Bnibling/Acoustic Lab

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(New page: <center> '''Spectroscopy''' Barrett Nibling, Travis Nokes, Kurt Strovink November 6th, 2007 </center> ---- == Abstract == This experiment uses a diffraction grating and rotating eyepiec...)
 
(→Introduction)
 
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<center>
 
<center>
−
'''Spectroscopy'''
+
'''Harmonics'''
  
−
Barrett Nibling, Travis Nokes, Kurt Strovink
+
Barrett Nibling
  
−
November 6th, 2007
+
December 4th, 2007
 
</center>
 
</center>
 
----
 
----
 
== Abstract ==
 
== Abstract ==
  
−
This experiment uses a diffraction grating and rotating eyepiece to determine the emission spectrum of helium and sodium light sources, which are then compared to published values. The error present in the measurements is less than 1%, and published values agree with experimental results within that error.
+
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 1% of the theoretical data.
  
 
== List of Figures ==
 
== List of Figures ==
 +
[1] Schematic of Harmonics Apparatus
  
−
*Schematic of Spectroscopy Apparatus
+
[2]Measured Frequencies Compared to Theoretical Frequencies Graph
−
 
+
−
*Helium Spectrum Analysis (m=1)
+
−
 
+
−
*Helium Spectrum Analysis (m=2)
+
  
 
== Introduction ==
 
== Introduction ==
  
−
This experiment is a comparison of the calculated wavelength of light emitted by an excited gas with published values. The angle of diffraction is obtained from measurements along the Vernier scale as observed through a telescope with a mobile eyepiece. A diffraction grating is placed perpendicular to the path of the collimated beam, allowing for the spectral pattern of the source to be observed. Using this measured angle of diffraction and the given values for grating spacing and incident angle, the calculation of the wavelength of light is elementary. This angle is measured to within .1 degrees by the mobile lens apparatus. By comparing the experimental wavelength values for multiple orders of refraction to published wavelength values, the accuracy of these measurements can be determined.
+
Sound produces unique frequency patterns when travelling through a resonant cavity, such as a tube, known as harmonics. These patterns depend on the frequencies sent into the body, the material, but more importantly the geometry of the structure. A computer was used to produce sound waves in the form of white noise through a speaker into one end of the cavity and by placing a microphone recording the frequency patterns on the other end, we could record the data on the computer for analysis. The computer software represents the data as a plot and the patterns on a graph shows the resonant peaks which occurred in the cavity. These peaks can then be compared to expected peaks by using previously derived equations for the tubes we used. The derived peaks and the expected peaks were then compared and were found to agree within experimental error.
  
 
== Theory ==
 
== Theory ==
 +
When a sound wave of a specific frequency enters a cavity, such as a musical instrument, the cavity will absorb the energy of the wave and produce a standing wave pattern that matches the resonant frequency. This only occurs when the specific frequency of the waves entering the system are close to the frequency of the acoustic resonance of the cavity. These resonant frequencies are known as harmonics. Each system of this type will have an infinite number of harmonics. The lowest frequency harmonic is called the fundamental frequency. Each harmonic following is a nth multiple of the fundamental frequency, known as the nth harmonics.
  
−
A diffraction grating allows the observer to distinguish the various colors emitted from an excited gas. The grating consists of an evenly spaced 300 or 600 slit array, with a grating spacing of d. The principal intensity maxima occur where [1]:
+
The constraint that determines the harmonic frequencies is the system itself. In the case of a pipe, which was used for our experiment, the resonance depends mainly on the length of the pipe. Since the pipe is open at both ends, the following previously derived equation can be used to approximate the harmonic frequency,
  
 
<center>
 
<center>
 
<math>
 
<math>
−
Sin(\theta_{inc})+ Sin(\theta_{diff})=\frac{m \lambda}{d}
+
f = \frac{n v_s}{2 L},
−
</math>,
+
</math>
 
</center>
 
</center>
  
−
where m is an integer representing the order and <math>\lambda</math> is the wavelength of light.
+
where <math>n</math> is a positive constant integer, <math>v_s</math> is the speed of sound, and <math>L</math> is the length of the pipe. The speed of sound is given to be at 334 m/s[1]. This isn't the best equation that matches the model. The radius of the pipe effectively makes the pipe long, the bigger the radius, the more air the waves must travel through[2]. To account for this, the end correction factor of 0.6R, R being the radius of the pipe, must be implemented into the equation (1).  Giving the following new equation,
  
