During this experiment, the speed of sound was investigated using two different methods.
Both methods produced figures for the speed of sound which were different to the commonly used value (343 meters per second). The first method used involved using different tuning forks and a column of air to investigate the relationship between tube length, frequency and speed of sound. This method produced a value of 371.6 ± 11.2 meters per second. The second method used an oscillator and receptor to determine velocity by measuring wavelength.
This method gave the value of 344.5 ± 20.1 meters per second. There were many possible reasons these do not match the previous number which will be discussed during this report. NASA defines the speed of sound as “the speed of transmission of a small disturbance through a medium”. Sound is transmitted as a longitudinal wave and during this experiment, the medium used was air.
The importance of this investigation cannot be underestimated as sound is a vital part of the way information is transmitted. Whether it be through speech, music or signals from ultrasound scans, sound is arguably the most important means of communication. Many other attempts to measure the speed of sound have been carried out using a variety of methods with differing levels of success. For example, one of the earliest investigations recorded was by Pierre Gassendi in 1635 who measured the speed of sound by comparing the time taken to see the flash of a cannon and the time taken to hear the explosion. This method was fairly reliable because of the huge difference in the speed of light and sound and so it was also used to measure the speed of sound in water by Colladon and Sturm in 1827.
However, this method can be inaccurate as it was measured by humans and often humans do not have consistent reaction times. This is called the ‘personal equation’ of the recorder and explains difference in time between the event occurring and it being recorded. The personal equation is very hard to eliminate because most of the time, it is not constant.
Therefore, this lead to a lot of random errors in the method which decreased the precision.A more modern method was devised to eliminate this error. In this procedure, the humans were substituted for microphones linked up to an electrical timer. The speed of the sound would then be calculated using equation 1.
Of course, the personal equation of the microphones and the timer still affected the results but this error is more likely to be constant and so can be accounted for.In 1942, an investigation was carried out at the Pennsylvania state college. This experiment resulted in a value for the speed of sound at zero degrees celsius (331.45 meters per second). This was then corrected to 331.29 meters per second in 1984 and this is the current value used for the speed of sound.
The sound waves in this experiment were set up in the air by a source of sound at the open end of the tube. When this happens, the air molecules at the mouth of the tube oscillate with simple harmonic motion and form a wave that travels down the length of the tube with a constant frequency. We can plot the wave as a sine graph (figure 1).If a tuning fork is sounded and held against the open end of the tube, resonance can occur. Resonance is when the wave is reflected back off the closed end of the tube to increase the amplitude of the sound (if the tube is the correct length). However, there is more than one length of tube which will cause the sound to resonate. Each resonant sound is called an overtone and these always occur at multiples of the lowest resonant frequency, often called the fundamental frequency. This tends to be the harmonic used in most musical instruments.
When resonance happens, two waves of the same period and end up travelling in opposite directions and this can lead to interference. Interference can happen in two different ways- constructive and destructive. Constructive interference (figure 2) is when the two waves are added and the resultant wave has a higher amplitude than either of the two original waves. Destructive interference (figure 3) is when the sum of the two waves has a lower amplitude than either of the two original waves because they are not in the same phase.
In an open tube, the waves involved in the interference have the same frequency and wavelength but they move in opposite directions and are in different phases. Therefore, you get a standing wave in the tube. This standing wave will have equally spaced stationary points on the graph where the amplitude is zero (caused by destructive interference) and places where the amplitude is at its maximum (caused by constructive interference). These places on are called nodes and antinodes and are shown in figure 4.The fundamental frequency will be heard if the length of the tube is equal to one quarter of the wavelength (equation 2, figure 5). Therefore, in the tube, there will be two nodes and one antinode.
The first overtone will be heard if the length of the tube is equal to three quarters of the wavelength (equation 3, figure 6). There will be three nodes and two antinodes. This pattern continues endlessly. The equation used in this experiment was the equation for the fundamental frequency so we can combine equation one and equation two to form equation four. Now, it is simple to calculate velocity of the waving using the length of the tube and the wavelEquation four can be compared to the equation for a straight line (y=mx + c) and so can be plotted on a graph of 1/f against L. The gradient of this graph will be one quarter of the velocity of sound in air.
