Final answer:
To match an amplifier with 500 Ω output impedance to a low-impedance speaker, a transformer with a turns ratio based on the square root of the impedance ratio is used.
Step-by-step explanation:
To address the mismatch between an audio amplifier with an output impedance of 500 Ω and a low-impedance loudspeaker rated at 8 - 22 Ω, a transformer must be used to match the impedances properly. The turns ratio of the transformer is crucial in this process and is calculated based on the square root of the impedance ratio. As such, the transformer turns ratio (τ) can be found using the formula τ = √(Z_{secondary} / Z_{primary}), where Z_{primary} is 500 Ω and Z_{secondary} represents the speaker impedance. Should the speaker impedance be 8 Ω, the turns ratio would be τ = √(8 Ω / 500 Ω).