−
The arrangement of the apparatus indicates that <math>\theta_{inc} = 0</math>, confirmed with symmetry about 0 degrees, so the working equation simplifies to:
 
 
<center>
 
<center>
 
<math>
 
<math>
−
Sin(\theta_{diff})=\frac{m \lambda}{d}.
+
f = \frac{n v_s}{2(L+0.6R)}.
−
</math>
+
−
</center>
+
−
 
+
−
Solving for <math> \lambda </math> results in
+
−
 
+
−
<center>
+
−
<math>
+
−
\lambda = \frac{d Sin(\theta_{diff})}{m}.
+
 
</math>
 
</math>
 
</center>
 
</center>
  
−
This experimental wavelength is compared to published spectra to determine the accuracy of this experiment.
+
Calculations from this equation will than be compared with the data acquired from the microphone.
  
 
== Procedure ==
 
== Procedure ==
−
As shown below, a collimator is placed in front of the helium/sodium lamp, focusing the light into one beam.  One of the two (300/mm, 600/mm) diffraction gratings is positioned level with the light source and perpendicular to the axis of the beam.  A  telescope is positioned level with the observed beam.  When properly arranged, the light seen through the telescope is observed at 0º, as read on the Vernier scale goniometer.
 
  
−
The angle of the telescope eyepiece changes with reference to this 0º starting point as it is moved along the scale. This allows the observer to measure the angle at which the maxima occur for each color emitted. The location of each color band is measured and recorded.  The diffraction grating is exchanged and the measurements repeated for m = 1,2.
+
1. Log on the computer and start up Baudline
  
 +
2. Begin emitting white noise from the speaker
  
 +
3. Place one opening of the pipe in front of the speaker and place the microphone on the opposite opening as shown in the figure below
  
 +
<center>
 +
[[Image:Harmonics.jpg]]
 +
''Schematic of Harmonics Apparatus[3]
 +
</center>
  
 +
4. Save the data, making sure to substract the baseline from the white noise.
  
−
<center>
+
5. Analyze the data into a plot and observe the resonant peaks that occur.
−
[[Image:Spectroscopy2.jpg]]
+
−
''Schematic of Spectroscopy Apparatus</center>
+
  
 
== Results ==
 
== Results ==
 +
The following table and graph are the results acquired from a pipe of Length 38.3cm and Radius 13.4mm
  
−
=== Helium Results ===
 
−
The following tables and graphs are the results acquired from the Helium Spectroscopy. All published values are from [2].
 
  
−
The First Order Spectrum:
 
 
<center>
 
<center>
 
{| class="wikitable" border="1" style="text-align:center"
 
{| class="wikitable" border="1" style="text-align:center"
Line 76: Line 67:
 
|-
 
|-
  
−
|+ Helium, d=1/600mm, m=1
+
|+ Data Table for Pipe 1, L=38.3cm <math>\pm</math> .05cm and R=13.4mm <math>\pm</math> .05mm
  
−
! Color
+
! n
  
−
! <math>\theta_{diff}</math> (degrees)
+
! Theoretical Frequency (Hz)
  
−
! <math>\lambda</math> (nm)
+
! Theoretical Frequency
 +
with End Correction (Hz)
  
−
! Error (nm)
+
! Error  
 +
with End Correction (Hz)
  
−
! Published <math>\lambda</math> (nm)
+
! Measured Frequency (Hz)
  
 
|-
 
|-
−
 
−
| Purple
 
−
|15.6
 
−
|448.0
 
−
|<math>\pm</math>2.0
 
−
|447.148
 
  
 
|-
 
|-
−
| Teal
+
|1
−
|16.4
+
|436.0
−
|470.3
+
|427.1
−
|<math>\pm</math>2.0
+
|<math>\pm</math> 6.4
−
|471.314
+
|421.9
  
 
|-
 
|-
−
| Green
+
|2
−
|17.2
+
|872.1
−
|492.6
+
|854.1
−
|<math>\pm</math>2.0
+
|<math>\pm</math> 12.8
−
|492.193
+
|843.75
  
 
|-
 
|-
−
| Green
+
|3
−
|17.5
+
|1308.1
−
|500.9
+
|1281.2
−
|<math>\pm</math>2.0
+
|<math>\pm</math> 19.2
−
|501.567
+
|1283.2
  
 
|-
 
|-
−
| Yellow//Orange
+
|4
−
|20.7
+
|1744.1
−
|588.8
+
|1708.3
−
|<math>\pm</math>2.0
+
|<math>\pm</math> 25.7
−
|587.562
+
|1699.2
−
 
