ANALYSIS ON KUNDT'S TUBE: VELOCITY OF SOUND IN SOLID
Everyone knows the old trick of putting your ear to a train track to get early warning of an approaching train or remember the during your childhood days where you use tin cans with attached strings to talk with your friends. Sound can travel great distances in many solid materials, and moreover, it travels quickly. The speed of sound in an iron rail is roughly ten times that in air!
Sound is a disturbance of mechanical energy that propagates through matter as a longitudinal wave. Sound is characterized by the properties of sound waves, which are frequency, wavelength, period, amplitude, and speed. The latter is sometimes referred to as 'sound velocity' but this is incorrect as it is not a vector quantity.
Humans perceive sound by the sense of hearing. By sound, we commonly mean the vibrations that travel through air and can be heard by humans. However, scientists and engineers use a wider definition of sound that includes low and high frequency vibrations in air that cannot be heard by humans, and vibrations that travel through all forms of matter, gases, liquids and solids. Sound can also be perceived by many other animals and is also used for echolocation.
The matter that supports the sound is called the medium. Sound propagates as waves of alternating pressure, causing local regions of compression and rarefaction. Particles in the medium are displaced by the wave and oscillate. The scientific study of sound is called acoustics while that underwater is called hydro acoustics.
Noise is often used to refer to an unwanted sound. In science and engineering, noise is an undesirable component that obscures a wanted signal. Sound is the movement of energy through a substance in longitudinal waves. Sound is produced when a force causes an object to vibrate.
Sound is perceived through the sense of hearing. Humans and many animals use their ears to hear sound, but loud sounds and low-frequency sounds can be perceived by other parts of the body through the sense of touch as vibrations. Sounds are used in several ways, notably for communication through speech and music. They can also be used to acquire information about properties of the surrounding environment such as spatial characteristics and presence of other animals or objects. For example, bats use echolocation, ships and submarines use sonar and humans can determine spatial information by the way in which they perceive sounds.
Humans can generally hear sounds with frequencies between 20 Hz and 20 kHz (the audio range) although this range varies significantly with age, occupational hearing damage, and gender; the majority of people can no longer hear 20,000 Hz by the time they are teenagers, and progressively lose the ability to hear higher frequencies as they get older. Most human speech communication takes place between 200 and 8,000 Hz and the human ear is most sensitive to frequencies around 1000-3,500 Hz. Sound above the hearing range is known as ultrasound, and that below the hearing range as infrasound.
The speed at which sound travels depends on the medium through which the waves are passing, and is often quoted as a fundamental property of the material. In general, the speed of sound is proportional to the square root of the ratio of the stiffness of the medium and its density. Those physical properties and the speed of sound change with ambient conditions. For example, the speed of sound in air and other gases depends on temperature. In air, the speed of sound is approximately 344 m/s, in water 1500 m/s and in a bar of steel 5000 m/s. The speed of sound is also slightly sensitive (to second order) to the sound amplitude, resulting in nonlinear propagation effects, such as the weak production of harmonics and the mixing of tones.
The behaviour of sounds can be observed, like the Doppler Effect and shockwaves. The Doppler Effect is a phenomenon observed whenever the source of waves is moving with respect to an observer. The Doppler effect can be described as the effect produced by a moving source of waves in which there is an apparent upward shift in frequency for the observer and the source are approaching and an apparent downward shift in frequency when the observer and the source is receding. The Doppler Effect can be observed to occur with all types of waves - most notably water waves, sound waves, and light waves.
There are several applications to sound namely, Ultrasonic Waves: Humans can normally hear sound frequencies between 20 and 20,000 Hz (20kHz). When a sound wave's frequency lies above 20 kHz, it is called an ultrasonic wave. While we cannot hear ultrasonic waves, we apply them in various technologies such as sonar systems, sonograms, surgical tools, and cleaning systems. Some animals also use ultrasonic waves in a specialized technique called echolocation that allows them to pinpoint objects and other animals, even in the dark.
In the experiment, we are allowed to observed longitudinal waves produced by pulling back and forth the rod connected to the Kundt's Tube. In a longitudinal wave the particle displacement is parallel to the direction of wave propagation. It shows a one-dimensional longitudinal plane wave propagating down a tube. The particles do not move down the tube with the wave; they simply oscillate back and forth about their individual equilibrium positions. The wave is seen as the motion of the compressed region (ie, it is a pressure wave), which moves from left to right. In a transverse wave, particles of the medium are displaced in a direction perpendicular to the direction of energy transport. In a longitudinal wave, particles of the medium are displaced in a direction parallel to energy transport. As one individual particle is disturbed, it transmits the disturbance to the next interconnected particle. This disturbance continues to be passed on to the next particle. The result is that energy is transported from one end of the medium to the other end of the medium without the actual transport of matter. In this type of wave - a longitudinal wave - the particles of the medium vibrate in a direction parallel to the direction of energy transport.
