Frequency Distribution of Sound Intensity in Train A

Based on the problem setup and the principles of the Doppler effect:

1. Relative Motion Between Source and Observer:
   The whistle (sound source) is mounted on train A, and the passengers observing the sound are also in train A. Therefore, there is no relative motion between the source and these observers:
   $v_{\text{source}} = v_{\text{observer}}$

2. Absence of Doppler Shift:
   Since the source of sound and the passengers in train A are at rest relative to each other, no Doppler frequency shift occurs for any emitted frequency.

3. Frequency Distribution:
   If the whistle emits a continuous distribution of sound frequencies with uniform intensity between the bounds $f_1$ and $f_2$, the observed frequency range will remain completely unchanged. That is, the sound intensity begins precisely at $f_1$ and ends precisely at $f_2$.

Examining the given plots of Intensity versus frequency:

• In (A), the rectangular pulse of intensity starts sharply at $f_1$ and terminates at $f_2$, representing zero frequency shift.
• In (B), the frequencies are shifted to lower values.
• In (C), the frequencies are shifted to higher values.
• In (D), the frequency bandwidth is stretched.

Thus, the observed intensity distribution in train A is correctly depicted in (A).