Magnetic induction is used to provide real-time amplifi cation to hearing-impaired audience members. The system taps into the amplifi cation system already in place in the room and routes the amplifi ed electric waveforms from the speaker’s microphone into two wire loops around the perimeter of the audience. (Figure P22.82 shows only one of these loops.) The bottom loop is at fl oor level, and the top loop is near the ceiling. The changing current in the loop induces changes in magnetic fl ux, which induces currents in smaller loops worn by audience members sitting within the main loop (photo), where the signal is then amplified and provided to headphones or earpieces.
(a) What is the inductance of two loops, separated by 2.5 m, that fi ts the perimeter of a rectangular room 7.0 m wide by 15 m long? (Approximate it as a solenoid.)
(b) The frequency of sound from speaking ranges from approximately 500 Hz to 4 kHz. Since the system should be sensitive to this range, what capacitance would give this system a resonant frequency of 2000 Hz? The expression for the inductance of a solenoid was derived in Chapter 20 (Eq. 21.21).

Transcribed Image Text:

Loudspeaker Audio amplifier - Wire loop Receiver Hearing-impaired listener Normal listener