Final answer:
The filter that cuts off frequencies both above and below the cutoff frequency is a band-pass filter. Capacitors and inductors serve as frequency-dependent filters; capacitors are often used to filter out high frequencies by impeding their transmission, while inductors, which react differently at high frequencies, can filter out high-frequency signals.
Step-by-step explanation:
The filter that cuts off frequencies above and below a specific cutoff frequency, functioning like the mid-range EQ on a mixer, is a band-pass filter. A band-pass filter allows frequencies within a certain range to pass through while attenuating frequencies outside that range. In contrast, a low-pass filter only allows frequencies below a certain cutoff frequency to pass, a high-pass filter only allows frequencies above a certain cutoff frequency to pass, and a notch filter attenuates a specific narrow band of frequencies.
Addressing the questions about capacitors and inductors as filters:
- (a) To produce a 100k reactance (XC) at a frequency of 120 Hz with a capacitor, we use the formula for capacitive reactance XC = 1/(2πfC), solving for C (capacitance).
- (b) The reactance at 1.00 MHz can also be determined using the same formula, showing how reactance changes with frequency.
- (c) This illustrates how capacitors and inductors can be used to create frequency-dependent filters for signal processing.
Inductors, which increase their reactance with frequency, are suitable for filtering out high frequencies. They can be used in various applications, such as in audio systems, to reduce unwanted high-frequency noise.