For the first part in this experiment, the purpose was to find the length of the pipe by applying the concept of speed sound. To be more specific, the length of the pipe had to be found without using the ruler to measure it. The tools which were used in this experiment were the pipe for creating the sound, the microphone for detecting the sound, and the Logger Pro to record the data. In order to find the lengh of the pipe, the pipe had to be spun in a slow speed (but the sound had to loud enough to be heard). Then the sound would be detected by the microphone and be sent to Logger Pro to get recorded. Since the length of the pipe is always constant and in order to calculate it, the pipe had to be spun with a higher speed, thus created a different frequency. This sound would then become the next scale, which also reffered to the next level of the tone, or it could also be called as the first overtone. The reason that the sound was to be believed as the next scale was because if one sclae was skipped(which is the third level of the tone), then the sound would not be heard as a clear sound but a mixed different level of the sounds.
Data and Analysis:
Recorded Data:
Pipe’s spinning speed
|
ω (rad/s)
|
Slow
|
3859±0.9736
|
Fast
|
5068±1.016
|
After obtaining the angular frequency (since the pipe was spun so it had a centripital acceleration), the equation v=λf, then the equation was rearranged to be λ=f/v, where f=2πω, and the v is the speed of sound, as well as 343(m/s). Since two different frequencies were obtained, so then two different wavelengths would also be calculated, one of the wavelengh would represent the first note (n/2), and the second would represent the next level of the tone(n+1)/2, which was the second note. (n/2)*λ=(n+1)/2*λ since the lenght of the pipe is constant, and n could be calculated with this equation. After obtaining n, substitue the value into either of the equations above, then the lengh of pipe could eventually obtained.
Calculated Data:
Pipe’s spinning speed
|
Frequency (Hz)
|
λ (m)
|
Slow
|
614.18
|
0.558
|
Fast
|
806.60
|
0.425
|
Pipe’s spinning speed
|
Lengthmeasured(m)
|
Lengthexperimental(m)
|
Percent error (%)
|
Slow
|
0.800
|
0.837
|
4.63
|
Fast
|
0.850
|
6.25
|
Length=First note:(n/2)*λ=(n/2)*v/k=(n/2)*v/(ω/2π)=(n/2)*2πv/ω
or=Second note:((n+1)/2)*λ=((n+1)/2)*v/k=((n+1)/2)*v/(ω/2π)=((n+1)/2)*2πv/ω
U_L = √[(∂L/∂*uω)^2]= First note: √[n*(2π/ω^2)*uω]^2
=Second note: √[(n+1)*(2π/ω^2)*uω]^2
Pipe’s spinning speed
|
Lengthuncertainty(m)
|
Slow
|
5.70x10^-6
|
Fast
|
3.91x10^-6
|
As a result, even with the uncertainty, the percent error could not be reduced. However, on the other side, the length of pipe obtained from both trials which were conducted with different speed had percent error less than 10%. This showed us that the length of the pipe could be calculated by measuring its angular frequency with the application of the sound's speed, hence obtaining the expected results without actually measuring it. If the factor which produced the error in this experiment, the error could be contributed by the temperature, or the flexibility of the pipe. With higher temperature, the speed of the sound might have a higer value. As for the flexibility of the pipe, the pipe could be stretched more when being spun due to the centriputal force. Therefore, if all the factors of errorness could be taken into consideration and got rid of, the results for the lengh of the pipe would definetely be closer to the measured value.
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