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Experiment 304: Kundt’s Tube: Velocity of Sound in Solid Raagas, Michelle Mae G. School of Chemical Engineering, Chemistry, Biological Engineering, and Material Science Engineering Mapua Institute of Technology, 658 Muralla St., Intramuros, Manila City, Philippines [email protected]

OBJECTIVE: The main goal of this experiment is to determine the velocity of sound precisely in a metal rod. In addition, it also aims to distinguish the behavior of sound waves also its motion using the principles of resonance. We wishes to discuss the relation of the velocity of sound and the wave length using the concept of resonance and prove it by performing the experiment.

Before performing the experiment, set-up the apparatus. But in our class, it is already arranged. There are powder inside the kundt’s tube which will made the waves and the center of the rod are properly clamp. Also, the rag has a rosin already. First thing to do is to get the temperature, it is needed to know the velocity of sound in air. Then, measure the length of the rod from the center to the other end. This experiment has a one simple step, it is to stroke the rod with the metal sample using the rag with rosin in it. See figure 2

METHODOLOGY: For the experiment to be successful, we will be using materials that are related to it. It will help us to acquire data that we will need later for the computations. See figure 1

Figure 2. stroking of metal rod Figure 1. Materials that are needed in the experiment (kundt's tube apparatus, meter stick, cloth, thermometer, rosin, lycopodium powder)

Expect a high pitch sound and vibration inside the tube. Repeat the stroking of the rod until it forms a wave. Be sure that the powder inside the kundt’s tube is enough as well as the rosin in the jar because it

sharpen the friction on the rod to be able to produce wave to encounter less errors in this experiment. See figure 3

After the gathering of all the data, you are now able to compute for the velocity of sound in the metal rod using the two equations. L

Vr = Va (Lr )

(equation 1)

a

𝛾

𝑉𝑟 = √𝜌

(equation 2)

And compare it to the actual value of the velocity of sound in a metal rod which is 3475 m/s. Figure 3. Formed waves After the formation of waves, measure the length of its segment. See figure 4 and 5

Figure 4. measuring the segment

DATA and SAMPLE COMPUTATIONS KUNDT’S TUBE: VELOCITY OF SOUND IN SOLID 91.5 cm Length of metal rod, 𝐿𝑟 Average Length of powder 9.3 cm segment, 𝐿𝑎 Temperature of air, t 27 ℃ 348.2 m/s Velocity of sound in air, 𝑉𝑎 m/s Velocity of sound in the rod, 𝑉𝑟 3425.84 from equation 3 m/s Velocity of sound in the rod, 𝑉𝑟 3475 from textbook Percentage error 1.41 % Density of the rod, 𝜌 8700 g/𝐜𝐦𝟑 m/s Velocity of sound in the rod, 𝑉𝑟 3390.32 from equation 4 Percentage error 2.44 % Sample computation: 𝑽𝒓 from textbook = 3475 m/s Va = 332

m

+ 0.6(27) = 348.2 m/s

s

Lr Vr = Va ( ) La 91.5

= 348.2( 9.3 ) = 3425.84 m/s (from eq. 3) 3425.84−3475

% error = |

9.1𝑥1010

𝛾

| 𝑥 100 = 1.41%

3475

𝑉𝑟 = √𝜌 = √

8700

= 3390.32 m/s (from eq. 4)

3390.22−3475

Figure 5. Length of the segment

% error = |

3475

| 𝑥 100 = 2.44 %

GRAPH

CONCLUSION The two objectives of this experiment was attained which is to determine the velocity of sound precisely in a metal rod and to distinguish the behavior of sound waves and its motion. It is accomplished by performing the experiment through the given instructions by our professors and by the laboratory manual that is provided.

Velocity of sound Vs. Wavelength Velocity of air

WAVELENGTH (M)

98 96

95.96 94.54

94

93.16

92

91.82 90.51

90 88

We also are able to discuss the relationship of the velocity of sound and the wave length and by the graph that I prepared, I observed that as the wavelength increased, the velocity of sound decreases.

