Dan's Wiki test page

distance (cm)	[math]\displaystyle{ \theta\ }[/math] (degrees)	expected [math]\displaystyle{ \omega_b \ (kHz) }[/math]	measured [math]\displaystyle{ \omega_b \ (kHz) }[/math]
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

[math]\displaystyle{ \omega_b=\mid\omega_1-\omega_2\mid \ }[/math]

[math]\displaystyle{ \omega_1 \ }[/math] is the frequency before the Doppler shift

[math]\displaystyle{ \omega_2 \ }[/math] is the frequency after the Doppler shift

[math]\displaystyle{ \omega_1=\frac{c}{\lambda} \ }[/math]

[math]\displaystyle{ f_d=\frac{c}{\lambda}-\frac{V_r}{\lambda} \ }[/math]

[math]\displaystyle{ V_\amalg=sin(\theta)\omega r \ }[/math]

[math]\displaystyle{ \omega_b=\frac{sin(\theta)\omega r }{\lambda} \ }[/math]

[math]\displaystyle{ \theta\ }[/math]

[math]\displaystyle{ \phi \ }[/math]

[math]\displaystyle{ \omega_b=cos(\theta)* \ }[/math]

[math]\displaystyle{ cos(\theta-\frac{\pi}{2})=sin(\theta) \ }[/math]

[math]\displaystyle{ \omega_1=\frac{c}{\lambda}-\frac{cos(\theta)\omega r}{\lambda} \ }[/math]

[math]\displaystyle{ \omega_2=\frac{c}{\lambda} \ }[/math]

[math]\displaystyle{ \omega_b=\frac{\omega r}{\lambda}(cos(\theta)) \ }[/math]

[math]\displaystyle{ V_\amalg \ }[/math]

[math]\displaystyle{ \frac{dVol}{dt}=A v \ }[/math]

[math]\displaystyle{ V_\perp \ }[/math]

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

Navigation menu