Sound In Air Lab

Speed of Sound in Air

By: James Chen

Lab Partner: Jin Zhang and Jake Salpeter Phys 130, Lab section: EE11

TA: Khaled Elshamouty

Date of lab: October 29, 2013

Introduction

Sound is a longitudinal (compressional) wave caused by a vibrating source. In this experiment, we use standing sound waves created by the tuning forks to determine the speed of sound in air in a tube when it reaches different resonances. In this lab we focused primarily on using standing sound waves (compressional waves) created by tuning forks in order to determine the speed of sound in air in a tube when it reaches resonance.

v=λf v  speed of sound in a medium (m/s)  wavelength of the waves (m)
  frequency of the sound source vibrations (Hz)
n  number of resonance  wavelength of the waves (m)
Ln  the length of the air column (m)   wavelength of the waves (m) n  number of resonance
Ln  the length of the air column (m)
Dn  the length of the inside pipe chamber (m)
Xo  the small distance between the antinode at the open end of the tube and the pipe (m) v  speed of the waves (m/s)
Dn  the length of the inside pipe chamber (m)  frequency of the sound source vibrations (Hz)
Xo  the small distance (m)  constant n  number of resonance

v  speed of sound in air vo  speed of sound in dry air at 0°C (273.15K), which is 331.3m/s
T  toom temperature (K)

R  radius of the tube (m)
Xo  the small distance (m)  constant

Experimental Method
First, start the experiment with the plunger positioned at the open end of the tube.
Strike the tuning fork with the rubber rod and hold it at the open end. Slowly move the plunger back into the tube until aloud amplification of the tone is hear. It might be necessary to strike the tuning fork several times in order to keep the tuning fork vibrating. Adjust the plunger for maximum amplification and this would be the first resonance point. Measure the length of the standing wave column. Then, continue pulling out the plunger till you hear the second maximum amplification point and third if possible. These length correspond to D1, D2, D3 for n = 1, 2, 3, and etc. Repeat the steps for the other three tuning forks and record all the data and do all the related
calculations.

Results

Throughout many trials using different tuning forks, below is the results of air chamber distance recorded at resonance for different frequency tuning forks.

Frequency (Hz)
Dn (m) ± 0.001m
N of resonance

384
0.208
1
0.000651
384
0.646
2
0.001953
426.7
0.183
1
0.000586
426.7
0.559
2
0.001758
426.7
0.924
3
0.002929
480
0.168
1
0.000521
480
0.517
2
0.001563
480
0.845
3
0.002604
512
0.165
1
0.000488
512
0.488
2
0.001465
512
0.830
3
0.002441
Length of the tube = 1.000m ± 0.001m
Temperature = 22.0°C ± 1.0°C
Diameter of the tube = 0.043m ± 0.001m
Radius of the tube = 0.0215m ± 0.0005m

Discussion
Part one,

From the slope intercept form y = mx +b,

Part two,
Slope = 324.9m/s ± 6.1m/s
Y-intercept = 0.0021m ± 0.0108m

Therefore,
The speed of sound v ± δv = 324.9m/s ± 6.1m/s
The end correction factor Xo ± δXo = 0.0021m ± 0.0108m

Part three,

Calculations for the theoretical value for the speed of sound in air using the above equation:

However, the calculated and graphical values for the speed of sound do not agree within error.
Part four,

Calculations for the theoretical approximation for the end correction Xo using the above equation:

The theoretical and experimental values for the end correction do agree within error.

Question:

Part one,

At the closed end of the pipe, there must be a node because there is no motion occurring at the end of the pipe and there is no displacement, the air molecules cannot move.
If the pipe was closed at both ends, L1 = /2 and L2 = ,

therefore, L2/L1 = 2

Part two,

If the pipe was closed at one end as used in the experiment, then

This ratio of the single open-ended pipe is 1.5 times larger than the pipe closed at both ends. This means that in order to produce the same harmonic, the single-open ended pipe needs to be 1.5 times larger than the pipe closed at both ends.

Part three,

The first resonance occurs at, the maximum length is the tube length which is 1.000m ± 0.0001m. Therefore, in order to find the lowest frequency, we need to find the largest, and the maximum length will produce the largest. So, and.
Conclusion
In this lab, we examined the resonances of a cylindrical pipe closed at one end and manipulated the tuning forks with different frequencies. Also, after constructing the graph, we calculated the experimental value of v – the speed of sound in air, which is 324.9m/s. We also calculated the theoretical value of v, which is 331.3m/s.
From these values, the % discrepancy will be:

These two values do not agree within error, but the small value of % discrepancy shows that the results of the experiment is pretty accurate. In this experiment, we also calculated the end correction Xo, and the theoretical and graphical value agree within error. Nevertheless, there might be some possible errors with this lab and they might be incorrect measurements or imperfection of the equipment. Also, one thing our group noticed, the tube itself makes a big noise when we move the plunger back into the tube which affects the hearing of the resonance tone. However, this is a very successful lab.