Answer :
The Problem is based on the concept of Doppler's Effect. The formula for the Stationary observer and moving source is to be used. The provided value of velocity of source is to be converted in standard unit and then all the provided values are to be substituted into the formula to calculate the observed frequency for the person standing in front of the car beside the road. This is to be repeated for the Person standing behind the car. The Doppler effect can be defined as the change of the wavelength of the observer and the origin. Mathematically can be described as,
[tex]f_0 = (\frac{v+v_0}{v-v_s})f_s[/tex]
Here
[tex]f_0[/tex] = Frequency observed by observer
[tex]v[/tex] = Velocity of sound
[tex]v_0[/tex] = Velocity of Observer
[tex]v_s[/tex] = Velocity of source
[tex]f_s[/tex] = Frequency of source
PART A) Observer is not moving so; its velocity will be zero. Consider the provided velocity and the velocity of the observer velocity and the frequency of the source to find the frequency of the observer. The frequency of the observer is
[tex]f_0 = \frac{340+0}{340-25}(400)[/tex]
[tex]f_0 = 431.74 Hz[/tex]
Therefore the observed frequency is 431.74Hz
PART B) Source is not moving, so, its velocity will be zero. Remaining quantities are known so the value of the frequency of the observer can be calculated as,
[tex]f_0 = \frac{v+v_0}{v-vs}[/tex]
Now the listener is friend and the observer earlier is source
[tex]f_0 = \frac{340+25}{340+0}(400)[/tex]
[tex]f_0 = 429.41Hz[/tex]
Therefore the frequency is 429.41Hz