Bnibling/Acoustic Lab

Harmonics

Barrett Nibling

November 6th, 2007

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Procedure

Schematic of Harmonics Apparatus

Results

Helium, d=1/600mm, m=1

Color	θdiff (degrees)	λ (nm)	Error (nm)	Published λ (nm)
Purple	15.6	448.0	$\pm$2.0	447.148
Teal	16.4	470.3	$\pm$2.0	471.314
Green	17.2	492.6	$\pm$2.0	492.193
Green	17.5	500.9	$\pm$2.0	501.567
Yellow//Orange	20.7	588.8	$\pm$2.0	587.562
Red	23.6	666.9	$\pm$2.0	667.815
Dim Red	25.1	706.7	$\pm$1.9	???

Error Analysis

$\frac{\delta \lambda}{\delta \theta_{i}}=\frac{d}{m}Cos(\theta_{i}) Sin({\delta \theta_{i}}).$

Then the total error is the sum of the two partial derivatives added in quadrature,

$\delta \lambda=\frac{d}{m} \sqrt{(\frac{\delta \lambda}{\delta \theta_{i}})^{2}+(\frac{\delta \lambda}{\delta \theta_{d}})^{2}}.$

References

[1]

[2]