Kundt’s Tube: Velocity of Sound in Solid

METHODOLOGY
Two experiments were done last time due to some circumstances that made the class to lack time and to be late compared to the official class syllabus. The students were able to accomplished the job by equally dividing the time into two. The first experiment was about Kundt’s tube. In this experiment, longitudinal sound waves will be produced in a metal rod and an air column. Using the properties of wave motion , the frequency of the sound and the speed of sound in the rod can be determined.

For this experiment setup, following materials are needed such as a Kundt’s tube apparatus, a meter stick, a piece of cloth, a thermometer, rosin, and lycopodium powder.

This experiment was done fast because of the fact that some of the procedures like placing a thin layer of lycopodium powder at least two millimetres wide as uniformly as possible inside the tube along its entire length was done already for us by the laboratory assistants. Then, a stopper was inserted in the end of the tube. Then, with the rod securely clamped at its center, the glass tube was positioned so that the disk on the end of the rod is a few centimeters within the tube and centered with respect to the sides. Before proceeding, the rod was confirmed to be at the right position by measuring the rod and make sure that it was clamped at the center as seen on Figure 1.

Figure 1: Measuring the length of the rod in order to confirm that it is clamped at the center.

A small amount of the rosin was placed on a piece of leather cloth or chamois skin. Gripping the rod with the rosined leather, it was pulled toward the end of the rod as seen on Figure 2.

Figure 2: Stroking the rod back and forth

The students avoided pulling the cloth completely off the rod because by doing so it will set up transverse waves in the rod and may break the glass tube. At first try, the students failed to do the right technique or form in order to produced the right vibrations. But after doing it for many times, the students finally done it without ease and produced satisfactory vibrations. Afterwards, the glass tube was rotated a short distance one way or the other while continuing the stroking until the most distinct dust heaps are obtained. The distance between successive powder heaps is difficult to measure accurately because the exact center of the dust heap cannot be ascertained definitely. However, a good average was obtained by the students by measuring the distance over a large number of powder heaps as possible and dividing by this number as seen on Figure 3.

Figure 3: Measuring the length of the segments

It was found that twice this value is the wave length of the sound. After doing so, the room temperature was recorded and the velocity of sound in air at the found temperature was calculated. The frequency of the sound was found using Equation 1.

V = f λ(Equation 1)

The velocity of sound in the metal rod was computed using Equation 3

(Equation 3)

For the second time, the velocity of sound in the metal rod was computed but using a different equation which is Equation 4
(Equation 4)

Then, we compared the results with the textbook values.

Figure 4: Figure shows the overall setup along with all the names of the materials used.

DATA AND RESULTS
KUNDT’S TUBE: Velocity of Sound in Solid
Length of metal rod, Lr
91.5 cm
Average length powder segments, La
10 cm
Temperature of air, t
26 oC
Velocity of sound in air, Va
347.6m/s
Velocity of sound in the rod, Vr
From Equation 3
3180.54m/s
Velocity of sound in the rod, Vr
From textbook
3475 m/s
Percentage error
8.47 %
Density of the rod, p
8400m/s
Velocity of sound in the rod, Vr
From Equation 4
3291.40m/s
Percentage error
5.28 %

The table above shows the results found by using the gathered data through the experiment. The velocity of sound in air Va was computed using Equation 2.

Vair = 332 m/s + 0.6t(Equation 2)

Where t is the temperature. We can conclude that when the temperature increases, the velocity of sound in air also increases. Therefore, the temperature is directly proportional to the velocity of sound in air. Comparing the velocity of sound in the rod and the velocity of sound in air, the velocity of sound in the rod is greater than the velocity of sound air since the molecular arrangement of solids are very much compact that allows the waves to easily travel along the medium. The molecular arrangement of gases is far apart from each other. Because of this, it makes it hard for the wave to travel the energy from one particle to the other thus allowing the velocity of the sound to move slower.

