A client has given you an equivalent AC circuit of a sheet of glass. They need to find out how to break the glass with high frequency sound energy. The equivalent circuit contains an AC voltage source which replicates the input energy from the sound waves hitting the glass. The inductor and capacitor replicate the resonance characteristics of the glass and the resistor replicates the energy being converted by the glass as it vibrates. When the energy converted in the resistor is over 200J/s the glass can no longer support the vibration and shatters.

1. Find the resonant frequency of the glass

2. Find the magnitude of the voltage across the resistor required to break the glass at resonant frequency.

3. Find the magnitude of voltage source required to break the glass at resonant frequency.

4. Using voltage found above, find the gain in dB where gain = 20log(Vout/Vin) where Vout is across resistor vs. frequency for the points; 0.01 x wo, 0.1 x wo, wo, 10 x wo, 100 x wo (where wo is the resonant frequency).

5. The clients plan to use a sound generator that is only accurate to within 20% of the desired frequency.

(a) how much sound power do they need to be sure to break the glass?

(b) find the voltage magnitude and phase shift across each component source, inductor, capacitor and resistor at worst case scenario eg (20% away from the desired frequency).

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