Introduction of the Experiment
The sound waves laboratory experiment is aimed at studying the resonancebehaviour of an air column when the air is disturbed in a closed tube. In the process, the speed at which the air travels is determined. The laboratory experiment is also purposed to understand how temperature affects the speed of sound in air and finally it is aimed at observing the relationship that co-exists between the wavelength and frequency of sound as it travels through air and other media. At the end of the study, all these factors are compared to the theory and deductions made.
Background of the Experiment
A standing sound wave condition in a system is attained when there exists an anti-node at the open end of the system and a node at the closed end of the air column (Triklen, Fredric, 1990). The amplitude of longitudinal or transverse sound waves a factor of air motion. It is highest when the air can achieve greater motion. This only occurs at the anti-node. The amplitude of sound waves is lowest in circumstances when the air is at a standstill and this occurs at the node. From theory, the speed of sound at 0 Degrees Celsius is around 331.5 m/s, and this increases with increase in temperature (Carl, 1995). Sound travels in less dense media at high speed as compared to high dense media. In addition to air temperature and density of the media, the air pressure and molecular mass of the media also play a significant role in the way the sound travels.
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The methodology of the Experiment
The experiment is set up with the help of virtual sound waves apparatus that enables the study of standing waves in a system that is closed on one end and opened on the other end. The open end is subjected to the atmospheric air while the closed end is achieved by having a water column. With the virtual environment, the air temperature, the column of air, and the frequency of the sound are varied, and the waves observed. Form the sound waves, the wavelength is measured, and thus the only parameter remaining for a complete study is the speed at which the sound travels under such conditions. The sound wave velocity is a function of frequency and wavelength and is computed as;
……………………… Equation 1
The wavelength is calculated from the relation;
…………………………………………………………….Equation 2
Figure 1: Nodes length measurement
The air in the column is also replaced with Helium and SF6 to study further how sound travels in other media.
Figure 2: Sound wave laboratory experiment set-up
The experiment apparatus set-up is as shown in figure 1 above. They include; a sound speaker, water reservoir, graduated cylinder, water hose temperature control thermostat, a keyboard interface for the generation of different tones, loudness gauge, gases tab, and the volume adjustment slider.
Experiment Data and Results
The experiment is run at 0 ℃, 10 ℃, 20 ℃, 30 ℃, and 40 ℃ at different air column height while keeping the sound frequency constant as played from the keyboard keys and the wavelength calculated and the data recorded.
Medium: Air
Frequency: 261.63 Hz (C4)
Figure 3: Sound wave at 0 ℃ Figure 4: Sound wave at 10 ℃
Figure 5: Sound wave at 20 ℃ Figure 6: Sound wave at 30 ℃
Figure 7: Sound wave at 40 ℃ Figure 8: A plot of Velocity Vs Temperature
Figure 9: Properties of the V-T plot Figure 10: Sound wave data at 261.63Hz
Medium: Helium
Frequency: 261.63 Hz (C4)
Figure 11: Sound wave at 0 ℃ Figure 12: Sound wave at 10 ℃
Figure 13: Sound wave at 20 ℃ Figure 14: Sound wave at 30 ℃
Figure 15: Sound wave at 40 ℃ Figure 16: A plot of Velocity Vs Temperature
Figure 17: Properties of the V-T plot Figure 18: Sound wave data at 261.63Hz
Data Analysis
Determination of sound wave speed and wavelength from the experiment
These calculations are a typical case for the air as the medium of sound waves travel.
You are determining the speed of sound in air at 0 ℃ from the experiment at a frequency of 261.63 achieved by playing tone C4 from the keyboard.
Theoretical speed of sound in air at 0 ℃ = 331.5 m/s
Table 1: Sample calculation for speed and wavelength of sound waves
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Determining the speed of sound in air at 0 ℃ Reference frequency; C4 261.63 Hz |
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L 1 =0.31m |
L 2 =0.94m |
L 3 =1.26 |
L 4 =2.36 |
The wavelength is obtained from the average of the three wavelengths as follows;
The velocity v, of the sound wave, is determined from the following relation;
The percentage error for the velocity is calculated as follows;
The relationship between the sound waves speed and the air temperature
In this relationship, the wavelength will be used since it is the most accurate of the three wavelengths.
Medium: Air, Frequency 261.63 Hz
Table 2: Variation of sound wavelength and velocity with air temperature
| Temperature (℃) | L 1 (m) | L 4 (m) | Wavelength (m) | Velocity (m/s) |
| 0 | 0.315 | 2.360 | 1.37 | 312.2118 |
| 10 | 0.315 | 2.370 | 1.37 | 358.4331 |
| 20 | 0.31 | 2.380 | 1.38 | 361.0494 |
| 30 | 0.31 | 2.385 | 1.38 | 361.0494 |
| 40 | 0.30 | 2.390 | 1.39 | 364.5378 |
Medium: Helium
Frequency 261.63 Hz, in this case, is applied in the calculation of velocity.
Table 3: Variation of sound wavelength and velocity with helium temperature
| Temperature (℃) | L 1 (m) | L 2 (m) | Wavelength (m) | Velocity (m/s) |
| 0 | 0.315 | 0.945 | 1.26 | 329.5538 |
| 10 | 0.31 | 0.930 | 1.24 | 324.4212 |
| 20 | 0.31 | 0.930 | 1.24 | 324.4212 |
| 30 | 0.30 | 0.900 | 1.20 | 313.9560 |
| 40 | 0.30 | 0.900 | 1.20 | 313.9560 |
As the temperature is increased from 0 ℃ to 40 ℃, the loudness of the sound increased. Theoretically, the air molecules are energized by an increase in air temperature (Carl, 1995). This is achieved as energized air molecules vibrate at a higher rate; thus the loudness is realized. At the same time, the velocity at which the sound wave travel increased.
When the water level in the graduated cylinder was reduced thus increasing the air column, the wavelength increased since there are more air molecules for sound waves to travel thus velocity increased. The wavelength is directly proportional to velocity thus will increase.
From the plot of velocity against temperature, the velocity increased linearly with increase in temperature as expected in theory following the following relation;
where,
From theory, the y-intercept, b is calculated from the following relation;
where,
For instance, at 0 ℃, the y-intercept = 356.980m/s and this corresponds to the experimental value that the sound wave travels in the air at 0 ℃.
The percentage error for the y-intercept is calculated as follows;
End correction for the graduated cylinder
Since the sound wave resonated at an air column above the graduated cylinder opening, there is the need to correct this.
Figure 19: The cylinder end correction
From the theory, the resonating air column height above the cylinder opening is computed as;
where,
The experimental
The percentage error is calculated as follows;
The relationship between the frequency of a sound wave with velocity and wavelength
From the experiment, the frequency of the sound wave is not affected by either an increase or decrease in velocity and wavelength, and thus it can be deducted that;
Conclusion
The experimental results varied slightly from the theoretical values due to errors and assumptions made in the virtual lab set-up. Some of the error sources include; the graph tool as it did not give a smooth curve for each data points, precision and accuracy during the placing of the line tool on the exact node points, and the limitations of the measuring instruments such reading values in between the divisions of the graduated cylinder. These errors can be minimized in the future by developing and upgrading of the virtual lab tool. Helium is less dense than air at 0, and thus the sound waves travel at high speed in helium than in air.
References
Carl, R. (1995) Hyper Physics: Speed of Sound . Georgia, Georgia State University Press.
Trinklein, A, Fredric, E. (1990). Modern Physics . New York, Powerhouse Books Publishers.
