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Introduction |
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Very often, energy is generated at one place but consumed elsewhere. The transportation of energy from its source to the receiving end can be done in two ways: By actually moving the matter carrying kinetic energy and delivering it to the other end. |
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Formation of Waves |
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One of the familiar types of waves is the wave on the surface of water. Let a pebble (P) be dropped gently on the calm surface of water in a pond. Before the pebble is dropped the surface of water is flat. When the pebble falls, it pushes the water under it, downwards. Water, being practically incompressible, gets displaced and rises up all-around in a ring. The pebble passes through water and reaches the bottom of the pond. |
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Types of Waves |
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Mechanical wave motion can be defined as the propagation of a disturbance through a material medium due to the repeated periodic motion of the particles of the medium about their mean positions, the disturbance being handed over from one particle to the next. |
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Transverse and Longitudinal Waves |
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In this type of wave motion, the particles of the medium vibrate at right angles to the direction of propagation of the wave. |
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Wave Properties |
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On observing waves, it may be observed that they travel with a definite speed through a uniform medium. If we watch a particular spot, we find that the waves pass that spot at regular intervals of time. The following definitions help in describing wave motion. |
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Characteristics of Wave Motion |
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Wave motion is the propagation of a disturbance produced in a medium by the repeated periodic motion of the particles of the medium. |
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Equation for a Progressive Wave |
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The simplest type of wave is the one in which the particles of the medium are set into simple harmonic vibrations as the wave passes through it. The wave is then called a simple harmonic wave. |
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Intensity of a Wave |
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In all progressive waves, energy travels through the medium in the direction in which the wave travels. Each particle of the medium has energy of vibration and passes energy on to succeeding particles. |
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Superposition of Waves |
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When a number of similar waves pass through a medium simultaneously, each wave travels through the medium as though the others were not present. |
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Analytical Treatment of Interference of Waves |
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Let two similar waves of amplitudes A1 and A2 having same frequency and wavelength travel past a point in a medium, producing individual displacements y1 and y2. |
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Ratio of Intensities at Maxima and Minima |
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It has already been proved that the intensity of a wave is proportional to the square of the amplitude. At a point where constructive interference has occurred, the intensity will be maximum and the amplitudes of the two waves will have added. |
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Experiment to Demonstrate Interference of Sound Waves |
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Interference of sound waves can be demonstrated using Quincke's tube. It consists of two U-tubes ABCDE and FGH, whose limbs can be inserted telescopically into each other. |
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Stationary Waves |
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Stationary or standing waves are formed in a medium when two waves having equal amplitude and frequency moving in opposite directions along the same line, interfere in a confined space. Generally, such waves are formed by the superposition of a forward wave and the reflected wave. Both longitudinal and transverse types of waves can form a stationary wave. |
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Analytical Treatment of the Formation of Stationary Waves |
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In this case, there will be no reversal of phase due to reflection. |
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Characteristics of Stationary Waves |
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In stationary waves, there are certain points called nodes where the particles are permanently at rest and certain other points called antinodes where the particles vibrate with maximum amplitude. The nodes and antinodes are formed alternately. |
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Comparison between Progressive Waves and Stationary Waves |
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The disturbance produced in the medium travels onward, it being handed over from one particle to the next. Each particle executes the same type of vibration as the preceding one, though not at the same time. |
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Modes of Vibrations in Pipes |
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An organ pipe is the simplest form of a wind instrument. Figure (a) shows the longitudinal section of an organ pipe whose one end is closed and figure (b) shows an organ pipe, both ends of which are open. It consists of a hollow tube BD in which air can be blown through a pipe A (also called the mouthpiece). |
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Resonance |
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A mechanical system which is free to vibrate like a hacksaw blade clamped at one end, a diving spring board or the air in pipes has a natural frequency of vibration f0, which depends on its dimensions. When a periodic force of a frequency different from f0 is applied to the system, it vibrates with a small amplitude and undergoes forced vibrations. |
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Vibration of Stretched Strings |
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In physics, the word 'string' is used in a more general sense than what it normally denotes. In olden days, musical instruments employed strings of twisted intestines of animals, such as cat-gut. Nowadays, the strings of musical instruments like the veena, violin and guitar are made of metal wires. |
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Sonometer |