+
−
|-
+
−
| Red
+
−
|23.6
+
−
|666.9
+
−
|<math>\pm</math>2.0
+
−
|667.815
+
−
|
+
−
 
+
−
|-
+
−
| Dim Red
+
−
|25.1
+
−
|706.7
+
−
|<math>\pm</math>1.9
+
−
|???
+
 
|}
 
|}
−
</center>
 
  
−
[[Image:Hspec1.JPG]]
+
[[Image:Pipe1Graph.jpg ]]
  
−
The graph above is a comparision between the wavelength calculated using the working equation and the published values, with all values when the error bars.
+
''Measured Frequencies Compared to Theoretical Frequencies
−
 
+
−
The following is the first order spectrum of Helium using a 300mm grating
+
−
<center>
+
−
{| class="wikitable" border="1" style="text-align:center"
+
−
 
+
−
|-
+
−
 
+
−
|+ Helium, d=1/300mm, m=1
+
−
 
+
−
! Color
+
−
 
+
−
! <math>\theta_{diff}</math> (degrees)
+
−
 
+
−
! <math>\lambda</math> (nm)
+
−
 
+
−
! Error (nm)
+
−
 
+
−
! Published <math>\lambda</math> (nm)
+
−
 
+
−
|-
+
−
 
+
−
| Purple
+
−
|7.7
+
−
|446.4
+
−
|<math>\pm</math>4.1
+
−
|447.148
+
−
 
+
−
|-
+
−
| Teal
+
−
|8.1
+
−
|469.4
+
−
|<math>\pm</math>4.1
+
−
|471.314
+
−
 
+
−
|-
+
−
| Green
+
−
|8.5
+
−
|492.5
+
−
|<math>\pm</math>4.1
+
−
|492.193
+
−
 
+
−
|-
+
−
| Green
+
−
|8.6
+
−
|498.2
+
−
|<math>\pm</math>4.1
+
−
|501.567
+
−
 
+
−
|-
+
−
| Yellow//Orange
+
−
|10.2
+
−
|590.0
+
−
|<math>\pm</math>4.1
+
−
|587.562
+
−
 
+
−
|-
+
−
| Red
+
−
|11.5
+
−
|664.2
+
−
|<math>\pm</math>4.1
+
−
|667.815
+
−
|
+
−
 
+
−
|-
+
−
| Dim Red
+
−
|12.2
+
−
|704.0
+
−
|<math>\pm</math>4.1
+
−
|???
+
−
|}
+
 
</center>
 
</center>
 +
The following table is the data collected from a smaller pipe of Length  L = 18.2cm and Radius 24.55mm.
  
−
Due to the higher amount of error associated with the 300mm grating compared to the 600mm grating, about twice as much, we opted to discontinue any further data collection using the 300mm and stuck with the 600mm for the remainder of the lab.
 
−
 
−
 
−
The Second Order Spectrum:
 
 
<center>
 
<center>
 
{| class="wikitable" border="1" style="text-align:center"
 
{| class="wikitable" border="1" style="text-align:center"
Line 225: Line 123:
 
|-
 
|-
  
−
|+ Helium, d=1/600mm, m=2
+
|+ Data Table for Pipe 2, L=18.2cm <math>\pm</math> .05cm and R=24.55mm <math>\pm</math> .05mm
  
−
! Color
+
! n
  
−
! <math>\theta_{diff}</math> (degrees)
+
! Theoretical Frequency (Hz)
  
−
! <math>\lambda</math> (nm)
+
! Theoretical Frequency
 +
with End Correction (Hz)
  
−
! Error (nm)
+
! Error  
 +
with End Correction (Hz)
  
