Resonance in a Closed Air Column Investigation.

7. Reading errors that may have occurred when reading the 1st resonant length and identifying the 1st resonance. It was hard to tell the climax of the sound, the point of the first resonance. In other words, even though the group thought the resonance was heard at a certain point, in actuality it may have been a little later or a little earlier. This may have led to recording a length that might have been a little above or below the 1st resonance.  Another reading error is when the tube was lifted and the sound at 1st resonance was produced the person identifying the length would have to make a close approximate of the length at which the sound was produced. The lengths were recorded as whole numbers because it was easier estimate the resonance length as whole numbers than to record the exact figured involving decimal numbers. A systematic error in the experiment was the tube placed in the water wasn’t exactly levelled to the rim of the bucket. However, the ruler was placed on the rim for simplicity which means the length of the tube at 1st resonance wasn’t measured from 0 cm. At times when the tuning fork hit the rubber, the vibrations would end so fast that by the time it was placed above the tube so there was no sound or very low sound produced which made it hard to hear the 1st resonance. This may have been caused by air resistance that slows down the vibrations, of the tuning fork, to stop overtime, similar to the pendulums that are swinging stop over time due to air resistance. Finally the difference in measurements is probably caused by systematic error. Looking at tuning fork 1 and 2 room temperature lengths, the values are within 0 – 1 cm difference. However the tuning fork 1 and 2 different temperature lengths have one value each that are outside the 0 – 1 cm range, the 10cm (tuning fork 1) and the 12 cm (tuning fork 2). The odd numbers are probably caused by the placement of the ruler or the reader. I think that all the average wavelengths should be altered to   0.2. This is because, when we were trying to read the numbers we would level the tube and the ruler with our hands and the whole number than the hand touched closest to was recorded. In that case, the 1st resonant length recorded can be either 0.2 higher or lower than the number recorded. With a change in resonant length there is bound to be a change in wavelength and speed as well. So, using the  0.2 of the resonant length, the wavelengths should be  0.8. This figure was determined by calculating the wavelengths using resonant lengths that were  2 or  2. This gave answers that were 0.8 above or below the calculated wavelengths above. This same method is used to find that the speed should  384 (if significant digits weren’t used).

8. The one thing I would change about this lab is probably putting the ruler in the bucket and starting from the exact value that the tube started. So, before the lab started I would check the length at which the tube started from in or the length of the tube. Then as I hear the 1st resonance at a certain length, I can just subtract the starting length from the length I hear the sound to find the measure of the 1st resonant length. Even though it’s more work, it’s much more accurate since the tube would start from a distinct length rather than at approximately 0 cm. As already mentioned, while performing the experiment, the ruler was placed on the rim of the bucket so there a bit of distance between the tube and the ruler. So when it came time to read the 1st resonant length we just used our eyes or our hand to draw a line from the top of the tube to the ruler to record the length. The ruler in the water will be fairly close to the tube making it easier to read the length. Another thing I would change is to stop the tube when the mechanical resonance was created or the sound was produced to measure the exact length. In the experiment, the person in control of the tube would continue to lift even after the 1st resonance was produced and the reader would have to identify the length when the sound was heard without any assurance.

9. The speed of sound can change in different frequencies. I think the conclusions formed by this lab are correct. When a high frequency and low frequency object (tuning fork) is used, the high frequency object should have shorter wavelengths than the low frequency object. The experiment did demonstrate a shorter wavelength for the higher frequency tuning fork. I assumed that since frequency changes the wavelength it must affect speed in the same way. However there is no relationship between frequency and speed of sound. Objects with different frequencies can have the same speed. For example, the speed of light is always the same but if frequency increases, the wavelength will decrease to balance out the wave equation. The speed of sound will change in terms of temperature because there is an existing relationship between speed of sound and temperature. With normal atmospheric pressure ( the speed of sound is 332 m/s but with every temperature increase the speed of sound increases by 0.59 m/s. However if the temperature is below 0 the speed of sound will be less than 332 m/s. According to these guidelines, the conclusions formed by the lab were accurate. The speed of sound for both tuning forks decreased when sound was produced outside, with the lower temperature.

Application

10. When pushing a child on a swing, just like the observed resonance in a closed air column, it demonstrates resonance. When a person pushes a swing, the frequency at which the swing is pushed should match the frequency at which the swing is swinging. The matching frequency of both the swing and the driving force (person pushing) creates the mechanical resonance. In the same way, when the tuning fork hits the rubber, it produces a sound which travels down the tube and reflects off the water (closed end) and come back out of the tube which resembles a reflected wave. The reflected wave translates into a standing wave which is the reason for the different resonant lengths. Resonance is evident in this scenario because the natural frequency of tuning fork (or the waves sent out by the tuning fork) matches the frequency of the reflected wave. The tuning fork vibrates matches the frequency of air inside the tube to vibrate which leads to the vibration of the tube. When the incident wave and its reflected wave have the same amplitude and frequency, in other words a standing wave, the presence of mechanical resonance is present. In a standing wave, produced by the closed air column, the same number of cycles are covered per second except the incident wave starts as a crest and the reflected wave begins as a trough. This represents identical frequencies just like the pushing frequency matches the frequency of the swing. Also, interference is clear in the closed air column because as the crests of the incident waves meets the crests of reflected rays a supercrest is formed. It is when the supercrests are formed, as a result of interference, that the sound is heard the loudest after a long pause (because of the node, there is no sound produced. Similarly, it is interference that causes the matching frequency of the driving force and the natural frequency of the swing to swing higher and higher. The swing goes higher and higher just like when the crests or troughs of the sound waves meet, the amplitude of the crests get higher and higher causing a louder sound.

11. Unlike brass instruments, the source of vibrations of a wood instrument is not the lips but the vibration of the reed. As mentioned in the question, the tube or the body of the instrument is the column of open air. In a wind instrument, the reed placed at the end of the instrument causes resonance. The reed is placed under the mouthpiece of the instrument. In this way, when the musician blows into the mouthpiece, the air is blown is through the reed. As the air is blown through the reed, the reed starts to vibrate which creates a wide range of tremoring frequencies. Resonance occurs when the vibration of the reed is equivalent to the vibration of the air column inside the metal tube (the body of the instrument) just like the tuning fork and tube. When the frequencies match (supercrest/supertrough), the instrument produces a loud noise. The length of the tube is changed by opening and closing the holes on the instruments. When the tube is shortened, it results in a shorter wavelength and according to the wave equation a shorter wavelength means a higher frequency. This means that the more holes that are covered, the shorter the tube resulting in a higher pitch. So, when there are no holes covered the tube of the instrument is at its highest length which creates a low pitch sound.