Speed of Wave
vr = λ f
:. vr = 0.5474 * 512
:. vr =280.2688 m/s-1 ± 0.003 m/s-1
Literary Value for Speed of Sound
vl = 331 + (25 * 0.6)
:. vl = 331 + 15
:. vl = 346 m/s-1
Discussion and Analysis
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The experimental speed of sound was 280.2688m/s-1 ± 0.003 m/s
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% Difference = (346 - 280.2688) / 346 * 100
= 65.7312 / 346 * 100
= 0.18997456647398843930635838150289 * 100
= 18.997456647398843930635838150289
:. % Difference ≈ 19.0 %
:. vr = 280.2688 m/s-1 ± 19%
Conclusion
The investigation provided some interesting results. The experimental speed of sound was found to be 280.2688 ± 0.003 m/s-1, while the literature value was found to be much higher at 346 m/s-1. This is a percentage difference of 19%, or a real difference of 65.7312 m/s-1. However, although a large amount of error was involved, the practical succeeded in its aims of determining an experimental speed of sound, even if it was severely inaccurate.
Evaluation
The data obtained was very unreliable. This can be shown by the extremely high level of percentage error. In order to determine when the 1st or 3rd harmonic length had been reached, we had to listen for the emitted sound to double in volume. This is as in a closed end tube, the 1st and 3rd harmonics end in an open end, or a place of maximum displacement, and as such, maximum constructive interference. As we were only using our ear to find the loudest sound possible, there is no guarantee that the distance we measured is actually the true value for the 1st and 3rd harmonics for the frequency used, as there was no way of verifying if the reflected sound had indeed doubled from the emitted sound. This potentially large source of systematic error could account for a large portion of the difference between the accepted literature value and the determined value for the speed of sound.
Further unreliability could come from the tuning fork. While the frequency was embossed on the fork, the actual frequency of the fork may be different from what it is supposed to be. This would then affect speed of the wave, and could account for a portion of the difference between the accepted literature value and the determined value for the speed of sound.
The humidity of the experiment would have also affected results, causing further unreliability. The literature value of the speed of sound is based on speed in dry air, and as the experiment did not take place in 0% humidity, the humidity level would also account for a portion of the differences in speed of sound values.
The procedure was largely unreliable due to the sources of error mentioned above. As such, the results cannot be said to be reliable to a large degree. The addition of measuring devices for humidity and volume would result in far greater accuracy of measurements. A frequency which is more accurate i.e. one generated electronically, would also result in more valid results. The apparatus that were used performed well, although the tuning fork may have contributed to errors, as stated above. The measuring cylinder was effective, and the millimeter increments made it easier to measure the distance of the open tube. The method of displacing water to change the tube length is effective, however, obtaining the desired tube length can be difficult, as the water level did not match with the wing nut used to lengthen the tube as hoped. Therefore there was an element of guess work involved in setting up the tube length, followed by trial and error.
Modifications to improve the practical could be to test several different frequencies to attempt to determine a correlation between frequency and wavelength. Another modification could be to attempt to determine more than just the 1st and 3rd harmonics, in order to gain more accuracy in the wavelength measurement. However, in order to achieve this, a far smaller frequency should be used (as well as lower frequencies), which may prove hard to hear if the practical was conducted with the same apparatus as this one was.