The floor is assumed to reflect all the power and so need not be included in the measuring surface. We can choose any enclosing surface as long as no other sources or sinks (absorbers of sound) are present within the surface. First we need to define this hypothetical surface. The sound power is the average normal intensity over a surface enclosing the source, multiplied by the surface area. The use of sound intensity rather than sound pressure to determine sound power means that measurements can be made in situ, with steady background noise and in the near field of machines. Using Sound Intensity To Determine Sound Power This reduction produces the cosine directivity characteristic. For sound incident at an arbitrary angle θ to the axis the intensity component along the axis, will be reduced by the factor cosθ. Hence there will be zero particle velocity and zero intensity.
The full vector is made up of three mutually perpendicular components (at 90° to each other) – one for each coordinate direction.įor sound incident at 90° to the axis there is no component along the probe’s axis, as there will be no difference in the pressure signals. With a two-microphone probe, we do not measure the vector however we measure the component in one direction, along the probe axis. In contrast, sound intensity is a vector quantity. Since pressure is a scalar quantity, a pressure transducer should have an equal response, no matter what the direction of sound incidence (that is, we need an omnidirectional characteristic). This is due to the probe and the calculation within the analyzer. The directivity characteristic for the sound intensity analyzing system looks (two-dimensionally) like a figure-of-eight pattern – known as a cosine characteristic. The choice of spacer depends on the frequency range to be covered. Three solid spacers define the effective microphone separation to 6, 12 or 50 mm. This arrangement has been found to have better frequency response and directivity characteristics than side-by-side, back-to-back or face-to-face without solid spacer arrangements. The Brüel & Kjær probe has two microphones mounted face to face with a solid spacer in between. The analyzer does the integration and calculations necessary to find the sound intensity. The probe simply measures the pressure at the two microphones. The pressure and particle velocity signals are then multiplied together and time averaging gives the intensity.Ī sound intensity analyzing system consists of a probe and an analyzer.
The pressure is also approximated at this point by taking the average pressure of the two microphones. The estimate of particle velocity is made at a position in the acoustic centre of the probe, between the two microphones. The pressure gradient signal must now be integrated to give the particle velocity. It can be thought of as an attempt to draw the tangent of a circle by drawing a straight line between two points on the circumference. This is called a finite difference approximation. With two closely spaced microphones, it is possible to obtain a straight line approximation to the pressure gradient by taking the difference in pressure and dividing by the distance between them. The pressure gradient is a continuous function, that is, a smoothly changing curve. Integrating the acceleration signal then gives the particle velocity.
With knowledge of the pressure gradient and the density of the fluid, the particle acceleration can be calculated. With Euler’s equation it is the pressure gradient that accelerates a fluid of density ρ. Using Sound Intensity To Determine Sound Power.If we know the force and the mass, we can find the acceleration and then integrate it with respect to time to find the velocity. Newton’s second law relates the acceleration given to a mass to the force acting on it. With this equation, it is possible to measure this pressure gradient with two closely spaced microphones and relate it to particle velocityĮuler’s equation is essentially Newton’s second law applied to a fluid. The particle velocity, however, can be related to the pressure gradient (the rate at which the instantaneous pressure changes with distance) with the linearized Euler equation. But measuring particle velocity is not as simple. A single microphone can measure pressure – this is not a problem. Sound intensity is the time-averaged product of the pressure and particle velocity. How Is Sound Intensity Measured? The Euler Equation