SAMPLE COMPUTATION
Given:

Length of metal rod, Lr = 91.5 cm
Average length powder segments, La = 10 cm
Temperature of air, t = 26 ­­oC
Young’s Modulus of rod, = 9.1 x 1010
Density of the rod, p = 8400 m/s

Solution:

For Velocity of sound in air, using

For Velocity of sound in the rod using equation 3:

For Velocity of sound in the rod from textbook:

For percentage error of velocity of sound in the rod from equation 3 and velocity of sound in the rod from textbook:

For Velocity of sound in the rod using equation 4:

For percentage error of velocity of sound in the rod from equation 4 and velocity of sound in the rod from textbook:

DISCUSSION
The overall experience was not that enjoyable and it was quite messy to begin with. The students are not able to actually experience the experiment since the given apparatus by the department was broken. But observing other groups performing the experiment, I can see that it was really hassle to perform since it is indeed perform by man power, and it sounds really annoying and hurting to the ears. I regret the time we have to perform the experiment since ours is broken and we are just observing. I wish the physics department to buy new sets of equipments for the said experiment and rather choose a more modern apparatus to be use to demonstrate more easily the theory.

Kundt’s tube is an acoustical apparatus, invented by German Physicist, August Kundt. Knowing the speed of sound in air, the speed of sound V in a solid rod can be calculated based on the measurement of sound wavelength, λ. If the frequency of the sound wave. Sound is a mechanical wave that results from the back and forth vibration of the particles of the medium through which the sound wave is moving. If a sound wave is moving from left to right through air, then particles of air will be displaced both rightward and leftward as the energy of the sound wave passes through it. The motion of the particles is parallel and anti-parallel to the direction of the energy transport. This is what characterizes sound waves in air as longitudinal waves.

With regards to the experiment, the Kundt’s tube experiment is a demonstration of a standing wave. We can conclude that the velocity of sound in air is directly proportional to the temperature of the medium. The propagation of sound in solids differs with the propagation of sound in a liquid or a gas. When a longitudinal wave is propagated in a solid like a rod, the solid expands sideways slightly when it is compressed due to the property of the sides of a solid to freely bulge and shrink a little as the wave travels. The propagation of sound in gas like the air differs as that of the solids. The bulk modulus of a gas depends on the pressure of the gas. The greater the pressure applied to a gas, the more it resists further compression and the greater the bulk modulus. Through data gathering and experimentation the hypothesis is indeed true.

The possible cause of errors and inaccuracy of the experiment must be the following: The measuring of the temperature since the room the room is constantly changing because the room is installed with aircondition. The measuring of the segment since it is really hard to accurately measure powder which is unclear to see and the powder inside the tube is many compared to what it should be. Lastly is the placement of the rod, somehow it might not be at the very center or at the right location.

CONCLUSION
The objectives of this experiment is to determine the velocity of sound in a metal rod and to determine the speed of sound in the tube applying the principles of resonance. Through experimentation and data gathering, the students determine the velocity of sound in a metal by using two equations. The first equation is where, Va is the velocity of sound in air, Lr is the length of the metal rod and La is the average length powder segments. The students have calculated and solved the results by basing or applying the principles of resonance.

Musical instruments are set into vibrational motion at their natural frequency when a person hits, strikes, strums, plucks or somehow disturbs the object. Each natural frequency of the object is associated with one of the many standing wave patterns by which that object could vibrate. The natural frequencies of a musical instrument are sometimes referred to as the harmonics of the instrument. An instrument can be forced into vibrating at one of its harmonics with one of its standing wave patterns if another interconnected object pushes it with one of those frequencies. This is known as resonance. When one object vibrating at the same natural frequency of a second object forces that second object into vibrational motion.

ACKNOWLEDGMENT
First of all, I want to thank our Almighty God for without Him all of this are not possible.

I gratefully acknowledge the important contributions and guidance provided by the following members of Group 5:

Joren Angeles, for the computations and listing of records of the experiment. Eleazar Carlo Parazo, for the setup and photo records of the experiment. James Ramirez, for performing and maintaining the cleanliness of the experiment Emil Salazar, for performing and for the laughter.

John Yambing, for the computations and for his MS Excel expertise.

Lastly, I would love to express my gratitude to our hardworking Professor, Mr. Ricardo De Leon, who guided us and gave us encouragement on times of problems.

REFERENCES
[1] R.A. Serway and J.W. Jewett, Physics for Scientists and Engineers, 6th Ed. (Thomson, Belmont, CA, 2004), pp. 100-102 [2] Beiser, Arthur, Concepts of Modern Physicss, 5th Ed., McGraw-Hill, 1995 [3] Halliday and Resnick, Fundamentals of Physics, 9th Ed., Wiley 2011 [4] Laboratory manual, General Physics 3, Department of Physics, Mapúa Institute of Technology [5] Padua, A., Practical and Explorational Physics, 2003