Physics IA: Band Frequencies
Design:
Aspect 1:
Research Statement:
We tested how frequency changes with change in band length. We measured, with a ruler, the
length the band was stretched, while keeping the same original length (the same fraction of the
rubber band the whole time) our independent variable. We measured how the varying band
lengths affected the frequency of the band when plucked, our dependent variable. To control the
experiment to ensure its veracity, we maintained the same band throughout the experiment,
used the same stationary microphone, measured with the same sound recording system,
utilized the same devices used to keep the band at a specified distance and pulled the band
back at the same distance to determine actual frequency. Throughout the experiment, we
realized it was imperative to continue using the same materials and the same experimenter to
ensure our results’ validity.
Aspect 2:
List of Controlling Variables:
28 cm rubber band (value unstretched)
vocal or instrument microphone and cable
tuner able to read the signal from the microphone (we did this through a computer)
tape
hook to pull rubber band back
stationary ruler
stationary object to keep band isolated at one end
movable hockey puck used to keep band stationary (with line drawn vertically to ensure correct
measurement)
Aspect 3:
First, we set up the experiment. To do so, we placed a rubber band around a bolted
piece of plastic and a movable hockey puck. The rubber band was at the same height
between the two. Then, we placed a microphone with very high gain, being held by a
music stand, directly above the rubber band to increase the sound received and
therefore get a more accurate reading. Next, to ensure precision in measurement, we
taped a ruler directly next to the band. After that, we used another measuring device to
mark out a specific distance that we would pull the band out to. Each trial proceeded in
the following manner. First, we would finitely measure the distance the band was
stretched e.g. our first trail was at (10 ± .05) cm. Then, with a hook, one of us pulled the
rubber band back to a point we had previously measured out and designated (kept
constant through each band length) and let go. The ensuing sound was then measured
using an Apple computer tuner. For each band length, to increase the accuracy of our
results, we enacted 5 trials. The tuner would give measurements in cents with regards
to notes, so we then used audio verification to determine the octave the notes were
being played in and used a chart to find the exact frequencies. Cents is the distance in
between two notes out of one hundred (cents divided by one hundred divided by the
difference of the note frequencies added to or subtracted to the accepted frequency,
dependent upon whether the note was sharp or flat, respectively).
Computer and tuner
The ruler would be taped on the table in the real trials, along with a line on the puck to ensure
exact distance, and a mic hanging about two inches overhead. This picture simply illustrates the
pull back and the rubber band.
Data Collection and Processing
Aspect 1:
10.0
15.0
20.0
25.0
30.0
Trial 1
102.96 95.80 88.04 85.20 79.96
Trial 2
104.57 95.03 87.73 84.13 76.60
Trial 3
104.14 94.98 87.52 83.73 77.21
Trial 4
103.71 95.53 87.21 83.64 77.26
Trial 5
102.72 94.70 87.26 83.59 77.21
avg value in Hz
103.62 95.21 87.55 84.06 77.65
Uncertainty Range/2
0.92
0.55
0.41
0.81
Uncertainty Without outlier
Instrument uncertainty *
Total Uncertainty (MAX)**
1.68
0.33
0.29
0.29
0.29
0.29
0.29
1
1
1
1
1
The value for trial one when stretched to 30cm can be discarded for it is possible that this one
was not correctly recorded for the rubber band was slightly shorter than it should have been
with the round hockey puck. Judging from the precise nature of our other results, we concluded
this error was random and inconsequential within the whole of the experiment.
*Instrument uncertainty is calculated by the greatest difference between musical notes
multiplied by the uncertainty in cents (5 cents or 5%) which is equal to .29 Hz
**The total uncertainty can be calculated by the sum of the highest range/2 and the instrument
uncertainty (equals 1.2) rounded to one significant figure (1).
Slope (line of best fit): (*1.29 ± .327 Hz/cm)
Slope (line of best fit): (*1.29 ± .327 Hz/cm)
Conclusion and Evaluation:
Aspect 1:
Instrument uncertainty:
ruler (± .05 mm)
Tuner (± 5 cents or 0.3 Hz)
We can conclude that the downward progression of the data signifies that as the length
of the band increases, the frequency emitted decreases in Hertz. The fade or
deterioration of the rubber band’s elasticity had some effect and would be classified as
systematic error. Also, the length in this rubber band had more of an effect on the
frequency than the tension did, resulting in a lower frequency.
Aspect 2:
Throughout the duration of the experiment, we attempted to mitigate the uncontrollables to
improve our experiment’s validity. For example, we conducted the experiment in the quietest
room possible. However, background noise could have affected our sound measurements.
Another uncontrollable aspect of our experiment was our rubber band. After each trial, our
rubber band would lose elasticity and as a result produce a lower frequency. This can even be
shown throughout the trials and each trial is a lower frequency. Also, each resultant value would
differ based on the force exuded by the experiment who pulls the band back. Again, to lessen
the error between each trial, we used an apparatus to hold the band in place and simply let go.
Furthermore, each measuring device has instrument uncertainty. The uncertainty in the
microphone and frequency reader could seriously affect our results as our experiment is based
on the change in frequency. Also, unintended movement in the hockey puck, microphone, band
or ruler could also affect the way in which our experiment was conducted.
Aspect 3:
To improve our experiment, we should have changed our materials in order to keep the
controlling variables still. For example, the hockey puck could have moved during a trial
without us seeing. To guard against the band’s deterioration of elasticity, we could have
used a different band, of the same makeup, for each trial. Also, we should have pulled
the rubber band to another stationary object and released it from said object, or used a
clamp of some sort. Sometimes during the trials, it appeared that the force the
experimenter exuded on the band when releasing caused the band to push forward,
thus interrupting its natural frequency. We also could have improved our experiment by
using a soundproof room and having higher quality measuring recording equipment
which would remove much of the instrument error evident in our experiment. Using an
instrument to pull back and let go would erase this systematic error. Judging from the
precise nature of our results, this experiment would be easily reproduced and anyone
who did reproduce would find the same result. To minimize the amount of fade we could
have used a new rubber band each trial. This would remove the obvious systematic
error. Overall, even with our limited experience and equipment, our experiment provided
us with precise, telling results and can be used to learn about frequency and rubber
band behavior.