e304

ANALYSIS OF DATA I

INTRODUCTION

Sound is a mechanical wave specifically longitudinal wave which is created by vibrating an object and travels through a vibrating medium such as air, water, or any other types of matter. The vibration of the object sets particles in the surrounding medium in a vibration motion. Hence, it transports energy through the medium. Waves of sound energy move outward in all direction from the source. Longitudinal waves are waves that have the same direction of travel. This is the type of wave in which we use to transfer sound. The medium particles vibrate parallel to the motion of the pulse. Thus, the movement of the medium is the same direction as or the opposite direction to the motion of the wave. This experiment wants the students to understand the principle about longitudinal wave and how an individual hears a sound. The purpose of conducting 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. This experiment uses the Kundt’s Tube apparatus with the lycopodium powder inside. In order for the rod to produce vibration, we are asked to rub the rod by using a cloth with rosin on it. The velocity of the sound of the rod has been determined through Young’s Modulus, density relationship and principle of resonance. The vibration which produces sound has been transferred to the glass pipe that has the same frequency as that of the solid rod. Hence, the frequency of air is equal to the frequency of the rod. As a conclusion, the speed of sound will travel fastest in solids in comparison with the liquid and gas. That is because the distances between molecules in solid are very small and denser that they can collide very quickly compared to liquid and gas.

II

THEORY Sound waves are longitudinal waves travelling through an elastic

medium. It is also defined as the pattern of disturbance caused by the movement of energy travelling through a medium such as air, water, or any other liquid or solid matter as it propagates away from the source of the sound. As one particle becomes disturbed, it exerts a force on the next adjacent particle, thus will disturb that particle from rest and will transport the energy through the medium. The pattern of the disturbance creates outward movement in a wave pattern. Among the three mediums (solid, liquid, and gas), sound waves will travel the slowest through gas, faster through liquids, and fastest through solids. This is because the denser the medium, the faster the sound will travel.

Fig 1.1 Longitudinal Waves – Movement of air molecules

Longitudinal waves are compressional waves which travel through the air through a series of compressions and rarefactions. Compression happens when particles are forced or pressed, together. While,

1 Department of Physics Experiment 304 : Kundt’s Tube: Velocity of Sound in Solid – Analysis of Data

rarefaction, on the other hand, occurs when particles are given extra space and will be allowed to expand. Also, longitudinal waves are waves that have the same direction of vibration as their direction of travel, which means that the movement of the medium is in the same direction as or the opposite direction to the motion of the wave. The motions of the particles of the medium are back and forth along the same direction that the wave travels. The speed of sound in the rod, and frequency, can be determined by using the speed of sound in air and its wave relationship. When the rod is properly stroked and is set into vibration, standing waves are set up in the vibrating rod. The velocity of any wave is given by the equation:

The wave speed or the velocity of the wave is a wave moving through a medium which travels at a certain speed. The speed of any wave depends upon the properties of the medium through which the wave is travelling. Typically, there are two essential types of properties that can affect wave speed. Those are inertial and elastic properties. Elastic properties are those properties related to the tendency of a material to maintain its shape and not deform whenever a force or stress is applied to it. The phase of matter has an impact upon the elastic properties of the medium. In general, solids have the strongest interactions between particles, followed by liquids and then gases. For this reason, longitudinal sound waves travel faster in solids than they do in liquids than they do in gases. Inertial properties, on the other hand, are those properties related to the material’s tendency to be sluggish to changes in its state of motion. The density of the medium is an example of an inertial property. The greater the inertia of individual particles of the medium, the less responsive they will be to the interactions between neighbouring particles and the slower that the wave will be. Within a single phase of matter, the inertial property of density will tend to be the property that has a greatest impact upon the speed of sound. The velocity of solid in the air depends on the temperature expressed as:

The velocity of sound in a solid rod can be computed by using the two formulas shown below: (

)

√

The importance of conducting this experiment is we will be able to compute for the frequency of the sound, velocity of sound in the metal rod, and the velocity of sound in the metal rod. We would also be able to know how the speed of sound will differ for the three mediums (solid, liquid, and gas). We would also be able to know the factors affecting the speed of sound.

