Answer:
The beat frequency is [tex]\Delta f = 0.0011[/tex]
Explanation:
From this question we are given that
The velocity blood flow is [tex]v = 0.32 m/s[/tex]
The velocity of the wave is [tex]v_w = 1.54*10^3 m/s[/tex]
The frequency of the ultrasound is [tex]f= 4.30MHz[/tex]
During the time it is been directed along flow the blood cell is moving away frequency of the ultrasound wave(f) hence we are going to employ the Doppler's effect to obtain the frequency
[tex]f' = \frac{v_w-v}{v_w} f[/tex]
[tex]= \frac{1.540 *10^3 -0.32}{1.540*1063} *4.30MHz = 4.2991MHz[/tex]
When the red blood cell reflects the wave in this case the source of the wave is the blood cells and its frequency([tex]f'[/tex]) is moving away from the observer (blood cells) and this case the Doppler's effect is mathematically given as
[tex]f'' = \frac{v_w}{(v_w +v)}f[/tex]
[tex]= \frac{v_w}{v_w +v} *\frac{(v_w - v)}{v}f[/tex]
[tex]= \frac{(v_w - v)}{v_w+v }f[/tex]
[tex]= \frac{(1.540*10^3 -0.32)}{.54*10^3 + 0.32 } *4.30MHz[/tex]
[tex]=4.2982 MHz[/tex]
The beat frequency is mathematically represented as
[tex]\Delta f = f'' -f' = 4.2991 - 4.2982[/tex]
[tex]=0.0011MHz[/tex]
