Answer:
No, duration is not the sole reason.
Explanation:
The frequency is reciprocal of time period, so we can calculate the frequency differences between the waves as, (The frequency will not match with the actual waves frequency, since here the time for observing the wave is different)
Δf₁ = 1/5 - 1/20 = 0.15 Hz
Δf₂ = 1/200 - 1/400 = 2.5 x 10⁻³ Hz
So, the person will be able to differentiate between the waves which are farther apart. The duration of the individual tones is also important, since as the duration of the tones decreases, the number of frequencies in the wave increases (Fourier Transform), whereas a longer duration tone, has lesser number of frequencies.
One more reason is that the 200 msec and 400 msec duration waves are in frequency region of 1-5 Hz which cannot be heard by Humans.