86

Graph 1. The relationship between the wavelength and the velocity of sound.

By performing this experiment, I therefore conclude that the velocity is directly proportional to the frequency times the wave length. It is also directly proportional to the young’s modulus and inversely proportional to the given density of a material.

ANALYSIS OF DATA

ACKNOWLEDGMENT

Based on our gathered data, we observed that we encountered less percentage errors. Since the kundt’s tube is the main apparatus that is designed for this type of experiment, the results that are taken are more precise. Also, everything is already setup inside the tube, all we have to do is to stroke the metal using the rod with rosin in it. As I said earlier, the powder inside the tube must be enough to produce waves. Unlike on our group’s tube, we are lack in powder so we have to borrow other group mate’s kundt’s tube. On the other hand, by using the second equation on determining the velocity of the sound in a solid we also had a small percentage error it is because we didn’t use any of our gathered data to compute it for the density and young’s modulus of a metal is constant.

I would like to thank everyone for making this experiment possible. First, to our professor Mr. Ricardo De Leon for explaining the process of this experiment and for suggesting best kundt’s tube in our class for us to be able to borrow it. To my groupmates Ferdinand Almoite, Liam Domingo, Jonen Ibañez, Joshua Mariñas, and Rodrigo Patches, thank you for the cooperation and for taking such an effort for this experiment especially to Rodrigo for the demo, we enjoyed that part and Jonen for helping me in organizing the data that we gathered and for the computations. I would also like to thank the lab assistant for assisting and for proving us the materials that we need. Lastly, I would like to thank the third group for their kindness for letting us borrow their kundt’s tube. Thank you so much !

Using the first equation is more reasonable for me since it is determined using the gathered data by performing our experiment unlike in the second equation because the main goal of this experiment is to determine the velocity of sound in solid experimentally.

REFERENCES

332

337 342 VELOCITY (M/S)

347

352

[1] Halliday, F., Fundamentals Of Physics, 9th Edition, 2011 [2] Kinsler, F., The Quantification of Sound and the Wave Equation, pg 99-111

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OBJECTIVE: The main goal of this experiment is to determine the velocity of sound precisely in a metal rod. In addition, it also aims to distinguish the behavior of sound waves also its motion using the principles of resonance. We wishes to discuss the relation of the velocity of sound and the wave length using the concept of resonance and prove it by performing the experiment.

Before performing the experiment, set-up the apparatus. But in our class, it is already arranged. There are powder inside the kundt’s tube which will made the waves and the center of the rod are properly clamp. Also, the rag has a rosin already. First thing to do is to get the temperature, it is needed to know the velocity of sound in air. Then, measure the length of the rod from the center to the other end. This experiment has a one simple step, it is to stroke the rod with the metal sample using the rag with rosin in it. See figure 2

METHODOLOGY: For the experiment to be successful, we will be using materials that are related to it. It will help us to acquire data that we will need later for the computations. See figure 1

Figure 2. stroking of metal rod Figure 1. Materials that are needed in the experiment (kundt's tube apparatus, meter stick, cloth, thermometer, rosin, lycopodium powder)

Expect a high pitch sound and vibration inside the tube. Repeat the stroking of the rod until it forms a wave. Be sure that the powder inside the kundt’s tube is enough as well as the rosin in the jar because it

sharpen the friction on the rod to be able to produce wave to encounter less errors in this experiment. See figure 3

After the gathering of all the data, you are now able to compute for the velocity of sound in the metal rod using the two equations. L

Vr = Va (Lr )

(equation 1)

a

𝛾

𝑉𝑟 = √𝜌

(equation 2)

And compare it to the actual value of the velocity of sound in a metal rod which is 3475 m/s. Figure 3. Formed waves After the formation of waves, measure the length of its segment. See figure 4 and 5

