# Dan's Wiki test page

distance (cm) $\displaystyle \theta\$ (degrees) expected $\displaystyle \omega_b \ (kHz)$ measured $\displaystyle \omega_b \ (kHz)$
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

$\displaystyle \omega_b=\mid\omega_1-\omega_2\mid \$

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

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

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

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

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

$\displaystyle \theta\$

$\displaystyle \phi \$

$\displaystyle \omega_b=cos(\theta)* \$

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

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

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

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

$\displaystyle V_\amalg \$

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

$\displaystyle V_\perp \$

### next

MIDDLE!

V=9.4 Volts

time Volume Filled (mL) $\displaystyle \frac{dVol}{dt} (mL/s)\$ velocity (m/s) Single Shift Expected $\displaystyle \omega_b \ (kHz)$
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