## 3 Results and Discussion  
The results obtained from the different cases are presented in this section. For case 1 (Figure 1), the speaker was used to play sine tones of different frequencies to generate acoustic vibrations. The time-dependent response of the wavelength shift of the FBG was recorded with the MOI. Figure 5 shows the FFT of the wavelength shift data. In this case, the frequencies of 50 Hz, 80 Hz and 110 Hz were swept one after the other after using the speaker for different periods of time. The difference in the number of samples results in different magnitudes although all three frequencies are detected. Figure 4: Experimental configuration with beam bearing the FBG placed on a thin metal plate. The plate was simply supported along two edges. Speaker was placed at a distance of more than 10 cm away from the beam. The schematic shows that the sensing beam 2 is placed on the metal plate without any fasteners and the speaker is also placed on the plate. Figure 3: Experimental configuration with sensing beam moved closer to the acoustic source. The schematic shows positions A and B.  
Figure 2: The schematic shows phone replacing the speaker, with top end of sensing beam lightly taped and bottom end allowed to oscillate. The sensing beam 2 was made to oscillate by tapping. The sensing beam oscillation is negligible in comparison throughout the three-frequency sweep, which is shown as the small peak under 10 Hz. Due to the experimental arrangement and flexibility of the beam 2, the ends are touching the table. However, the FBG detects the forced vibrations. Figure 6 shows the time-dependent oscillation of the sensing beam with the pulsed vibrations that are superposed. The oscillation was generated by gentle tapping of the free end of beam 2 (Figure 2). In this case (case 2), the wedge end had a phone vibrating in beeps. The vibration was automatically superposed on the cantilever oscillation although there was a gap of several cm on beam 1. The vibration was applied in pulses due to the pattern of beeps selected as the cantilever was oscillating. When the cantilever oscillates at its natural frequency, the vibration is at frequencies of around 7-15 Hz, which depends on the length of the beam that is unconstrained. However, the superposed phone vibration is around 150 Hz. The forced vibration is detected by the sensor although it occurs together with the low frequency oscillation. The phone vibration was identified separately with a National Instruments (NI, Austin, TX, USA) accelerometer connected to NI SignalExpress system (2012). The PSD (power spectrum distribution) showed that the peak frequency of the vibration beeps was near 150 Hz. Figure 5: FFT (Fast Fourier Transform) data of consecutively swept frequencies at 50 Hz, 80 Hz and 110 Hz with random number of samples. Small peak observed near 7 Hz due to natural oscillations. Figure 6: Time varying data of central wavelength of FBG, showing that the damped oscillation of the sensing beam behaves as a cantilever. The pulsed vibrations from the phone are superposed as periodic high frequency waves. The x-axis scale is in samples of time (ms). Figure 7 shows the FFT of the time-domain signal that is plotted in Figure 6. In this case, the relative magnitude of the low frequency peak due to oscillation is higher than the forced vibration at 150 Hz (phone vibration). However, when the cantilever oscillation dies down and the pulsed vibration of the phone continues (Figure 8), the FFT data shows that the 150 Hz peak from the phone is the dominant peak (Figure 9). The section of the time spectrum that is selected in Figure 8 is the part where the phone vibration is dominant. Due to the low stiffness of the sensing beam, the high frequency vibrations are measured although there is no obvious or visible oscillation of the sensing beam. Figure 8: Time varying data of central wavelength position of FBG where the phone vibration is dominant. There was no oscillation and the sensing beam appeared to be static.