−
! Published <math>\lambda</math> (nm)
+
! Measured Frequency (Hz)
  
 
|-
 
|-
−
 
−
| Purple
 
−
|32.5
 
−
|447.5
 
−
|<math>\pm</math>.95
 
−
|447.148
 
−
 
−
|-
 
−
| Teal
 
−
|34.4
 
−
|470.6
 
−
|<math>\pm</math>.94
 
−
|471.314
 
  
 
|-
 
|-
−
| Green
+
|1
−
|36.4
+
|917.6
−
|491.6
+
|848.9
−
|<math>\pm</math>.94
+
|<math>\pm</math> 12.9
−
|492.193
+
|855.5
  
 
|-
 
|-
−
| Green
+
|2
−
|37.0
+
|1835.2
−
|501.3
+
|1697.8
−
|<math>\pm</math>.93
+
|<math>\pm</math> 25.8
−
|501.567
+
|1687.3
  
 
|-
 
|-
−
| Yellow//Orange
+
|3
−
|44.9
+
|2752.8
−
|588.0
+
|2546.6
−
|<math>\pm</math>.89
+
|<math>\pm</math> 38.7
−
|587.562
+
|2537.4
  
 
|-
 
|-
−
| Red
+
|4
−
|53.3
+
|3670.3
−
|667.9
+
|3395.5
−
|<math>\pm</math>.85
+
|<math>\pm</math> 51.6
−
|667.815
+
|3416.0
 
|}
 
|}
 
</center>
 
</center>
  
−
[[Image:Hspec2.jpg]]
+
=== Error Analysis ===
−
 
+
For the error analysis, there were three variables associated with error, L, R, and v. The following are the three partial errors for each variable,
−
In the second order domain, the error is about half of the error in the first order. Even so, all the values when compared to published values are within the error bars.
+
−
 
+
−
=== Sodium Results ===
+
−
The following tables are the result acquired from the Sodium Spectroscopy. Again, the published results are from reference [2].
+
−
 
+
−
The First Order Spectrum:
+
−
In the first order spectrum there are many lines and using the data from the Helium portion of the lab determined that the Sodium has Helium contamination. By substracting all the known Helium lines, all that was left is a bright orange line. By focusing the slit, it was determined to actually be 2 orange lines, this can be seen better in the second order spectrum. Due to the proximity of the lines, less than .1 degrees apart, one measurement was taken and the published values were averaged.
+
 
<center>
 
<center>
−
{| class="wikitable" border="1" style="text-align:center"
+
<math>
−
 
+
\frac{\delta f}{\delta v_c}=\frac{n \delta v_s}{2(L+0.6R)},
−
|-
+
</math>
−
 
+
−
|+ Sodium, d=1/600mm, m=1
+
−
 
+
−
! Color
+
−
 
+
−
! <math>\theta_{diff}</math> (º)
+
−
 
+
−
! <math>\lambda</math> (nm)
+
−
 
+
−
! Error (nm)
+
−
 
+
−
! Published <math>\lambda</math> (nm)
+
−
 
+
−
|-
+
−
 
+
−
|-
+
−
| Orange
+
−
|20.7
+
−
|588.8
+
−
|<math>\pm</math>1.99
+
−
|589.294
+
−
|}
+
 
</center>
 
</center>
−
 
−
Second Order Spectrum:
 
−
In the second order, all the contamination was removed and only the oranges lines were seen.
 
−
<center>
 
−
{| class="wikitable" border="1" style="text-align:center"
 
−
 
−
|-
 
−
 
−
|+ Sodium, d=1/600mm, m=2
 
−
 
−
! Color
 
−
 
−
! <math>\theta_{diff}</math> (degrees)
 
−
 
−
! <math>\lambda</math> (nm)
 
−
 
−
! Error (nm)
 
−
 
−
! Published <math>\lambda</math> (nm)
 
−
 
−
|-
 
−
 
−
|-
 
−
| Orange
 
−
|46
 
−
|594.14
 
−
|<math>\pm</math>.89
 
−
|589.294
 
−
|}
 
−
</center>
 
−
 
−
 
−
=== Error Analysis ===
 
−
 
−
For the error analysis, there are two variable associated with an error, <math>\theta_{d}</math> and <math>\theta_{i}</math>.
 
