# Sound Radiation of Aerodynamically Excited Flat Plates into Cavities
## 3 Materials and Methods
### Measurement Technology and Methods  
The wall pressure was measured over a period of 60 s with a sampling frequency of 100 Hz using the pressure system DTC Intium working with the DTC-technology (Digital Temperature Compensation). To determine the pressure coefficient, 64 positions on the plate in the direction of the flow are simultaneously recorded. The determination of the velocity and of the turbulence intensity is forming the basis for the flow characterization. To approach the true value of the flow velocity as accurately as possible, the velocity regulating differential pressure transducer Model 239 from Setra Systems (Boxborough, Middlesex, MA, USA) is calibrated with the Prandtl Probe TPL-03-200 from KIMO Instruments (Montpon Menestrol, France) working with very high accuracy. On this basis, the velocity field and the turbulence intensity distribution perpendicular to the flow direction in a certain distance to the nozzle outlet are measured by this Prandtl probe and a hot-wire anemometer with the miniature wire probe 55A53 from Dantec Dynamics (Skovlunde, Denmark). Using a traversing system, a zero point in the corner of the nozzle outlet is set as a reference for the 108 measurement points. They are arranged on a planar grid, parallel to \(yz\)-plane with equal spacing. The velocity profiles were measured at distances \(x=100\), 350 and 520 mm from the nozzle outlet with a sampling rate of 5 kHz and a measuring period of 20 s. The turbulence intensity is determined in the same planes. For the examination of the boundary layer, the boundary layer probe 55P15 from Dantec Dynamics is necessary in terms of measurements in direct wall proximity. The corresponding measurement setup with the nozzle, the flow-excited plate and the traversing system is shown in Figure 4. The measurement distances to the nozzle are chosen between the position of the front edge (\(x=350\) mm) and the rear edge (\(x=520\) mm) of the installed flexible plate. More precisely, different  
Figure 3: Assembly and exploded view of the cavity. not equidistant points in \(z\)-direction perpendicular to the plate are measured. While approaching towards the wall, the distance is successively decremented. The traversing system automatically moves the probe to all points till the contact point between probe and plate is reached. The microphones in the side panel and the top panel are arranged in such a way that they are able to collect the generated noise at anytime independent of the rear panel position. Moreover, one microphone row is placed in the middle of the minimum and the maximum volume in each case. The cavity volume and the microphone measuring positions are varied for the same plate thickness of the flexible plate structure. This results in different measuring configurations with the following variation possibilities:  
* Cavity volume: minimum and maximum
* Microphone arrangement: left, top and rear
* Flow velocity: 45 m s\({}^{-1}\)
* Plate thickness: 1 mm, 3 mm and 5 mm  
Additionally, a frame, milled from solid with a thickness of 20 mm, is precisely closing the square opening in the rigid aluminium plate and has been prepared for comparative purposes. It can be assumed that there is no noise transmitted through this frame. To detect structural vibrations of the flexible plate and to establish a correlation with the sound radiation in the cavity, Laser Scanning Vibrometer measurements are performed. The method is based on the Doppler-effect where two coherent light beams with different path lengths overlap and result in optical interference. The velocity of a certain point on the vibrating plate is determined through the known wavelength of the laser beam and the frequency shift due to the motion of the surface (Figure 5). Figure 4: Measurement setup and enlargement of the boundary layer probe. A square-shaped grid with 256 measuring points is generated and placed on the surface of the flexible plate using the Laser Scanning Vibrometer PSV-500 from Polytec (Waldbronn, Germany) with an automatic scanning mirrors system.