Obtain the equation of frequency observed by moving observer and stationary source.

Explanation

When the observe is moving with velocity `v _(0)` towards the source and the source is at rest, we have to proceed in a different manner. We work in the reference frame of the moving observer. In this reference frame the source and medium are approaching at speed `v _(0)` and the speed with which the wave approaches is `v _(0) +v .` Following a similar procedure as in the previous case, we find that the time interval between the arrival of the first and the `(n+1) ^(th)` crests is,
`t _(n+1) -t_(1) = n T_(0) -(n v _(0) T_(0))/(v _(0) +v)`
To observer thus, measures the period of hte wave to be,
` T = (t _(n +1) -t _(1))/(n)`
`T_(0) (1- (v _(0))/(v _(0) + v)) = T _(0) ((v)/(v _(0) + v ))`
`= T _(0) ((1)/(v _(0) //v + 1))`
`= T _(0) (1 + (v _(0))/( v))`
giving,
`v = v _(0) [ 1 + (v _(0))/(v)]`
When observer moves toward stationary source then observed frequency is less than original frequency.
When observe moves away from stationary source then `v _(0)` should be used in place of `-v _(0)` in equation
`therefore` Frequency observed by observer,
`v =v _(0) [1- (v _(0))/(v)]`
Thus, frequency observed by observer will be greater than original frequency.