−
 
−
The partial errors for each of the variable are calculated from the formulas
 
 
<center>
 
<center>
 
<math>
 
<math>
−
\frac{\delta \lambda}{\delta \theta_{d}}=\frac{d}{m}Cos(\theta_{d})Sin({\delta \theta_{d}}),
+
\frac{\delta f}{\delta L}=-\frac{n v_s \delta L}{(L+0.6R)^2},
 
</math>
 
</math>
 
</center>
 
</center>
−
 
+
and
−
and,
+
−
 
+
 
<center>
 
<center>
 
<math>
 
<math>
−
\frac{\delta \lambda}{\delta \theta_{i}}=\frac{d}{m}Cos(\theta_{i}) Sin({\delta \theta_{i}}).
+
\frac{\delta f}{\delta R}=-\frac{0.3 n v_s \delta R}{(L+0.6R)^2}.
 
</math>
 
</math>
 
</center>
 
</center>
−
Then the total error is the sum of the two partial derivatives added in quadrature,
+
Then the total error is the sum of the three partial derivatives added in quadrature,
 
<center>
 
<center>
 
<math>
 
<math>
−
\delta \lambda=\frac{d}{m} \sqrt{(\frac{\delta \lambda}{\delta \theta_{i}})^{2}+(\frac{\delta \lambda}{\delta \theta_{d}})^{2}}.
+
\delta f = \sqrt{(\frac{\delta f}{\delta v_c})^{2}+(\frac{\delta f}{\delta L})^{2}+(\frac{\delta f}{\delta R})^{2}}.
 
</math>
 
</math>
 
</center>
 
</center>
  
−
The values for <math>\delta \theta_{d}</math> and <math>\delta \theta_{i}</math> used are half the value of the smallest unit of measure on the device, .05 degrees.
+
The value for <math>\delta L</math> is 0.05cm, for <math>\delta R</math> is 0.05mm, and for <math>\delta v_s</math> was 5 m/s since speed of sound varies at different altitudes.
  
 
== Conclusion ==
 
== Conclusion ==
−
 
+
For the experiment, the measured data fit well with the theoretical values. All values calculated were within 1% error of the theoretical values. Also, it determined that there was an increase in accuracy with the end correction. Without the end correction, the data would have been off by almost an order of magnitude at some frequencies. Surprisingly the biggest source error came associated with the speed of sound. But it is minimal since there is plenty of background to determine the speed at different altitudes.
−
The emission spectrum for the sodium and helium sources is determined accurately; the error is under 1% and published values fall within that error. The sole exception, the error present in the second order sodium band, is considered to be due to human error during data collection rather than any deviation from the model. The symmetry about <math>\theta_{diff}</math> allows each measurement to be confirmed, resulting in confidence in these results.
+
  
 
== References ==
 
== References ==
 +
[1] Wikipedia, “Speed of Sound“, en.wikipedia.org/wiki/Speedofsound
 +
 +
[2] "FAQ in music acoustics: The End Correction",  http://www.phys.unsw.edu.au/jw/musFAQ.html#end
  
−
[1]Kowalski et al., Spectroscopy, 2007.<p>
+
[3] “Modes in a Resonator“, http://ticc.mines.edu/csm/wiki/images/5/5b/Acoustics_07.pdf
−
[2]Jenkins, F A and White, H E , Fundamentals of Optics, 4E, McGraw-Hill, 1976.
+

Latest revision as of 15:32, 4 December 2007

Harmonics

Barrett Nibling

December 4th, 2007

Contents

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 1% of the theoretical data.

List of Figures

[1] Schematic of Harmonics Apparatus

[2]Measured Frequencies Compared to Theoretical Frequencies Graph

Introduction

Sound produces unique frequency patterns when travelling through a resonant cavity, such as a tube, known as harmonics. These patterns depend on the frequencies sent into the body, the material, but more importantly the geometry of the structure. A computer was used to produce sound waves in the form of white noise through a speaker into one end of the cavity and by placing a microphone recording the frequency patterns on the other end, we could record the data on the computer for analysis. The computer software represents the data as a plot and the patterns on a graph shows the resonant peaks which occurred in the cavity. These peaks can then be compared to expected peaks by using previously derived equations for the tubes we used. The derived peaks and the expected peaks were then compared and were found to agree within experimental error.

Theory

When a sound wave of a specific frequency enters a cavity, such as a musical instrument, the cavity will absorb the energy of the wave and produce a standing wave pattern that matches the resonant frequency. This only occurs when the specific frequency of the waves entering the system are close to the frequency of the acoustic resonance of the cavity. These resonant frequencies are known as harmonics. Each system of this type will have an infinite number of harmonics. The lowest frequency harmonic is called the fundamental frequency. Each harmonic following is a nth multiple of the fundamental frequency, known as the nth harmonics.