As the rod was being pulled back and forth with a cloth, longitudinal standing waves are observed to be formed from the dust inside. Those waves are set up in it with a minimum vibration (node) at the clamped part (at the center) and maximum vibration (antinode) at each end. Since the distance between two consecutive nodes or antinodes in a standing wave is exactly half of its wavelength, then, the wavelength of the tone in the rod is twice the length of the rod. Since the wave loops are visible, we can easily measure its wavelength using the meter stick. As we all know, all waves segments are in the same sizes. Thus, we can measure the length of one segment by measuring two or more segment and get its average.
To solve for the experimental values of velocities using different equations, some constants to be used are:
| Length of metal rod | 92 cm |
| Average length powder segments | 9.1 cm |
| Temperature of air t | 26 °C |
| Velocity of sound in air | 347.6 m/s |
Velocity of sound in air was achieved by using the formula,
where t is the temperature in Celsius. t= 26°C
This equation to get the value of velocity is air is directly proportional to temperature of surrounding as shown in the table.
As the powder in the cloth is being displaced, the sound waves are produced in the metal rod as if its molecules are vibrating consecutively. In addition, the frequency of the vibrations in a given metal rod varies on the length of the rod and the position of the clamp. The wavelength and velocity change as the wave chain goes from one medium to another, but the frequency is still consistent. The vibrations are transmitted to the disk, which in turn transmits them into the air column at the same or equal frequency.
| Velocity of sound in the rod | 3514.20 m/s |
| Velocity of sound in the rod | 3475 m/s |
To solve for the velocity of the sound in rod using the formula derived in Equation 3,
Computing for percentage error, we attained 3.40% and that is not that bad. Other formulas were used to get these details shown below.
Density of the rod, | 8400 m/s |
| Velocity of sound in the rod | 3273.27 m/s |
This time,another formula was used to find the velocity.
Where 
stands for Young's modulus (coefficient of elasticity) of brass and 
stands for its density.
As observed in the solution, we can notice that if Young's modulus of the object was changed and increased, velocity of the rod will also increase and vice versa. Also, if the object or material used was altered, its density will also change. If its density was changed and was increased, its velocity decreases.
As seen in the graph, the density of material that will be used in the experiment is directly proportional to the velocity of the rod. As the density increases, the velocity also increases and as the density decreases, its density decreases. On the other hand, the relationship of Young's modulus to velocity is inversely proportional. It is opposite of the density. As Young's Modulus increases, the velocity decreases and as it decreases, velocity increases.
Since the Kundt's tube is a special apparatus made just for this type of experiment, there is a great chance that the data obtained has a great accuracy when we are using it. The possibility of having an uncertainty is also diminished since the over all set up is already prepared by the professional laboratory assistants. Probable source of error for the determination of velocity of the sound in metal rod are as follows: The tube is not horizontally placed in the table, the tube is somehow open at the end where it should be closed, the uncertainty in measuring the length of the segments by around 
CONCLUSION ON KUNDT'S TUBE: VELOCITY OF SOUND IN SOLID
The goals of this lab were to determine the velocity of sound in metal rod and the speed of sound in the tube applying the principles of resonance. This experiment had covered the relationship of velocity of sound in both gas-air and solid-metal rod through manipulation of certain condition to produce resonance. Formulas in the manual were provided to get its different velocities in many ways to show its accuracy. By obeying the instructions such as clamping the rod at its midpoint, closing the one end of the glass tube while the other end is free, and by making the disk in the rod not to be in contact with the glass tube, and not pull the cloth completely off the rod, objectives were achieved.
Longitudinal wave is produced as rod was stroked that has equal frequency making a resonance, and produces sound where visible wave patterns were produced inside the tube. Then velocity of sound was acquired.
Close type of velocity of sound of air was used in the experiment that states that an antinode is seen on the open end while a node is seen at the close end. The velocity of sound in an air column of this type is proportional to the frequency and twice the length of each segment.
We can get two different velocities at different medium by applying the principle of resonance where frequencies of each corresponding longitudinal wave are equal .Besides from the application of the resonance, velocity of sound in rod can also be evaluated by considering the elasticity and density of the material where the sound wave travels. The velocity is directly proportional to the Young's modulus of elasticity and inversely proportional to the density of the material being used.
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