E303 - Kundts.docx

Analysis In this experiment we tackled the “Kundt’s Tube: Velocity of Sound in Solid”. Our objective is to determine the velocity of sound inside a metal rod and to determine the speed of sound in the tube using the idea of resonance. Through longitudinal wave we produce nodes as a fundamental mode of vibration. However,” longitudinal waves the displacement of the medium is parallel to the propagation of the wave. A wave in a "slinky" is a good visualization. Sound waves in air are longitudinal waves” [1]. Through experimentation we first determined the length of the rod which is 92 cm, and then we get the average length of segments produced and temperature of air by putting the thermometer at the opening of the tube. After getting the fundamental values that are going to be used in this experiment we then have to determine the velocity of sound in air through the equation: 𝑉𝑎 = 331.5m/s + (0.6 ∗ t)m/s Where in our data: 𝑉𝑎 = 348.3m/s. After getting Va we the needed to find the velocity of sound in rod by using the other equation: Vr = Va (

Lr ) La

Input Data: 𝑉𝑟 = 348.3 (

92 ) 10

𝑉𝑟 = 3204.36 m/s The actual velocity of sound is: 3475 m/s We then needed to find the percentage error of the velocity of sound in rod through the equation: 𝐴𝑉−𝐸𝑉

% error = |

𝐴𝑉

| 𝑥 100

3475−3204.36

% error = |

3475

| 𝑥 100

% error = 7.78 %

But then we still have to compute the velocity of sound using the 4th equation which involves Young’s modulus of rod and the density of rod which is:

𝑉𝑟 = √

𝛾 𝜌

where: 𝛾 = 9.1 𝑥 1010 𝑁/𝑚2 𝜌 = 8400 𝑘𝑔/𝑚3 Input Data: 9.1 𝑥 1010 √ 𝑉𝑟 = 8400 𝑉𝑟 = 3291.403 𝑚/𝑠 Computing for percentage error 3475−3291.403

% error = |

3475

| 𝑥 100

% error = 5.28 % By obtaining a less than 10% of percentage error as a confidence level, the experiment that we performed has satisfied the objective.

Error Analysis In this experiment there wasn’t much of error that occurred but basically some error maybe met by not obtaining enough nodes inside the tube. By following the procedure that was instructed to us we have immediately finished the experiment in time and some of our data where somewhat correct.

Conclusion Therefore in this experiment upon determining the velocity of sound in the rod and the tube there must be a great force applied into the rod in order to produce resonance that will trigger the velocity of sound inside the tube that will move the powder and make enough nodes to satisfy the data needed. The first result of the velocity that we obtained by using Eqn. 3 is 3204.36 m/s which is near to the actual value of sound from the textbook which is 3475 m/s that results to a less than 10% of percent error which is 7.78%. And by using Eqn. 4 in the next part that involve Young’s Modulus of Rod and the density of Rod, we obtained a velocity of 3291.403 m/s which is also near to the actual value 3475 m/s that results to a percentage error of 5.28%. Overall, through the propagation of sound in air by means of longitudinal waves the frequency of sound and speed of sound can be determined. Application In my field of study as an Industrial Engineer, the idea of velocity of sound in solid plays a focal part wherein in order for us to run a machine or produce a certain product, frequencies from the different part of machine must run in a certain limit that will not damage the product and through also through communication, if we operate in some areas where the sound of environment is very noisy like the welding of cars, cutting of wires and rods. These are just some of the application of the Kundt’s Tube: Velocity of Sound in solid, but there are more out there and I think that it will help a lot especially in the field of engineering.

Reference [1]

Transverse Waves. (n.d.). Retrieved from http://hyperphysics.phyastr.gsu.edu/hbase/Sound/tralon.html

[2]

(n.d.). Retrieved from http://hyperphysics.phy-astr.gsu.edu/hbase/Class/PhSciLab/kundt2.html