A two-way loudspeaker box contains a woofer and a tweeter

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electronics, Instrumentation & Communication · Circuit foundations and passive networks

Electricity, Magnetism and Electromagnetism, Ch AC circuits: phasors, complex impedance, resonance and power

Problem

A two-way loudspeaker box contains a woofer and a tweeter. Over the range of interest each driver behaves as a pure resistance of

6.0\,\Omega

. The crossover is to be first order and is to hand over at

f_c = 3.0\,\mathrm{kHz}

: an ideal lossless coil is put in series with the woofer, and an ideal lossless capacitor in series with the tweeter, each reactive element chosen so that its reactance equals

6.0\,\Omega

f_c

, which is where the voltage across its driver has fallen to

1/\sqrt{2}

of the source amplitude. The amplifier is an ideal sinusoidal voltage source of zero output impedance. ((a)) Find the inductance

L

of the coil. ((b)) Find the capacitance

C

of the capacitor. ((c)) A technician wires the box wrongly, putting both the coil and the capacitor in series with the woofer alone (the tweeter is left disconnected). Find the resonant frequency of that series loop. ((d)) Find the quality factor

Q_{\mathrm{f}}

of that loop.

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