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Two trains A and B moving with speeds 20...

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`.
(4) The speed of sound of the whistle is

A

`340 m//s` for passengers in `A` and `310 m//s` for passengers in `B`

B

`360 m//s` for passengers in `A` and `310 m//s` for passengers in `B`

C

`310 m//s` for passengers in `A` and `360 m//s` for passengers in `B`

D

`340 m//s` for passengers in both the trains.

Text Solution

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The correct Answer is:
To solve the problem, we need to determine the speed of sound of the whistle as perceived by passengers in both trains A and B. ### Step-by-Step Solution: 1. **Identify the Given Information:** - Speed of Train A, \( v_A = 20 \, \text{m/s} \) - Speed of Train B, \( v_B = 30 \, \text{m/s} \) - Speed of sound in still air, \( v_s = 340 \, \text{m/s} \) 2. **Determine the Speed of Sound for Passengers in Train A:** - Since Train A is moving in the same direction as the sound, the speed of sound relative to passengers in Train A will be the speed of sound in still air plus the speed of Train A. \[ v_{sA} = v_s + v_A = 340 \, \text{m/s} + 20 \, \text{m/s} = 360 \, \text{m/s} \] 3. **Determine the Speed of Sound for Passengers in Train B:** - Train B is ahead of Train A and also moving in the same direction. Therefore, the speed of sound relative to passengers in Train B will be the speed of sound in still air minus the speed of Train B. \[ v_{sB} = v_s - v_B = 340 \, \text{m/s} - 30 \, \text{m/s} = 310 \, \text{m/s} \] 4. **Conclusion:** - The speed of sound for passengers in Train A is \( 360 \, \text{m/s} \). - The speed of sound for passengers in Train B is \( 310 \, \text{m/s} \). ### Final Answer: - The speed of sound of the whistle is \( 360 \, \text{m/s} \) for passengers in Train A and \( 310 \, \text{m/s} \) for passengers in Train B.
To solve the problem, we need to determine the speed of sound of the whistle as perceived by passengers in both trains A and B. ### Step-by-Step Solution: 1. **Identify the Given Information:** - Speed of Train A, \( v_A = 20 \, \text{m/s} \) - Speed of Train B, \( v_B = 30 \, \text{m/s} \) - Speed of sound in still air, \( v_s = 340 \, \text{m/s} \) ...
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