Bnibling/Acoustic Lab

Harmonics

Barrett Nibling

December 4th, 2007

---

Abstract

This experiment dealt with the unique frequency patterns, known as harmonics, that sound produces in a resonator. Using white noise generated by a computer and transmitted through a speaker into our resonant cavity, a pipe, and at the other end was placed a microphone to record the outgoing frequencies. Using the geometry of the pipe and derived equations, theoretical values were calculated were calculated and compared to the measured values. The experimental data was within <insert %>% of the theoretical data.

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]