2 Department of Physics Experiment 304 : Kundt’s Tube: Velocity of Sound in Solid – Analysis of Data

III

MATERIALS USED

MATERIALS USED 1 pc Kundt’s Tube Apparatus 1 pc Meter Stick 1 pc Cloth Steam Generator 1 pc Thermometer Rosin Lycopodium Powder Hose

Fig 1.2 Set-up of the whole experiment

In this experiment, we didn’t have a hard time setting up the apparatus because we simply followed the procedure and set it up right. The experiment is all about getting the velocity of sound in solid by using the kundt’s tube in order to observe sound wave. The kundt’s tube apparatus is consist of a glass tube supported on a metal base, a clamp at one end of the base holds a metal rod which has a metal disk attached to one end. The rod and disk extend inside the glass tube, whose position can be adjusted to center the tube about the disk. Lycopodium powder is a yellow-tan powder which is used to make sound-waves in air visible for observation and measurement. This lycopodium powder will help us to determine the lengths of the wavelength of the sound in air which is created inside the glass tube.

IV

OBJECTIVES

1.

To determine the velocity of sound in a metal rod

2.

To determine the speed of sound in the tube applying the principles of resonance

V

DATA AND OBSERVATIONS

In conducting this experiment, our group has encountered several problems and difficulties upon doing the experiment. One of the difficulties our group has encountered is the one who is rubbing the rod isn’t properly stroking the rod. Another difficultly that our group has encountered is the determination of the length of the dust heaps produced. However, after we have measured several heaps and get their average, we were able to overcome that difficulty.

3 Department of Physics Experiment 304 : Kundt’s Tube: Velocity of Sound in Solid – Analysis of Data

What we did in this experiment was we produced longitudinal waves through rubbing the rod with the use of a rag with rosin. We had difficulty in producing the waves because if we just rub the rod gently the wavelength of the waves formed is to short and if we try to rub it really hard the glass tube shakes from time to time disturbing lycopodium powder and the

Fig 1.3-1 Properties of wave motion produced in the metal rod

waves formed. Through practice we were able to minimize errors The temperature of the room is also significant since it affects the velocity of sound in air, wherein as the temperature rises the velocity of sound in air increases. What we used as actual values for the velocity of sound in air is the value from the textbook and the one obtained by dividing the young’s modulus of the rod by its density and then taking its square root. KUNDT’S TUBE: VELOCITY OF SOUND IN SOLID length of metal rod Lr

91.948 cm

average length powder segments La

10.414 cm

temperature of air t

25 °C

velocity of sound in air va

347 m/s

velocity of sound in the rod vr from Equation 3 velocity of sound in the rod vr from textbook

3063.756 m/s 3,475 m/s

percentage error

11.83 %

density of rod ρ

8,600 kg/m3

velocity of sound in the rod vr from Equation 4

3234.983 m/s

percentage error

6.91 %

Table 1.1 The table above shows the data that we have gathered from the experiment which is needed for the computation of velocity of sound in air, the frequency of the sound, velocity of sound in the metal rod by using equations 3 and 4. By obtaining those data, it also allows us to compute for the percentage error of the experimental value of the velocity of sound in the rod using equation 3 and the velocity of sound in the rod using equation 4.

Analyzing the obtained data and results, since the rod is clamped at its center point, this point is a node (zero amplitude of motion) and the ends which are free to vibrate are antinodes (maximum amplitude of particles' motion along the direction of the rod). When the rod is vibrating in this manner it is vibrating with its fundamental frequency and the wavelength of the standing

Fig 1.3-2 Properties of wave motion produced in the metal rod

wave is twice the length of the rod.

