circuit, (iii) the mixing circuit adds various frequencies together to produce the final signal, and finally, (iv) the amplifier and speaker system make the sound loud enough to be heard. The shape of the sound waves produced by a synthesizer can be controlled; as a result, synthesizers can emit sounds that resemble the sound of almost any musical instrument. There are 4 basic waves that can be used to create more complex waves: (i) sinusoidal wave, (ii) sawtooth wave, (iii) square wave, and (iv) triangular wave. Electronic Instruments can also control the attack and decay patterns of a sound: The required wave can be synthesized in several ways: () Additive Synthesis the wave is produced by adding together waves of many different frequencies called harmonics. The wave is further to give the desired sound. () Subtraction Synthesis The synthesizer begins with a wave that contains many harmonics (different frequencies). The required wave shape is formed by selectively filtering out some of the harmonics. (3) FM Synthesis The wave shape is created by frequency modulation of a basic wave. (4) Sampling This method begins by actually sampling at regular intervals the longitudinal wave produced by an instrument whose sound is to be imitated. In all of the above methods, the frequency and amplitude variations are mimicked by variations in an electric current. The current is then used to drive a piezoelectric crystal or a speaker in order to produce the actual sound. The qualities of a room or auditorium that determine how well sound is heard are called acoustics. Reverberation time is the time for the intensity of a sound in a room to diminish to the point that it is inaudible. The types and locations of sound reflectors in a building determine its acoustical properties, including reverberation time.