The second method used in this experiment used an oscilloscope with two inputs to investigate interference effects and to use these two inputs to calculate the speed of sound. Other factors may affect the speed of sound such as temperature. Temperature can affect the speed of sound as when it is warmer, the air molecules will oscillate faster as they have more kinetic energy. The first method was set up by gathering a set of tuning forks of frequencies ranging from 256Hz to 512Hz and two tubes, one sealed at one end and one open tube. The closed tube (a) was filled with water and the open tube (b) placed inside so one end was immersed (as in figure 7). One tuning fork (c) was sounded on the rubber pad (d) and held horizontally above the open tube.
The length of the column of air was then adjusted by moving the open tube up and down until an amplified sound was heard. The length of the column of air at this point was measured using a ruler (e). The ruler used had an error of 0.0005m so this was also recorded. This method was repeated for all of the tuning forks. The frequencies and errors on the frequencies were recorded. For some of the forks, two points at which the amplified sound were found. In order to keep the method consistent and calculations simple, only the smaller of the two lengths was written down.
The data from this method was then used to plot a graph of 1/frequency against length of column. The gradient of the graph was taken and this value was used as ¼ of the velocity of sound according to equation (4).In the second method, a signal generator, microphone and oscilloscope were used. The signal generator was placed next to the oscilloscope on a ruler on the desk. The microphone was placed on the ruler, about 80 cm away from the signal generator, facing towards it. The signal generator and microphone were then connected to the two channels on the oscilloscope so two sine waves of almost identical frequencies were produced. However, due to the distance travelled by the wave, the phases were not always in sync. The distance between the transmitter and detector was varied and the points at which the phases of the two waves matched up were recorded.
The wavelength of the sine wave was recorded by measuring the distance between the points where the phases were equal. An average wavelength was calculated and the frequency was read from the oscilloscope. Using equation 1, the velocity of sound can be calculated using these values.
ResultsThe results from method one showed that as the frequency of the tuning forks increased, the length of the column of air decreased. This ranged from lengths of 0.147m at 512 Hz to 0.312m at 256 Hz.
As the graph is a plot of 1/frequency against length of column, it showed positive correlation and was approximately linear. The errors calculated on this data come from the error on the ruler used to measure the column of air and the error on the frequency of the tuning fork. The error on the ruler was 0.0005m and the errors on the tuning forks were 0.
5 Hz which make the error bars on this very small and they could not be drawn. Two lines of best fit were drawn, a maximum line and a minimum line. A value for the gradient of each line was calculated and so two values were found for the velocity of sound. An average of the two was used as the result of this method.The errors were propagated using equation 5 for multiplication or division of values.
Table one. This table shows the difference in the positions of the receptor when the phases of the two sine graphs matched up. As the wavelength should be constant, it was expected that these measurements would be similar. The results collected matched these as shown. The error on the ruler was constant at 5×10-4.The results obtained for the speed of sound were both close to the widely recognised value. The result from the first method (371.6 ± 11.
2 meters per second) was slightly larger than the expected number. One reason for this could be that this method was carried out in a slightly smaller room than the second method. Therefore, it might have been warmer and this would cause the speed of sound to be slightly faster than normal. This would be a systematic error so, if the experiment was repeated and the temperature measured, this could be taken into account in the calculations. Also, the pressure in this room may have been different and this is another systematic error which could be eliminated. However, the most likely reason that this is not exactly the expected result is that all the measurements were done by people. This leads to many random errors which can affect the result and is very hard to eliminate.
Therefore, the less accurate result achieved using this method was expected.The second method produced a value which was more accurate. This was expected as the errors on the equipment used in this method were very small.In conclusion, using an oscilloscope with a transmitter and microphone is a more accurate way to measure the speed of sound than with tuning forks and a column of air.