Two trains `A and B` moving with speeds `20m//s` and `30m//s` respectively in the same direction on the same straight track, with `B` ahead of `A`. The engines are at the front ends. The engine of train `A` blows a long whistle.
Assume that the sound of the whistle is composed of components varying in frequency from `f_(1) = 800 Hz` to `f_(2) = 1120 Hz`, as shown in the figure. the spread in the frequency (highest frequency - lowest frequency) is thus `320 Hz`. the speed of sound in still air is `340 m//s`.
(5) The distribution of the sound intensity of the whistle as observed by the passengers in train `A` is best represented by

Options

A.
B.
C.
D.

Explanation

To solve the problem step by step, we need to analyze the situation involving two trains and the sound emitted by train A's whistle.

### Step 1: Understand the scenario
We have two trains A and B moving in the same direction. Train A is moving at 20 m/s and train B at 30 m/s. The engine of train A blows a whistle that produces a sound with frequencies ranging from \( f_1 = 800 \, \text{Hz} \) to \( f_2 = 1120 \, \text{Hz} \).

### Step 2: Determine the speed of sound relative to the trains
The speed of sound in still air is given as \( v = 340 \, \text{m/s} \). Since both trains are moving in the same direction, we need to find the effective speed of sound relative to train A.

### Step 3: Calculate the frequency heard by passengers in train A
The passengers in train A are moving at the same speed as the sound emitted from the whistle. The frequency of the sound heard by the passengers can be calculated using the Doppler effect formula. However, since the passengers are moving with the same speed as train A, they will perceive the frequency as it is emitted, without any Doppler shift.

### Step 4: Analyze the frequency distribution
The frequency of the whistle varies from \( f_1 = 800 \, \text{Hz} \) to \( f_2 = 1120 \, \text{Hz} \). The spread in frequency is:
\[ \Delta f = f_2 - f_1 = 1120 \, \text{Hz} - 800 \, \text{Hz} = 320 \, \text{Hz} \]

### Step 5: Determine the sound intensity distribution
Since the passengers in train A are moving at a constant speed, they will perceive the sound intensity of the whistle as uniform across the frequency range. This means that the intensity of the sound does not change with frequency for the passengers in train A.

### Step 6: Conclusion
The distribution of sound intensity of the whistle as observed by the passengers in train A is best represented by a uniform distribution. This means that the intensity remains constant across the frequency range from \( f_1 \) to \( f_2 \).

### Final Answer
The distribution of the sound intensity of the whistle as observed by the passengers in train A is uniform.

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