Respuesta :
Answer:
The source speed toward the station and away from the station are 3.79 m/s and 3.87 m/s.
Explanation:
Given that,
Frequency of the whistles f = 1.80\times10^{2}\ Hz[/tex]
Beat frequency = 2.00 b/s
We need to calculate the frequency
Using formula of beat frequency
[tex]\Delta f=f'-f[/tex]
[tex]f'=\delta f+f[/tex]
Put the value into the formula
[tex]f'=2.00+180[/tex]
[tex]f'=182.0\ Hz[/tex]
When the train moving towards station, then the frequency heard is more than the actual
We need to calculate the source speed
Using Doppler effect
[tex]f'=f(\dfrac{v}{v-v_{s}})[/tex]
[tex]v-v_{s}=(\dfrac{f}{f'})v[/tex]
Therefore, the source speed is
[tex]v_{s}=v-v\dfrac{f}{f'}[/tex]
Put the value into the formula
[tex]v_{s}=345-345\times\dfrac{180}{182}[/tex]
[tex]v_{s}=3.79\ m/s[/tex]
When the train moving away from the station, then the frequency heard is
Again from beat frequency,
[tex]\Delta f=f-f'[/tex]
[tex]f'=\Delta f-f[/tex]
Put the value into the formula
[tex]f'=180-2[/tex]
[tex]f'=178\ Hz[/tex]
We need to calculate the source speed
Using Doppler effect
[tex]f'=f(\dfrac{v}{v+v_{s}})[/tex]
[tex]v+v_{s}=(\dfrac{f}{f'})v[/tex]
Therefore, the source speed is
[tex]v_{s}=v\dfrac{f}{f'}-v[/tex]
Put the value into the formula
[tex]v_{s}=345\times\dfrac{180}{178}-345[/tex]
[tex]v_{s}=3.87\ m/s[/tex]
Hence, The source speed toward the station and away from the station are 3.79 m/s and 3.87 m/s.
