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distance (cm)  \theta\ (degrees) expected  \omega_b  \ (kHz) measured  \omega_b  \ (kHz)
0 0 0 0
.74 5 24.5 ± 2.235 53
1.48 10 48.8 ± 2.235 73
2.20 15 72.8 ± 2.235 95
2.91 20 96.2 ± 2.235 121
3.59 25 118.9 ± 2.235 140
4.25 30 140.6 ± 2.235 188
4.88 35 161.33 ± 2.235 188
5.46 40 180.8 ± 2.235 226
6.01 45 198.9 ± 2.235 226
6.96 50 215.5 ± 2.235 249
7.36 55 230.4 ± 2.235 264
7.70 60 243.9.66 ± 2.235 270

 \omega_b=\mid\omega_1-\omega_2\mid  \

 \omega_1 \ is the frequency before the Doppler shift
 \omega_2 \ is the frequency after the Doppler shift

 \omega_1=\frac{c}{\lambda}  \

 f_d=\frac{c}{\lambda}-\frac{V_r}{\lambda}  \

 V_\amalg=sin(\theta)\omega r  \

 \omega_b=\frac{sin(\theta)\omega r }{\lambda}  \

 \theta\

 \phi \

 \omega_b=cos(\theta)*  \

 cos(\theta-\frac{\pi}{2})=sin(\theta) \

 \omega_1=\frac{c}{\lambda}-\frac{cos(\theta)\omega r}{\lambda}  \

 \omega_2=\frac{c}{\lambda}  \

 \omega_b=\frac{\omega r}{\lambda}(cos(\theta))  \

 V_\amalg  \

 \frac{dVol}{dt}=A v \

 V_\perp  \


next

MIDDLE!

V=9.4 Volts

time Volume Filled (mL)  \frac{dVol}{dt} (mL/s)\ velocity (m/s) Single Shift Expected  \omega_b  \ (kHz)
11.86 200 16.8634 1.6863 689.72
13.67 240 17.5567 1.7557 718.08
12.9 210 16.9753 1.6975 694.30
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