2.3.4 Optical method for determination of resonant frequency

The optical method for determining the resonance frequencies of the membranes [19] was used to calculate the velocity of transverse wave on the homogeneous circular membrane CM. The main components of the system were the digital camera (Olympus—System i-SPEED2), a LCD display panel of 8.4″, and a transparent tube (see Figure 8). The test sample was fixed inside the tube. The incident plane sinusoidal sound wave was excited by a speaker located at end of the tube. The membrane began to oscillate after the impact sound waves reached, and its movement was picked by the high-speed digital camera and in turn was displayed on the LCD.

In order to determine the resonant frequency of the membrane, the 1-1500 Hz frequency range was studied by taking measurements at every 20 Hz to obtain a rough estimate of the resonant frequency. The deflection size of the nanofibrous membrane under the frequency range of 1–1500 Hz was measured using the closed tube. The resonant frequencies of the circular membrane of radius 0.05 m and 1gm<sup>2</sup> basis weight have been detected as can be seen in Table 1. The velocity of transverse wave on the homogeneous circular membrane CM has been determined by the relationship Eq. (2) based on the measured first resonant frequency f0,1 equal to 90 Hz.

3. Sound absorption results

Scheme of the measuring system. Took from [19].

Figure 8.

Table 1.

weight (6 g m<sup>2</sup>

31

In this arrangement, the idea is connecting the membrane (nanofibrous) resonator together with the mesh frame. The resonant frequencies fm,n of rectangle membrane with a variation of the side dimension are determined according to formula Eq. (10). The calculated resonant frequencies relating to vids m and n are shown in Tables 2–5. The dependence of the measured sound absorption coefficient on the sound frequency is shown in the following Figures 9–16. In Figures 9–12, the measured frequency dependence of the sound absorption coefficient for samples

Calculation of the velocity of transverse wave on the membrane CM based on measured resonant frequency of

Circular membrane f0,i (Hz) R (m) CM (m s<sup>1</sup>

a0,1 2.4048 90 0.05 11.76 a0,2 5 5201 207 0.05 11.76 a0,3 8 6537 324 0.05 11.76 a0,4 11 7915 441 0.05 11.76 )

From the curves on Figures 9–12 describing the frequency dependence of the sound absorption coefficient for samples of the same basis weight and different mesh size, it can be seen that the two clear sound absorption peaks occur in the case of small mesh size (1G and 2G), while in the case of large meshes (3G and 4G), only one clear sound absorption peak exists. It can be seen, therefore, that the mesh size of the grid has a major impact on the amount of the sound absorption coefficient. It can also be observed from Figure 9 that the nanofibrous membrane of highest basis

in the range of approximately 1500 Hz and 4000–5000 Hz, while the nanofiber layer deposited on the larger meshes is better at dampening frequencies of 2500–3000 Hz. Appearance of the peak for the smaller mesh (1G, 2G) at similar frequencies can be explained by the fact that the both meshes have the same width

) applied on the smaller meshes is better at dampening frequencies

of the same basis weight and different mesh size is compared.

vibrating circular membrane of radius 0.05 m and 1 g m<sup>2</sup> basis weight (a).

Sound Absorbing Resonator Based on the Framed Nanofibrous Membrane

DOI: http://dx.doi.org/10.5772/intechopen.82615

Figure 7. Illustration of the deflection of vibrating membrane inside the meshes of a grid.

Sound Absorbing Resonator Based on the Framed Nanofibrous Membrane DOI: http://dx.doi.org/10.5772/intechopen.82615

#### Figure 8. Scheme of the measuring system. Took from [19].


#### Table 1.

it. The amount of sound energy which is absorbed is described as the ratio of sound energy absorbed to the sound energy incident and is termed the sound absorption coefficient α. The average of the five measurements was shown. The nanofiber layer was set at a distance of 30 mm from the reflective wall so that the nanofibrous membrane was able to vibrate under the incident sound wave as it is demonstrated

The optical method for determining the resonance frequencies of the membranes [19] was used to calculate the velocity of transverse wave on the homogeneous circular membrane CM. The main components of the system were the digital camera (Olympus—System i-SPEED2), a LCD display panel of 8.4″, and a transparent tube (see Figure 8). The test sample was fixed inside the tube. The incident plane sinusoidal sound wave was excited by a speaker located at end of the tube. The membrane began to oscillate after the impact sound waves reached, and its movement was picked by the high-speed digital camera and in turn was displayed

In order to determine the resonant frequency of the membrane, the 1-1500 Hz frequency range was studied by taking measurements at every 20 Hz to obtain a rough estimate of the resonant frequency. The deflection size of the nanofibrous membrane under the frequency range of 1–1500 Hz was measured using the closed tube. The resonant frequencies of the circular membrane of radius 0.05 m and 1gm<sup>2</sup> basis weight have been detected as can be seen in Table 1. The velocity of transverse wave on the homogeneous circular membrane CM has been determined by the relationship Eq. (2) based on the measured first resonant frequency f0,1 equal

2.3.4 Optical method for determination of resonant frequency

Illustration of the deflection of vibrating membrane inside the meshes of a grid.

on Figure 7.

Acoustics of Materials

on the LCD.

to 90 Hz.

Figure 7.

30

Calculation of the velocity of transverse wave on the membrane CM based on measured resonant frequency of vibrating circular membrane of radius 0.05 m and 1 g m<sup>2</sup> basis weight (a).
