声速的测定实验报告

驻波法测量
实验数据L/mm				波长λ/mm
L1	3.620	L7	28.920	\(\(\lambda_{1} = 2 \ast \frac{L7 - L1}{6} = 8.433\)\)
L2	7.495	L8	33.489	\(\(\lambda_{2} = 2 \ast \frac{L8 - L2}{6} = 8.665\)\)
L3	12.019	L9	37.890	\(\(\lambda_{3} = 2 \ast \frac{L9 - L3}{6} = 8.624\)\)
L4	16.728	L10	42.413	\(\(\lambda_{4} = 2 \ast \frac{L10 - L4}{6} = 8.562\)\)
L5	20.931	L11	46.886	\(\(\lambda_{5} = 2 \ast \frac{L11 - L5}{6} = 8.652\)\)
L6	25.176	L12	50.928	\(\(\lambda_{6} = 2 \ast \frac{L12 - L6}{6} = 8.584\)\)

f/kHz	39.76
t/℃	15.1

\[\overline{\lambda} = \frac{1}{6}\sum_{}^{}\lambda_{i} = 8.586\ mm\ \ \ \overline{v} = \overline{\lambda}*f = 341.399\ m/s\]

\[u_{\lambda A} = \sqrt{\frac{1}{n(n - 1)}\sum_{i = 1}^{n}{(x_{i} - \overline{x})}^{2}} = \sqrt{\frac{1}{6 \ast 5}\sum_{i = 1}^{6}{(\lambda_{i} - \overline{\lambda})}^{2}} = 0.0346\ mm\ \ \ u_{\lambda B} = \frac{\mathrm{\Delta} \ast f}{\sqrt{3}} = 0.0040\ mm\]

\[u_{\lambda} = \sqrt{{u_{\lambda A}}^{2} + {u_{\lambda B}}^{2}} = 0.0348\ mm\ \ \ u_{f} = 0.010\ kHz\ \ \ \ u_{v} = v\sqrt{{(\frac{u_{\lambda}}{\lambda})}^{2} + {(\frac{u_{f}}{f})}^{2}} = 1.386\ m/s\]

\[有：v = (341.399 \pm 1.386)\ m/s\]

\[\because v_{t} = 331.45 \ast \sqrt{1 + \frac{t}{275.15}} = 340.488\ m/s\ \ \ \therefore E = \frac{\left| v_{t} - \overline{v} \right|}{v_{t}} = \frac{|340.488 - 341.399|}{340.488} = 0.27\%\]

驻波法测量
实验数据L/mm				波长λ/mm
L1	4.842	L7	30.412	\(\(\lambda_{1} = 2 \ast \frac{L7 - L1}{6} = 8.523\)\)
L2	8.778	L8	34.781	\(\(\lambda_{2} = 2 \ast \frac{L8 - L2}{6} = 8.668\)\)
L3	13.106	L9	39.274	\(\(\lambda_{3} = 2 \ast \frac{L9 - L3}{6} = 8.723\)\)
L4	18.739	L10	43.250	\(\(\lambda_{4} = 2 \ast \frac{L10 - L4}{6} = 8.170\)\)
L5	21.821	L11	47.627	\(\(\lambda_{5} = 2 \ast \frac{L11 - L5}{6} = 8.602\)\)
L6	26.184	L12	52.284	\(\(\lambda_{6} = 2 \ast \frac{L12 - L6}{6} = 8.700\)\)

\[\overline{\lambda} = \frac{1}{6}\sum_{}^{}\lambda_{i} = 8.564\ mm\ \ \ \overline{v} = \overline{\lambda} \ast f = 340.518\ m/s\]

\[u_{\lambda A} = \sqrt{\frac{1}{n(n - 1)}\sum_{i = 1}^{n}{(x_{i} - \overline{x})}^{2}} = \sqrt{\frac{1}{6 \ast 5}\sum_{i = 1}^{6}{(\lambda_{i} - \overline{\lambda})}^{2}} = 0.0847\ mm\ \ \ u_{\lambda B} = \frac{\mathrm{\Delta} \ast f}{\sqrt{3}} = 0.0040\ mm\]

\[u_{\lambda} = \sqrt{{u_{\lambda A}}^{2} + {u_{\lambda B}}^{2}} = 0.0848\ mm\ \ \ u_{f} = 0.010\ kHz\ \ \ \ u_{v} = v\sqrt{{(\frac{u_{\lambda}}{\lambda})}^{2} + {(\frac{u_{f}}{f})}^{2}} = 3.373\ m/s\]

\[有：v = (340.518 \pm 3.373)\ m/s\]

\[同理：v_{t} = 340.488\ m/s\ \ \ \therefore E = \frac{\left| v_{t} - \overline{v} \right|}{v_{t}} = \frac{|340.488 - 340.518|}{340.488} = 0.01\%\]