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Posted: January 31st, 2023

# Experiment for Determination of Speed of Sound in Air

Experiment for Determination of Speed of Sound in Air
Introduction
The aim of the experiment is to determine the speed of sound in air by observing the standing waves and the use of forks. The speed of sound in air is approximately 331.4 m/s, while the speed at room temperature is 344 m/sec (Shin & Hammond, 2008). The speed of sound is a factor that is dependent on temperature. Sound is a type of longitudinal wave, while a wave consists of oscillation in a medium. The other type of wave is called the transverse wave, which occurs in water. The sound wave is a longitudinal wave that propagates in water. The frequency of the sound is also an important parameter in the experiment. The frequency is defined as the number of waves per unit time or 1/period. The other parameters include the amplitude, period, wavelength, and velocity (Espinoza, 2018). The amplitude is related to how loud the sound is produced. The period is the time between one maximum point to another while the wavelength is the distance between the one maximum point to the other. The velocity is the speed of which the wave propagates in a medium.
The forks were used to accomplish the experiment. The tuning forks produce the vibration, which eventually results in the generation of the sound waves. The sound waves propagate in the tube and reflected upon reaching the surface of the water. The incoming and the reflected waves cause interference, thereby forming the standing waves.
Theory
The sound waves are reflected on the surface of the water causing a change of the phase by 180°. The generated waves are completely out of phase with the incident waves. The relationship suggests that the magnitude of the standing waves should be zero at the surface of the water. The intersection of the waves is called the node, while if the condition of resonance is met the amplitude of the standing wave is the antinode. Resonance is as a factor that emerges as a result of the vibration of the waves (Espinoza, 2018). The vibration of sound in air is weak at some point and strong in some cases. The resonant is due to the strong vibration of the frequencies. The resonance occurs due to the restriction of the ways of vibration of air. Therefore, for a wave traveling at a speed v and frequency f as well as the wavelength λ , the following equation holds (Shin & Hammond, 2008)
V=λf……………..Eqn. 1
The speed of sound is fixed at a constant temperature and similarly, the frequency of a given fork is fixed, which therefore suggests that the wavelength of sound is a fixed parameter. The resonance conditions can be satisfied considering the length of the tube L
Ln=1/4 (2n+1)λ……………………….Eqn. 2
Where n= 0, 1, 2, 3, 4…..et cetera. Ln is the distance from the open end of the tube to the surface of water.
Ln+1-Ln= 1/2λ………………….Eqn. 3
ΔL = 1/2λ …………………..Eqn. 4
Therefore a tube of a given length may vibrate in several ways. The number of vibration differs in terms of the nodes and antinodes in the tube resulting in different wavelengths and frequencies.

Health and Safety
The pipe was protected when filled with water by securing the region where the experiment was performed. Since the experiment involved the use of water, care was taken to avoid the damage of electric devices. The experiment was also performed far from high voltages.
Procedure
Apparatus
The apparatus used in the experiment include turning forks, graduated cylinders, water, ruler, wooden block.
Method

Figure 1 Representation of the apparatus used in the experiment
The graduated cylinders were filled with water, and the experiment was set up, as shown above. The tuning fork was tapped on the wooden block and brought near the opening of the graduated cylinder. The resonating sound was heard when the cylinder was moved. After the resonating sound was heard, the distance from the water to the top of the graduated cylinder was measured and the readings converted to meters. The readings were then multiplied by 4 to obtain the wavelength of the sound wave. The speed of the sound wave was calculated by using the equation: velocity= frequency x wavelength.
Results
Table 1 Experimental results
Frequency f (kHz) 1/f (kHz) Length λ/4 (m) Length 3λ/ (M) 4 x Length (M) Wavelength λ
1 2 3 Average 1 2 3 Average
512 0.00196 0.175 0.168 0.173 0.172 0.489 0.494 0.489 0.49067 2.65068 0.66267
480 0.00209 0.165 0.166 0.171 0.16734 0.517 0.518 0.511 0.51534 2.73072 0.68268
426.6 0.00235 0.192 0.194 0.198 0.19467 0.586 0.597 0.589 0.59067 3.14136 0.78534
384 0.00261 0.203 0.207 0.202 0.204 0.658 0.621 0.659 0.646 3.4 0.85
341.3 0.00293 0.236 0.248 0.242 0.736 0.739 0.7375 3.918 0.9795
320 0.00313 0.272 0.263 0.2675 0.798 0.786 0.792 4.238 1.0595
288 0.00348 0.304 0.311 0.3075 0.984 0.982 0.983 5.162 1.2905
256 0.00391 0.331 0.331 1.324 0.331

Analysis

Figure 2 A graph of 4L Against 1/f
Uncertainty of 3 λ/4 = 0.00167+0.0017+0.00467+0.0012+0.0015+0.006+0.001/7= 0.00191= 0.19%
Uncertainty of λ/4 = 0.003+0.00234+0.00267+0.001+0.006+0.0045+0.0035/7= 0.33%
Discussion
The graph of 4L against I/f is a straight line graph, and the gradient is the velocity of sound in the air. The errors experienced in the experiment were observation errors, errors due to the efficiency of the instruments, and the errors due to the external factors. The errors due to the temperature emerged as a result of human observation and the contribution of parallax. The instrument used, such as the meter ruler, was not 100% efficient, which led to the deviation of the results obtained during the experiment. Additionally, temperature influenced the results since the speed of sound in air varies with temperature. The variation of temperature, whether high or low, affected the outcome of the results, thereby introducing the errors in the experiment. The experiment had some limitations. For instance, it was not carried out under constant conditions of temperature and pressure. The other limitation was due to the disturbance of the transverse waves from water, which led to the instability of the experiment. The setup could not measure the desired accurate results because the forks could not send the required signals. The experimental results differed from the theoretical results due to the sources of errors. The results are important because they establish a constant which other parameters will be based on. The experiment can be improved by carrying it under constant conditions of temperature and pressure.
Conclusion
In conclusion, the experiment was successively conducted because the aim of obtaining the speed of sound in the air was accomplished. The speed of sound in air is a constant, and it is the gradient of the graph of 4L against 1/f. The graph is a straight line indicating that the variables are directly proportional to each other.
References
Shin, K., & Hammond, J. K. (2008). Fundamentals of signal processing for sound and vibration engineers. Chichester: Wiley & Sons.
Espinoza, F. E. R. N. A. N. D. O. (2018). Wave Motion As Inquiry: The Physics And Applications Of Light And Sound. Place Of Publication Not Identified: Springer International Pu.

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