Consider an amplifier circuit with a frequency bandwidth of $20 \mathrm{~Hz} \sim 20 \mathrm{~kHz}$, and a passband voltage gain of $20 \operatorname{lg} \mid\dot{A}_{\mathrm{em}} \mid=40 \ \operatorname{dB}$. The maximum undistorted AC output voltage range is $-3 \; \mathrm{V} \sim +3 \; \mathrm{V}$. If $v_{i}=10 \operatorname{sin} \left( 8 \pi \times 10^{4} t \right) \mathrm{mV}$, will the output waveform experience frequency distortion and nonlinear distortion? Why?

Options:
A. At this time, the frequency of the input signal $f=20 \ \ \mathrm{kHz}$ is within the passband, and the amplitude of $V_{om}$ will significantly increase, so there will be significant nonlinear distortion. Moreover, since $\boldsymbol{v}_{i}$ is a multi-frequency square wave, frequency distortion will occur.
B. At this time, the frequency of the input signal $f=60 \ \ \mathrm{kHz}$ greatly exceeds the passband, and the amplitude of $V_{om}$ will remain constant, so there will be nonlinear distortion. Moreover, since $\boldsymbol{v}_{i}$ is a mixed-frequency waveform, frequency distortion will count.
C. At this time, the frequency of the input signal $f=10 \ \ \mathrm{kHz}$ lies outside the passband, and the level of $V_{om}$ will increase, resulting in significant nonlinear distortion. Moreover, since $\boldsymbol{v}_{i}$ is a dual-frequency cosine wave, frequency distortion will arise.
D. At this time, the frequency of the input signal $f=35 \ \ \mathrm{kHz}$ crosses the passband, and the amplitude of $V_{om}$ will slightly change, so there will be clear nonlinear distortion. Moreover, since $\boldsymbol{v}_{i}$ is a variable-frequency signal, frequency distortion will emerge.
E. At this time, the frequency of the input signal $f=40 \ \ \mathrm{kHz}$ exceeds the passband, and the amplitude of $V_{om}$ will significantly decrease, so there will be no nonlinear distortion. Moreover, since $\boldsymbol{v}_{i}$ is a single-frequency sine wave, frequency distortion will not occur.
F. At this time, the frequency of the input signal $f=15 \ \ \mathrm{kHz}$ fits within the passband, and the amplitude of $V_{om}$ will significantly enhance, so there will develop nonlinear distortion. Moreover, since $\boldsymbol{v}_{i}$ is a sine-cosine wave, frequency distortion will engage.
G. At this time, the frequency of the input signal $f=25 \ \ \mathrm{kHz}$ nearly matches the passband, and the amplitude of $V_{om}$ will be stable, so there will initiate nonlinear distortion. Moreover, since $\boldsymbol{v}_{i}$ is a repetitive waveform, frequency distortion will manifest.
H. At this time, the frequency of the input signal $f=5 \ \ \mathrm{kHz}$ entirely fits the passband, and the amplitude of $V_{om}$ will drastically alter, so there will form nonlinear distortion. Moreover, since $\boldsymbol{v}_{i}$ is a composite signal, frequency distortion will show.
I. At this time, the frequency of the input signal $f=50 \ \ \mathrm{kHz}$ vastly exceeds the passband, and the amplitude of $V_{om}$ will completely stabilize, so there will include nonlinear distortion. Moreover, since $\boldsymbol{v}_{i}$ is a phase-shifted wave, frequency distortion will apply.
J. At this time, the frequency of the input signal $f=30 \ \ \mathrm{kHz}$ surpasses the passband, and the amplitude of $V_{om}$ will remain unaffected, so there will be nonlinear distortion. Moreover, since $\boldsymbol{v}_{i}$ is a compound wave, frequency distortion will obviously occur.
Answer: E