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We also showed that the particle velocity u and the acoustic pressure p are given by Where A is the displacement amplitude, k is the wave number (k = 2π/λ) and ω is the angular frequency (ω = 2πf). On the page on the sound wave equation, we wrote a solution for the particle displacement y as a function of position x and time t: For a one dimensional (plane) wave travelling to the right, these are shown in the animation below. We'll need the equation for a travelling sound wave that we found when we set up and solved the sound wave equation. The acoustic impedance at a particular frequency indicates how much sound pressure is generated by a given acoustic flow at that frequency. Usually, Z varies strongly when the frequency changes. The acoustic impedance Z is the property of a particular geometry and medium: we can discuss for example the Z of a particular duct filled with air. The specific acoustic impedance, z, is an intensive property of a medium. With this proviso, we can say thatĪcoustic impedance = pressure/flow and specific acoustic impedance = pressure/velocity In all cases, 'acoustic' refers to the oscillating component. So we define acoustic impedance Z and specific acoustic impedance z thus: ( There is a close analogy with electrical impedance, the ratio of AC voltage V to current I.) The specific acoustic impedance is a ratio of acoustic pressure to specific flow, which is the same as flow per unit area, or acoustic flow velocity, u. P = I*A = 10 -10 W/m -2* 20*10 6m 2 = 2*10 -3W.Acoustic impedance, which has the symbol Z, is the ratio of acoustic pressure p to acoustic volume flow U. S = 10*log(I/I 0) = 10*log(10 -10W/m -2/0 -12 W/m -2) = 20 dBĢ)From the previous exercise, determine the power generated if the normal propagation area is 20km 2.Īnswer: Using the intensity of sound given in the previous exercise. I 0 = sound intensity of zero decibels= 10 -12 W/m -2ġ)What is the level of sound sensation in decibels corresponding to an intensity wave 10 -10 W/m -2?Īnswer: The first thing to notice is that they are already giving us the intensity of sound, so we can easily calculate the sound sensation. The intensity in decibels = 10 * log 10 (intensity/ intensity of zero decibels) The conversion between intensity and decibels follows this equation: The scale of sound sensation is logarithmic, which means that an increase of 10 dB corresponds to an intensity 10 times greater for example, the noise of the waves on the coast is 1,000 times more intense than a whisper, which equals an increase of 30 dB.ĭue to the extension of this audibility interval, to express sound intensities is used a scale whose divisions are powers of ten and whose unit of measurement is the decibel (dB). For example, the hearing threshold is 0 dB, the physiological intensity of a whisper corresponds to about 10 dB and the noise of waves on the coast to about 40 dB. The physiological intensity or sound sensation of a sound is measured in decibels (dB). Sound intensity = acoustic power / normal area to the direction of propagation.Ī = normal area to the direction of propagation. The intensity of the sound that is perceived subjectively is what is called sonority and allows sounds to be arranged on a scale from the loudest to the weakest. Non-elastic media, such as wool, felt, etc., considerably weaken the sounds. Finally, the intensity also depends on the nature of the elastic medium between the source and the ear. The intensity of perception of a sound by the ear also depends on its distance from the sound source. The increase in the amplitude of the source and that of the vibrating surface causes the kinetic energy of the mass of air in contact with it to increase simultaneously this kinetic energy increases, in effect, with the mass of air that is put into vibration and with its average speed (which is proportional to the square of the amplitude). It also depends on the surface of the sound source. The usual context is the measurement of the intensity of sound in the air where the listener is. The intensity of sound is defined as the sound power per unit area.
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