4 Department of Physics Experiment 304 : Kundt’s Tube: Velocity of Sound in Solid – Analysis of Data

The vibrations of the rod are transmitted by the disk to the air in the glass tube closed at one end. The waves set up in the air in the glass tube have the same frequency as those in the rod. The waves are reflected at the closed end of the tube and the air in the tube is thus acted upon by two similar sets of waves travelling in opposite directions. When the length of the air column is some multiple of half wavelengths, the two oppositely travelling waves produce standing waves. The standing waves are characterized by alternate points of maximum and minimum disturbance called respectively nodes and antinodes. These nodes and antinodes may be detected by cork dust placed in the tube, the cork dust showing characteristic striated vibration patterns at the antinodes. The distance between two successive patterns is therefore one-half the wavelength of the sound in the air. Again, the problem that we are trying to solve in this experiment is getting the velocity of sound in a metal rod and the speed of the sound in the tube. The sample computation below shows how we computed for the experimental value of velocity of sound in air:

The sample computation below shows how we computed for the experimental value of velocity of sound in the rod by using equation 3 and its percentage error: ( |

)

(

)

|

|

|

The solution for equation 3 indicates that the data that we have gathered is acceptable but is kind of high since it has a percentage error of 11.83%. This is due to some possible sources of error like the length of the segment might have been measured inaccurately since we cannot determine the exact center of the dust heap. The sample computation below shows how we computed for the experimental value of velocity of sound in the rod by using equation 4 and its percentage error: √ |

√ |

The solution for equation 3 indicates that the data that we have gathered is accurate since it only has a percentage error of 6.91 %. The experimental value for velocity of sound in the rod is almost close to its actual value which is 3,475 m/s. Between equations 3 and 4, it is much more accurate to use equation 4 since it gives us a lower percentage error. Also, using equation 3 will give us errors in terms of determining the average length powder segments.

5 Department of Physics Experiment 304 : Kundt’s Tube: Velocity of Sound in Solid – Analysis of Data

CONCLUSION Upon carefully doing the necessary procedures of the experiment and by interpreting the obtained data and results, the two aims of this experiment were achieved. Those are to determine the the velocity of sound in a metal rod and to determine the speed of sound in the tube applying the principles of resonance

In this experiment, we examine longitudinal waves produced by the kundt’s tube, which travel through the air through a series of compressions and rarefactions. Compression happens when particles are forced or pressed, together. While, rarefaction, on the other hand, occurs when particles are given extra space and will be allowed to expand. Also, another main point of thing is that, the speed of sound in the rod can be determined by using the speed of sound in air and its wave relationship. When the rod is properly stroked and is set into vibration, standing waves are set up in the vibrating rod. The waves are reflected back and forth producing two distinct waves

that have nodes and antinodes as for its major parts. Also, based on the data gathered, I found out and I had come up to an idea that as one particle becomes disturbed, it exerts a force on the next adjacent particle, thus will disturb that particle from rest and will transport the energy through the medium. The pattern of the disturbance creates outward movement in a wave pattern. And among the three mediums (solid, liquid, and gas), sound waves will travel the slowest through gas, faster through liquids, and fastest through solids. This is because the denser the medium, the faster the sound will travel. The wave speed or the velocity of the wave is a wave moving through a medium which travels at a certain speed. The speed of any wave depends upon the properties of the medium through which the wave is travelling. Typically, there are two essential types of properties that can affect wave speed. Those are inertial and elastic properties. Elastic properties are those properties related to the tendency of a material to maintain its shape and not deform whenever a force or stress is applied to it. The phase of matter has an impact upon the elastic properties of the medium. In general, solids have the strongest interactions between particles, followed by liquids and then gases. For this reason, longitudinal sound waves travel faster in solids than they do in liquids than they do in gases. Inertial properties, on the other hand, are those properties related to the material’s tendency to be sluggish to changes in its state of motion. The density of the medium is an example of an inertial property. The greater the inertia of individual particles of the medium, the less responsive they will be to the interactions between neighbouring particles and the slower that the wave will be. Within a single phase of matter, the inertial property of density will tend to be the property that has a greatest impact upon the speed of sound.

6 Department of Physics Experiment 304 : Kundt’s Tube: Velocity of Sound in Solid – Analysis of Data