Mass Spring System - Essay Example

Mass Spring System The purpose of this project is to show how a mass spring system is similar to the oscillation movements of air molecules that are being influenced by longitudinal sound wave. Longitudinal waves cause air molecules to vibrate in the same direction as their propagation, which is the same motion in a mass spring system where the mass is disturbed by exerting a force that causes the spring to compress and observe the mass movement after the force ceases to be exerted. The mass spring system demonstrates the vibration movements of air molecules. Longitudinal Sound Waves, Mass Spring System and Air Molecules Oscillation A wave can be defined as a disturbance that is periodic within a medium that is carrying energy from one position to another. Waves normally require an origin or a source and a form or medium through which they propagate. Citing the mechanics of how vocal chords produce sound, we can explain how waves are produced and interact with air molecules. This interaction causes air molecules to vibrate in a manner similar to that of a mass that is being influenced by an external force in a mass spring system (Elmore & Heald, 2005). The two principle sorts of waves are longitudinal and transverse waves. By differentiation, the medium transmitting longitudinal waves sways in a course parallel to the bearing of the wave. The most normally examined manifestation of longitudinal waves is sound. At the point when the framework is dislodged from its balance position, the flexibility gives a restoring constrain such that the framework tries to come back to harmony. The dormancy property causes the framework to overshoot balance. This consistent play between the versatile and latency properties is the thing that permits oscillatory movement to happen. The least complex illustration of a wavering framework is a mass associated with an inflexible establishment by method for a spring. The spring steady k gives the flexible restoring energy, and the dormancy of the mass m gives the overshoot. By applying Newtons second law F=ma to the mass, one can get the comparison of movement for the framework: where a is the regular swaying recurrence. The answers for this comparison of movement takes the structure where xm is the abundancy of the swaying, and φ is the stage steady of the wavering. Both xm and φ are constants dictated by the starting condition (intial uprooting and speed) at time t=0 when one starts watching the oscillatory movement. Longitudinal waves are waves whose energy transfer is in the same direction as the displacements in the medium in which they propagate. In addition, they can have one or many pulses. They have regions of varying density whereby areas of high density are referred to as condensations and regions of low density are referred to as rarefactions. Sound wave is an example of a longitudinal wave. The origin of sound waves has a physical process known as simple harmonic motion (Rose, 2004). Systems that are used to demonstrate this motion are known as simple harmonic oscillators and the mass spring system is one of them. A spring is an item that has high elasticity, which enables it to be compressed or stretched (Simmons, 2003). In the reference diagrams, compression corresponds to the movement of the mass to the left and stretching corresponds to the movement of the mass to the right. The force used to stretch or compress the string will be opposed by the restoring force of the spring that enables it to be elastic. These forces are directly proportional to each other. The restoring force (F) is directly proportional to the distance of displacement of the mass (x). This law is called Hooke’s Law whose equation is: F = -kx In diagram 1, the spring is not in motion and neither compressed nor stretched. No forces are acting on the mass. In diagram 2, the mass has moved to the left hence the spring has undergone compression and the force (F) is the restoring force of the spring. In diagram 3, the restoring force (F) is acting on the mass towards the left. The diagrams above portray the production of a harmonic wave. Sound waves are forms of longitudinal waves that are transmitted through air and in this transmission; they displace air molecules causing them to oscillate in a particular direction (Rose, 2004). As an example, the human voice cords produces sound, which causes air molecules to oscillate in a similar frequency to the sound produced by the cords. When this happens, the vibration of the vocal cords, which is in the form of a transverse wave is converted into a longitudinal wave. When air molecules that are around the vocal cords oscillate, they cause other air molecules to oscillate by bumping into them. The molecules thus start moving back and forth in a linear motion by rushing towards and away from each other. This motion is similar to the mass in the mass spring system whereby the mass moves