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III. ANALYSIS
Sound moves by unlikely speeds depending on medium it travels
through. Of the three mediums (solid, liquid, and gas) sound waves travel
the slowest through gases, faster through liquids, and fastest through solids.
It travels fastest through solid since its molecules are much bonded together
compared to liquid and gas. Temperature also affects the speed of sound.
When a person hits, strikes, strums, plucks or somehow disturbs the
object, musical instruments are set into vibration motion at their natural
frequency. 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.
Kundt’s tube was invented in 1866 by German physicist August
Kundt for determining the speed of sound through different mediums. It is
used representing standing waves and acoustical forces today. The tube has
little quantity of fine powder such as cork dust, talc or Lycopodium
(Lycopodium was used in this experiment), which is visible since the tube is
transparent. Kundts utilized metal rod resonator for vibration before, but
modern demonstration generally use a loudspeaker attached to a signal
generator which produce a sine wave. The other end of the tube is enclosing
by a changeable piston which can be used to adjust the length of the tube.
Thus the velocity of any wave is given by:
v = f λ
where: v is the velocity, f is the frequency, λ is the wave length
The tube signifies that is at resonance when the sound generator is
turned on and changed in anticipation of the sound gets much loader. This
indicates that the tube is at resonance. The distance of the round-trip path of
the sound waves, from one end of the tube to the other and back again, is a
multiple of the wavelength λ of the sound waves. Hence, the length of the
tube is a multiple of half a wavelength. The sound waves in the tube are in
the form of standing waves, and the amplitude of vibrations of air is zero at
equally spaced intervals along the tube, called the nodes. The powder is
caught up in the moving air and settles in little piles or lines at these nodes,
because the air is still and calm there. The distance between the piles is one
half-wavelength λ/2 of the sound. By measuring the distance between the
piles, the wavelength λ of the sound in air can be found. If the frequency f of
the sound is known, multiplying it by the wavelength gives the speed of
sound c in air. The speed of sound in air can be determined by measuring the
air temperature t in Celsius degree:
vair = 332 m/s + 0.6(t)
where: vair is the velocity in air, t is the temperature in Celsius
The frequency of the sound in the air is the same as that in the metal
rodf rod, that is f air =f rod. Thus, this frequency can be used to calculate the
speed of wave in metal given by
vr = vaLrLa
where: vr is the velocity of the rod, va is the velocity of air, Lr is the
length of rod, and La average length of powder segment
The velocity of sound in a solid rod is given by
vr = √Yρwhere: vr is velocity of the rod, Y is the Young’s modulus of the rod,
ρ is the density of the rod
In this experiment Kundt’s Tube Apparatus, a meter stick, a piece of
cloth, a thermometer, rosin and Lycopodium powder will be used. The
Kundt’s tube consists of a long, narrow glass tube mounted in a metal frame
case. A metal rod (any desired material) is clamped in such a way that its
end containing the disk is inside the tube. The rod can be clamped at any
distance. However, it is better to clamp it at the center to make the
experiment not complicated. The Kundt’s tube is closed at one end by a
stopper.
(Materials Used)
The first picture shows the rod is pulled toward the end of the rod to
produce vibration.
The photo above shows that we measures the distance of successive
powder heaps. All the lengths needed in this experiment are measured using
the meter stick. A low accuracy instrument is just fit with the experiment
because it is not important to measure accurate lengths. Finally,
thermometers are the instrument used in measuring the temperature of the
room. Normally, we have to put the powder inside the glass tube. But in the
experiment, it is already prepared by the laboratory assistants to prevent
waste of materials.
The powder is evenly distributed throughout the tube. It is done to
make the wave visible later, that is in similar shapes and sizes. The kind of
material where the rod is made is to be recorded. The value of the constants,
Y and ρ, for the specific material used are obtained using any form of
resources. Furthermore, the length of the tube is to be measured using a
meter stick. We carefully adjusted if the rod is clamped horizontally at its
center. This allows the experiment performer to easily calculate the value of
velocity of the rod. The rod has a disk at its one end inside the tube. This
disk has not to touch the walls of the glass tube. It must be leave free to
vibrate. Also, it should be necessary to measure and record the temperature
of the room, inside the tube or near the apparatus itself.