Figure 4. measuring the segment

DATA and SAMPLE COMPUTATIONS KUNDT’S TUBE: VELOCITY OF SOUND IN SOLID 91.5 cm Length of metal rod, 𝐿𝑟 Average Length of powder 9.3 cm segment, 𝐿𝑎 Temperature of air, t 27 ℃ 348.2 m/s Velocity of sound in air, 𝑉𝑎 m/s Velocity of sound in the rod, 𝑉𝑟 3425.84 from equation 3 m/s Velocity of sound in the rod, 𝑉𝑟 3475 from textbook Percentage error 1.41 % Density of the rod, 𝜌 8700 g/𝐜𝐦𝟑 m/s Velocity of sound in the rod, 𝑉𝑟 3390.32 from equation 4 Percentage error 2.44 % Sample computation: 𝑽𝒓 from textbook = 3475 m/s Va = 332

m

+ 0.6(27) = 348.2 m/s

s

Lr Vr = Va ( ) La 91.5

= 348.2( 9.3 ) = 3425.84 m/s (from eq. 3) 3425.84−3475

% error = |

9.1𝑥1010

𝛾

| 𝑥 100 = 1.41%

3475

𝑉𝑟 = √𝜌 = √

8700

= 3390.32 m/s (from eq. 4)

3390.22−3475

Figure 5. Length of the segment

% error = |

3475

| 𝑥 100 = 2.44 %

GRAPH

CONCLUSION The two objectives of this experiment was attained which is to determine the velocity of sound precisely in a metal rod and to distinguish the behavior of sound waves and its motion. It is accomplished by performing the experiment through the given instructions by our professors and by the laboratory manual that is provided.

Velocity of sound Vs. Wavelength Velocity of air

WAVELENGTH (M)

98 96

95.96 94.54

94

93.16

92

91.82 90.51

90 88

We also are able to discuss the relationship of the velocity of sound and the wave length and by the graph that I prepared, I observed that as the wavelength increased, the velocity of sound decreases.

86

Graph 1. The relationship between the wavelength and the velocity of sound.

By performing this experiment, I therefore conclude that the velocity is directly proportional to the frequency times the wave length. It is also directly proportional to the young’s modulus and inversely proportional to the given density of a material.

ANALYSIS OF DATA

ACKNOWLEDGMENT

Based on our gathered data, we observed that we encountered less percentage errors. Since the kundt’s tube is the main apparatus that is designed for this type of experiment, the results that are taken are more precise. Also, everything is already setup inside the tube, all we have to do is to stroke the metal using the rod with rosin in it. As I said earlier, the powder inside the tube must be enough to produce waves. Unlike on our group’s tube, we are lack in powder so we have to borrow other group mate’s kundt’s tube. On the other hand, by using the second equation on determining the velocity of the sound in a solid we also had a small percentage error it is because we didn’t use any of our gathered data to compute it for the density and young’s modulus of a metal is constant.

I would like to thank everyone for making this experiment possible. First, to our professor Mr. Ricardo De Leon for explaining the process of this experiment and for suggesting best kundt’s tube in our class for us to be able to borrow it. To my groupmates Ferdinand Almoite, Liam Domingo, Jonen Ibañez, Joshua Mariñas, and Rodrigo Patches, thank you for the cooperation and for taking such an effort for this experiment especially to Rodrigo for the demo, we enjoyed that part and Jonen for helping me in organizing the data that we gathered and for the computations. I would also like to thank the lab assistant for assisting and for proving us the materials that we need. Lastly, I would like to thank the third group for their kindness for letting us borrow their kundt’s tube. Thank you so much !

Using the first equation is more reasonable for me since it is determined using the gathered data by performing our experiment unlike in the second equation because the main goal of this experiment is to determine the velocity of sound in solid experimentally.

REFERENCES

332

337 342 VELOCITY (M/S)

347

352

[1] Halliday, F., Fundamentals Of Physics, 9th Edition, 2011 [2] Kinsler, F., The Quantification of Sound and the Wave Equation, pg 99-111

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