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A sonometer, also called a monochord, was invented by Pythagoras (580-500 B.C.). It is a simple instrument used to verify the laws of stretched strings and to determine the frequency of a tuning fork. It consists of a long hollow rectangular wooden box (w) called the sound box, having three openings on one of its sides. |
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Melde's Experiment |
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Melde's electrically maintained tuning fork consists of a large tuning fork (F) made of a ferromagnetic alloy, whose shank is rigidly clamped to a heavy rectangular wooden board (W). |
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Sound - Introduction |
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Mechanical waves which can cause the sensation of hearing are called sound waves. These waves are produced by bodies vibrating at frequencies lying between the range of 20Hz and 20,000Hz, perceived by the human ear. |
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Propagation of Sound |
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Ordinarily, we hear sound, transmitted through the air. Unlike light, sound cannot pass through vacuum. This was discovered in 1654 by Otto Von Guericke. |
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Velocity of Sound in Gases (Newton's Formula) |
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The restoring force acting on the particles of the medium is intimately connected to the approximate elastic modulus of the medium and the inertial mass, to its density. |
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Laplace's Correction to Newton's Formula |
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Assuming isothermal conditions to prevail when sound travels through air, Newton has applied Boyle's law to the changes in pressure and volume. |
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Velocity of Sound in Different Gases |
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As seen from equation (1-28), the velocity of sound in a gas depends on g, the ratio of the principle specific heats of the gas. This, in turn, depends on the atomicity of the gas. |
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Velocity of Sound in Liquids and Solids |
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The velocity of sound in water was determined by Daniel Colladon and Jacob Sturm in the lake of Geneva in 1827. |
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Intensity and Loudness of Sound |
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Physically, a wave involves the propagation of energy. This transfer of energy by a traveling wave is expressed in terms of the intensity I. Intensity of sound waves is defined as the average energy transported per second per unit area perpendicular to the direction of propagation. It is measured in Js-1m-2 or Wm-2. |
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The Human Audiogram |
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The loudness of sound depends upon both intensity and frequency. For a given frequency, an increase in intensity produces an increase in loudness, but the sensitivity of the ear is so different in the various frequency ranges that equal intensities produce far different sensations in the different regions. |
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Factors Affecting the Intensity of Sound |
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A musical instrument like a guitar or veena gives louder sound when its string is plucked with a greater force. The intensity is directly proportional to the square of the amplitude of vibration of the source. The loudness which is a logarithmic function of intensity, also increases. |
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Phon - Another Unit of Loudness |
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As the threshold of audibility varies with frequency, sounds of the same intensity but different frequencies are found to differ in loudness. Therefore, another unit of loudness is defined. This unit measures the intensity of a sound relative to a reference tone of defined pressure and frequency. |
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Musical Sounds and Noise |
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Audible sounds are classified into two groups, namely musical sounds and noise. A musical sound is that in which the vibrations of the sounding body are periodic, follow each other regularly and rapidly, so as to produce a pleasing effect on the ear without any sudden change in loudness. |
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Beats |
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Whenever two wave motions pass through a single region of a medium simultaneously, the motion of the particles in the medium will be the result of the combined disturbance due to the two waves. This effect of superposition of waves, is also known as interference. |
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Doppler Effect |
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Let a stationary observer on a platform listen to the sound emitted by the whistle of an incoming train. As the train approaches the platform, an increase in the pitch of the sound will be observed. |
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Expression for the Apparent Frequency |
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Observer and source moving in the same direction as sound in a stationary medium. |
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Some Important Aspects of Doppler Effect |
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The Doppler effect can be observed in all kinds of waves so long as the speed of the source is small when compared to the speed of the wave. |
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Applications of Doppler Effect |
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The Doppler effect provides a convenient means of tracking a satellite that is emitting a radio signal of constant frequency. The frequency of the signal received on the Earth changes as the satellite is passing. |
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Acoustics of Buildings |
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An auditorium is a part of a building in which large number of people may be seated to listen to a speech or music. It is not uncommon to find an auditorium, which may be an architectural masterpiece but falls below standards on acoustic considerations. |
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Reverberation |
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The persistence of audible sound even after the source has ceased emitting sound is called reverberation. |
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Sabine's Formula |
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Prof. Wallace C. Sabine (1868 - 1919) of Harvard University investigated architectural acoustics scientifically, particularly with reference to reverberation time. |
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Summary |
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All vibrating and oscillating bodies are described by the length of time required for one complete cycle. |