After the preliminary assessment of the apparatus, we proceed on
vibrating the rod. The rosin is initially rubbed on the cloth. The rosin allows
the cloth to produce friction with the tube. The energy due to friction will
serves as a wave. Strokes on the rod are done after wards. It is ideal to do
smooth, high-pitch tone stroke in a lengthwise manner. It is important not to
let the hand slip off at end of the rod. This is because, it causes both ends of
the rod to vibrate transversely, and the vibrating disk may break the glass
tube.
When the dust inside the tube does not form visible waves, it is
advised to adjust the air column by moving it towards the tube in a minimal
distance. Continual adjustment can be made until best resonance condition is
achieved. This happens when dust agitated formed perfect waves which are
measurable and looks exactly the same from one another. When the rod gets
warmed greatly, we could cease the stroking and let it cool for a while.
Another problem encountered in this experiment is when one observed that
majority of the dust is concentrating on one side of the node. This can be due
to the apparatus is not oriented horizontally. We can minimize this problem
by removing some dust.
Once the visible waves formed, we proceed on measuring the length
of the waves (wavelength). On measuring, the first dust loop nearest to the
disk of the rod is neglected. It is an option to measure one, two, three or any
number of waves desired. However, it is more accurate to measure many
waves. From the measured distance, we determined the average half
wavelength of the sound in air column, La, by dividing it to the total number
of loops or segments measured. We calculate for the velocity of sound in air
at the temperature recorded earlier. Once done, solve for the value of the vr.
From the table of velocity of sound in solid in the textbook, we compared
the obtained experimental value with the theoretical value.
In the experiment, the group had accomplished the objective of the
experiment which determine the velocity of sound in metal rod and
determine the speed of sound in the tube applying the principles of
resonance. The wave produced in Kundt's tube follows the wave behavior of
the close type case. In vibrating the rod, energy comes from the friction
produced by stroking cloth at the rod. To produce friction, rosin is rubbed in
the cloth. The wave’s produced inside after vibration is visibly seen through
agitation of Lycopodium powder.
Table 1. Kundt’s Tube: Velocity of Sound in Solid
Length of metal rod Lr 91.5 cm
Average length of powder segments
La
8.75 cm
Temperature of air t 22 °C
Velocity of Sound in air va 345.2 m/s
Velocity of sound in the rod vr 3609.81 m/s
Velocity of sound in the rod vr 3475 m/s
Percentage Error % 3.88 %
Density of the rod ρ 8440 kg/m^3
Velocity of sound in the rod vr 3283.59 m/s
Percentage Error % 5.51 %
Based on the table above, the velocity of sound produce in the rod can
be computed using equation the equation: vr = vaLrLa
since the frequency of
the sound in the air is the same as that in the metal rod. The velocity of
sound computed can be obtained using the equation: vr = √Yρ using young's
modulus and density of the rod. Possible error encountered in this
experiment is when the majority of the dust is concentrating on one side of
the node. This can be due to the apparatus is not oriented horizontally.
IV. CONCLUSION
The second type of mechanical wave which longitudinal waves were
the velocity of the wave is parallel to the movement of particle. An example
of longitudinal wave is sound wave. For this experiment, the velocity of
sound in the rod and tube were determined.
The velocity of sound in rod depends on two things, the air
temperature, length and type of rod. First, high temperature permits sound to
travel faster. From the velocity of sound in air, a proportion was observed
that velocities of sound in rod and in air are indirectly proportional to the
average length of the successive heaps and length of the rod, respectively.
Hence, smaller ratio between lengths of the rod to the average length
successive powder heaps will produce higher value of the velocity.
Another factor that affects the velocity of sound in rod is its ability to
expand or the Young’s Modulus and the inertia resisting the return to
equilibrium, or the density. Velocity of sound is found to be directly
proportional to the square root of Young’s Modulus and indirectly
proportional to the square root of density. Thus, higher young’s modulus
will give higher velocity of sound and higher value of density will give low
value of velocity.
The experiment aims to determine the velocity of sound in metal rod
and determine the speed of sound in the tube applying the principles of
resonance. The velocity of sound can be determined using Kundt’s tube
apparatus. Using the principles of resonance and applying the velocity of
wave, the group computed the value of the velocity of sound in the rod vr
(computed) was 3283.59 m/s with a 5.51 % error compared to velocity of
sound in the rod vr (textbook) which is equal to 3475 m/s. These proves that
the velocity of the sound can be computed through applying principles of
resonance and verified that sound travels through the air and rod as its
medium and behaves longitudinal waves.
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