towards and away from the fixed point of the spring during oscillation (Elmore & Heald, 2005). When the molecules are close to each other, it is a compression and when apart from each other it is a rarefaction and these alternating motions are the constituents of a longitudinal wave. This motion, made up of compressions and rarefactions, moves through air at a speed of 344 metres per second at a temperature of 60 degrees Fahrenheit and pressure at sea level. Air molecules around a vibrating object oscillate in a similar way to the vibrating object and these oscillating air molecules will cause a surface they impact to oscillate in a similar way as they do and this is the system in which sound waves transfer energy from one place to another through air. In place for mechanical swaying to happen, a framework must forces two amounts: versatility and inactivity. At the point when the framework is dislodged from its balance position, the flexibility gives a restoring constrain such that the framework tries to come back to harmony. The dormancy property causes the framework to overshoot balance. This consistent play between the versatile and latency properties is the thing that permits oscillatory movement to happen (Simmons, 2003). The regular recurrence of the swaying is identified with the versatile and idleness properties. The spread of sound is the transmission of acoustic energy through a medium by means of a sound wave. Sound is an arrangement of waves of weight, which spreads through compressible media, for example, air or water or robust. Amid their proliferation, waves can be reflected, refracted, or constricted by the medium. In air, sound is transmitted by weight varieties from its source to the surroundings. While assimilation via air is one of the elements crediting to the debilitating of a sound amid transmission, separation assumes a more critical part in commotion lessening amid transmission. At the point when the string on a violin, the surface of a chime, or the paper cone in a stereo speaker wavers quickly, it makes beats of high gaseous tension, or compressions, with low weight spaces called rarefactions. These compressions and rarefactions are what might as well be called peaks and troughs in transverse waves: the separation between two compressions or two rarefactions is a wavelength. The flexible property of the swaying framework (spring) stores potential vitality, which is the latency property (mass) stores active vitality. As the framework sways, the aggregate mechanical vitality in the framework exchanges here and there and then here again in the middle of potential and active energies. The aggregate vitality in the framework, be that as it may, stays consistent, and depends just on the spring constant and the most extreme uprooting (or mass and greatest speed vm=ωxm). The diminishment of a sound is called attenuation. The impact of separation and weakening relies on upon the kind of sound sources. Most sounds or clamours people experience in their day by day life are from sources, which can be described as point or line sources. For a point source, the commotion level declines by 6db in every multiplication or separation from it. In the event that the sound source produces barrel shaped spreading of sound, for example, stream of engine vehicles on an occupied street at a separation, it might be considered as a line source. For a line source, the commotion level declines by 3db every multiplying of separation from. The general examination of wave movement is vital in light of the fact that the thoughts of wave spread are universal. In almost all areas of science, energy is expressed by means of the vibrations that make up waves. Illustrations of wave movement usually include waves on strings, water waves, seismic waves, sound, all electromagnetic radiation comprising of light, warm, and, x-beams. There are numerous normal components to all the different sorts of wave movement that can be portrayed. Longitudinal waves are waves whose energy transfer is in the same direction as the displacements in the medium in which they propagate. Sound waves are forms of longitudinal waves that are transmitted through air and in this transmission; they displace air molecules causing them to oscillate in a particular direction. The origin of sound waves has a physical process known as simple harmonic motion and the systems that are used to demonstrate this motion are known as simple harmonic oscillators and the mass spring system is one of them. References Elmore, W. C., & Heald, M. A. (1985). Physics of Waves. New York: Dover Publications. https://books.google.co.ke/books?id=IOXCAgAAQBAJ&printsec=frontcover&dq=Physics+of+waves.&hl=en&sa=X&ei=Pz_HVMOoGMvoUtqWgNAG&redir_esc=y#v=onepage&q&f=false Rose, J. L. (2004). Ultrasonic Waves in Solid Media. Cambridge [u.a.: Cambridge Univ. Press. Simmons, A. M. (2003). Acoustic Communication. New York [u.a.: Springer. Read More