Calculate the Velocity Difference Between Two Reflectors Moving Towards an Ultrasound Transducer
What is the velocity difference between two reflectors assumed to be moving directly towards an ultrasound transducer if the Doppler shifts are given?
The velocity difference between the two reflectors is 0.539 m/s.
Calculation of Velocity Difference:
The Doppler shift (fD) is given by the formula:
fD = 2vfr cosθ / c
Where: - fD is the Doppler shift, - v is the velocity of the reflector, - fr is the frequency of the reflected wave, - θ is the angle between the direction of the reflected wave and the direction of the incident wave, - c is the velocity of propagation of the wave. Assuming the reflectors are moving directly towards the transducer, θ = 0. Therefore, the velocity difference between the reflectors can be calculated. For Reflector 1:
v1 = (fD1 * c) / (2 * fr1)
v1 = (7000 Hz * 1540 m/s) / (2 * 5 MHz)
v1 = 1.078 m/s For Reflector 2:
v2 = (fD2 * c) / (2 * fr2)
v2 = (3500 Hz * 1540 m/s) / (2 * 5 MHz)
v2 = 0.539 m/s Therefore, the velocity difference between the two reflectors is:
v1 - v2 = 1.078 m/s - 0.539 m/s = 0.539 m/s
Hence, the velocity difference between the two reflectors is 0.539 m/s.