Respuesta :
Answer:
The speed of the train is 7.75 m/s towards station.
The speed of the train is 8.12 m/s away from the station.
Explanation:
Given that,
Frequency of the whistles f= 175 Hz
Beat frequency [tex]\Delta f= 4.05 Hz[/tex]
Speed of observer = 0
We need to calculate the frequency
Using formula of beat frequency
[tex]\Delta f=f'-f[/tex]
[tex]f'=\Delta f+f[/tex]
[tex]f'=4.05+175[/tex]
[tex]f'=179.05\ Hz[/tex]
When the train moving towards station, then the frequency heard is more than the actual
Using Doppler effect
[tex]f'=f(\dfrac{v-v_{o}}{v-v_{s}})[/tex]
[tex]v=v-\dfrac{vf}{f'}[/tex]
Put the value into the formula
[tex]v=343-\dfrac{343\times175}{179.05}[/tex]
[tex]v=7.75\ m/s[/tex]
The speed of the train is 7.75 m/s towards station.
When the train moving away form the station
Again beat frequency
[tex]\Delta f=f-f'[/tex]
[tex]f'=f-\Delta [/tex]
[tex]f'=175-4.05[/tex]
[tex]f'=170.95\ Hz[/tex]
We need to calculate the speed
Using Doppler effect
[tex]f'=f(\dfrac{v-v_{o}}{v+v_{s}})[/tex]
[tex]v=\dfrac{vf}{f'}-v[/tex]
Put the value into the formula
[tex]v=\dfrac{343\times175}{170.95}-343[/tex]
[tex]v=8.12\ m/s[/tex]
The speed of the train is 8.12 m/s away from the station.
Hence, This is the required solution.
