Lp. | l1 | l3 | l3 – l1 | λśr ± u(λśr) | T±(u(T)) | vT ±(u(vT)) | f ± u(f) | fgen. |
---|---|---|---|---|---|---|---|---|
[m] | [m] | [m] | [m] | [ K ] | [ m/s ] | [ Hz ] | [ Hz ] | |
1. | 0,103 | 0,512 | 0,409 | 0,411±0,002 | 293±0,58 | 332,71±0,36 | 809,51± | 800,1±5 |
2. | 0,104 | 0,519 | 0,415 | |||||
3. | 0,101 | 0,509 | 0,408 | |||||
4. | 0,106 | 0,524 | 0,418 | |||||
5. | 0,103 | 0,513 | 0,41 | |||||
6. | 0,102 | 0,51 | 0,408 | |||||
7. | 0,101 | 0,512 | 0,411 | |||||
8. | 0,1 | 0,508 | 0,408 | |||||
9. | 0,105 | 0,519 | 0,414 | |||||
10. | 0,102 | 0,511 | 0,409 |
III. Obliczenia i rachunek błędu
a) obliczenia
T=293K
VT=V0$\sqrt{1 + 0,004(T - T_{0}})$
VT=$331,4\sqrt{1 + 0,0004(293 - 273,16}$) ≅ 332,71[m/s]
λsr=$\frac{1}{n}\sum_{k = 1}^{n}\lambda_{k}$=$\frac{\lambda_{1 +}\lambda_{2 +}\lambda_{10}}{10} \cong$ 0,411[m]
f=$\frac{V_{T}}{\lambda}$=$\frac{332,71}{0,411} \cong$ 809,51[Hz]
b) rachunek błędu
Przyjęto
ΔT=1
Δl=0,01[m]
u(λśr)=$\sqrt{\frac{\sum_{k = 1}^{10}{(\lambda_{k -}\lambda_{sr})^{2}}}{n(n - 1)}}\ \cong$ 0,002[m]
u(T)=$\frac{wartosc\ dzialki\ elementarnej}{\sqrt{3}}\ $= $\frac{1}{\sqrt{3}} \cong$0,58
u(vT)=$\left\lbrack \frac{\partial V_{T}}{\partial T} \right\rbrack$*u(T)=$\left\lbrack \frac{V_{T}*\frac{1}{2}*0,004}{1 + 0,004({T - T}_{0})} \right\rbrack$*u(T)=$\left\lbrack \frac{331,4*\frac{1}{2}*0,004}{1 + 0,004*19,84} \right\rbrack$*0,58≅0,36$\frac{m}{s}$
u(f)=$\sqrt{\left( \frac{\partial f}{\partial\lambda} \right)^{2}*u(\lambda)^{2} + \left( \frac{\partial f}{\partial V_{T}} \right)*u(V_{T})^{2}} =$
$= \sqrt{\left( \frac{V_{T}}{\lambda^{2}} \right)^{2}*u(\lambda)^{2} + \frac{1}{\lambda^{2}}*u(V_{T})^{2}}$=$\sqrt{\left( \frac{332,71}{{0,411}^{2}} \right)^{2}*0,002 + \frac{1}{{0,411}^{2}}*0,36^{2}} \cong$2,14[Hz]