Final answer:
A first-order low-pass filter is used to attenuate noise with frequencies higher than 26 kHz. The largest cutoff frequency to achieve -20 dB attenuation is 2.6 kHz.
Step-by-step explanation:
A first-order low-pass filter is used to attenuate noise with frequencies higher than 26 kHz, and the goal is to achieve a -20 dB attenuation. The cutoff frequency is the frequency at which the filter starts attenuating the signal significantly. In this case, we need to find the largest cutoff frequency that will give us -20 dB attenuation.
The attenuation in a first-order low-pass filter can be calculated using the formula:
Attenuation (in dB) = 20 log10(f_cutoff / f_signal)
Where f_cutoff is the cutoff frequency and f_signal is the frequency of the noise we want to attenuate. Rearranging the formula, we get:
f_cutoff = f_signal * 10^(-Attenuation/20)
Substituting the given values, we have:
f_signal = 26 kHz, Attenuation = 20 dB
Calculating f_cutoff:
f_cutoff = (26 kHz) * 10^(-20/20)
= 26 kHz * 0.1
= 2.6 kHz
Therefore, the largest cutoff frequency to achieve -20 dB attenuation is 2.6 kHz.