The problem is attached as word document file with all mathematical expressions and pic.

Problem:

For continuous wave Doppler ultrasound the transmitting and receiving
transducers are usually mounted next to each other i.e. with
approximately zero angular separation. However, it is possible to have
the transmitter and receiver at different angles to the vessel. Use the
configuration shown below to derive the Doppler frequency as a
function of:
a) The angle between the transducers
b) The angle the transducers make with the flow vector.
What combination of values of   and  produce the largest Doppler
frequency, what values the smallest?

Set   equal to . For what range of values of   does the Doppler
frequency exceed 90% of the maximum Doppler frequency.