This experiment studied standing waves by measuring the length of an air column needed in a tube for a sound to be heard from different tuning forks. The length increased as the tuning fork period increased. A linear relationship was found between the tuning fork period and average air column length. The experiment could be improved by using more tuning forks and tubes of varying diameters to collect more data points and analyze additional variables.

1. Kelsey Noah
Period 3
Frequency
Introduction:
In the experiment sound waves were studied, in particular, standing waves. A standing
wave is a wave that vibrates up and down in place. For example, if a string is held at both ends, it
can be made to move up and down, but the wave does not move down the string. A wave moving
down the string is called a traveling wave. The points where the string is held never move, these
are fixed points and are called nodes. Halfway between the nodes are the antinodes or points of
the highest motion.
If the same string is taken and tied to a pole, the end attached to the pole is considered a
fixed end. If the string is shaken, a wave moves down the string, but when it hits the fixed end it
cannot move, so it sends an inverted reflected wave back. If the string is then held on one end
and the other end is loose, then the loose end generates a free end reflection. For example if the
sting is shaken, a reflected (none inverted wave) is sent back when it reaches the loose end of the
string.
Sound is a series of waves that move through air or other materials. As matter vibrates, it
causes the surrounding air to vibrate. The experiment shows how sound travels through a tube,
which as it vibrates causes, the air around it to vibrate and creates sound. Some materials as
water can be used to reflect the sound.
At the start of the experiment, a tube was put inside a graduated cylinder filled with water
and placed different turning forks above the tube. The tube was pulled the tube until a sound
could be heard. While the tube was in water, the water reflected the waves being formed in the
tube by the tuning fork. The bottom of the tube was the standing wave node. As the tube was
pulled from the water, the water reflected the waves more until eventually a sound could be
heard. When the sound was heard, the length of the tube was measured. The measurement was
close to where the antinodes are found. The length is not exactly equal to the antinode, because a
slight constant above the tube had to be accounted for.
The purpose of this experiment was to find how the frequency of a tuning fork effects the
length of the air column needed for the first harmonic. If the tuning fork period increases, then
tube has to be pulled out of the water more before a sound can be heard.
Using the wave equation
Equation 1: v=f*λ
And the equation for frequency
Equation 2: f= 1/T
It can be seen that
Equation3: 1/4λ= L + C
Because it is only one-quarter wavelength inside the tube when the sound is heard. Then final
equation for the experiment can be found to be
Equation 4: L=(v/4)*T-C.

2. The final equation in the experiment goes with the graph of tuning fork period in the x axis and
length of the tube out of water in the y-axis.
Procedures:
1. A graduated cylinder was filled with water and a tube was placed inside.
2. A tuning fork was hit and held above the tube.
3. The tube was then pulled out of the water until a sound was heard.
4. The length of the tube out of the water was then measured with a ruler.
5. Three trials were recorded for each tuning fork.
6. Steps 2 through 5 were repeated for three more tuning forks.
The type of tube, the amount of water in the graduated cylinder, the temperature, and the
diameter of the tube were controlled variables in this experiment. These were kept constant by
using the same tube for each trial, keeping the same amount of water, and taking the temperature
of the inside of the tube. The manipulated variable was the frequency of the tuning forks being
used, and this was measured by looking at the values on the side of the tuning fork. The
responding variable was the length of the air column, which was measured with a ruler. The
range of tuning fork frequency ranged between 329.6 Hz to 1024 Hz. Also three trials were
conducted for each frequency.
Image 1: Diagram of experimental setup

3. Data Collection:
Table 1: Frequency of tuning fork compared to the length at which the tube
resonates
Frequency (+/- 0.1 Length (+/- 1.9 mm)
Hz) Trial 1 Trial 2 Trial 3 Average Length
329.6 27.1 30.2 29.4 28.9
392.0 22.4 22.6 22.6 22.5
523.3 15.3 16.3 16.3 16.0
1024.0 29.9 26.1 26.8 27.6
Table 1: Half the largest difference in measurements in the trials was used as the uncertainty.
Image 2: Plot of frequency of tuning fork (x-axis) vs. average air column height
Table 2: Average air column length vs. Period of Tuning Fork
Average Length (cm) Period (seconds)
28.9 0.003034
22.5 0.002551
16.0 0.001911
27.6 0.000977
Image 3: Plot of period of tuning fork (x-axis) vs. average air column length.

4. Image 3: A linear equation can be used to represent the relationship.
Linear Fit: y=mx+b
m (slope) = 1.142E+04 cm/s
b (y intercept) = -6.060 cm
Final Equation
y = (1.142E+4)x – 6.060
Sample Calculations:
Sample for finding the average air column height when using a tuning fork with frequency of
329.6 Hz
Equation 5: (27.1 + 30.2 + 29.4)/3 = 28.9 cm. (average air column length)
Sample Period Calculation for frequency of 329.6 Hz
Equation 6: 1/329.6 Hz = 0.003034seconds (period of tuning fork)
Conclusions:
The experiment demonstrated how standing waves work, the relationships between the
average air column height when a sound can be heard versus a tuning forks frequency and period,
and how to determine an equation to represent these relationships. Image 2 shows that as the
tuning fork frequency increases, the length of the average column height increases before the
sound is heard. Image 3 shows that as the tuning fork period increases, the length of the average
column height increases before the sound is heard. Linear equations can be used to represent the
data in the graphs. Only 3 of the 4 data points were used in the experiment. The 4 th data point
with a tuning fork frequency of 1024 Hz was not used, because the frequency is the second

5. harmonic and falls outside of the data trend.
Evaluating Procedures:
The limitations in the experiment were the number of tuning fork used. Additional
tuning forks would allow for more data points collected and the experiment would be more
reliable compared to only having three data points. The other limitation was only using one tube
so it cannot be determined how different diameters affect the results.
Improving the Investigation:
The investigation could have been improved by providing a larger number of tuning forks
in order to gather additional data. Adding additional tubes with different diameters would also
help analyze different variables.