The constraint that determines the harmonic frequencies is the system itself. In the case of a pipe, which was used for our experiment, the resonance depends mainly on the length of the pipe. Since the pipe is open at both ends, the following previously derived equation can be used to approximate the harmonic frequency,

f = \frac{n v_s}{2 L},

where n is a positive constant integer, vs is the speed of sound, and L is the length of the pipe. The speed of sound is given to be at 334 m/s[1]. This isn't the best equation that matches the model. The radius of the pipe effectively makes the pipe long, the bigger the radius, the more air the waves must travel through[2]. To account for this, the end correction factor of 0.6R, R being the radius of the pipe, must be implemented into the equation (1). Giving the following new equation,

f = \frac{n v_s}{2(L+0.6R)}.

Calculations from this equation will than be compared with the data acquired from the microphone.

Procedure

1. Log on the computer and start up Baudline

2. Begin emitting white noise from the speaker

3. Place one opening of the pipe in front of the speaker and place the microphone on the opposite opening as shown in the figure below

Harmonics.jpg Schematic of Harmonics Apparatus[3]

4. Save the data, making sure to substract the baseline from the white noise.

5. Analyze the data into a plot and observe the resonant peaks that occur.

Results

The following table and graph are the results acquired from a pipe of Length 38.3cm and Radius 13.4mm


Data Table for Pipe 1, L=38.3cm \pm .05cm and R=13.4mm \pm .05mm
n Theoretical Frequency (Hz) Theoretical Frequency

with End Correction (Hz)

Error

with End Correction (Hz)

Measured Frequency (Hz)
1 436.0 427.1 \pm 6.4 421.9
2 872.1 854.1 \pm 12.8 843.75
3 1308.1 1281.2 \pm 19.2 1283.2
4 1744.1 1708.3 \pm 25.7 1699.2

Pipe1Graph.jpg

Measured Frequencies Compared to Theoretical Frequencies

The following table is the data collected from a smaller pipe of Length L = 18.2cm and Radius 24.55mm.

Data Table for Pipe 2, L=18.2cm \pm .05cm and R=24.55mm \pm .05mm
n Theoretical Frequency (Hz) Theoretical Frequency

with End Correction (Hz)

Error

with End Correction (Hz)

Measured Frequency (Hz)
1 917.6 848.9 \pm 12.9 855.5
2 1835.2 1697.8 \pm 25.8 1687.3
3 2752.8 2546.6 \pm 38.7 2537.4
4 3670.3 3395.5 \pm 51.6 3416.0

Error Analysis

For the error analysis, there were three variables associated with error, L, R, and v. The following are the three partial errors for each variable,

\frac{\delta f}{\delta v_c}=\frac{n \delta v_s}{2(L+0.6R)},

\frac{\delta f}{\delta L}=-\frac{n v_s \delta L}{(L+0.6R)^2},

and

\frac{\delta f}{\delta R}=-\frac{0.3 n v_s \delta R}{(L+0.6R)^2}.

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

\delta f = \sqrt{(\frac{\delta f}{\delta v_c})^{2}+(\frac{\delta f}{\delta L})^{2}+(\frac{\delta f}{\delta R})^{2}}.

The value for δL is 0.05cm, for δR is 0.05mm, and for δvs was 5 m/s since speed of sound varies at different altitudes.

Conclusion

For the experiment, the measured data fit well with the theoretical values. All values calculated were within 1% error of the theoretical values. Also, it determined that there was an increase in accuracy with the end correction. Without the end correction, the data would have been off by almost an order of magnitude at some frequencies. Surprisingly the biggest source error came associated with the speed of sound. But it is minimal since there is plenty of background to determine the speed at different altitudes.

References

[1] Wikipedia, “Speed of Sound“, en.wikipedia.org/wiki/Speedofsound

[2] "FAQ in music acoustics: The End Correction", http://www.phys.unsw.edu.au/jw/musFAQ.html#end

[3] “Modes in a Resonator“, http://ticc.mines.edu/csm/wiki/images/5/5b/Acoustics_07.pdf

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