How the Distance from the Midpoint of a Snare Affect the Frequency Its Sound - Research Proposal Example

How the distance from the midpoint of a snare affect the frequency its sound Research question: How does the distance from the midpoint of a snare affect the frequency its sound Aim: To find the effect of distance from the midpoint of a snare on the frequency emitted. Materials and equipment A Prologger or any other frequency recording device A computer system. A drum stick A microphone or any other device that can be used to amplify sound. A snare Background Sound occurs due to a vibration that is transmitted through matter. The freauqencies of the the waves must be such that they can be detected by the ears. The human ear can detect the waves ranging from twenty hertz to twenty kilohertz. Other animals have different ranges of sound detection. Dogs, for instance can detect vibrations with a frequency higher than twenty kilohertz. The matter through which sound waves travel is known as the medium, and that includes a vacuum. Sound is believed to be caused by small areas of low and high pressure vibrating outwards. Sound, like all other waves display various properties. These properties include wavelength, period, frequency,speed, amplitude, intensity and direction. Amplitude and loudness refer to a similar thing. It depends on how much compression is done. Sound waves disperse after leaving the source. This leads to a notable decrease in amplitude. In case of an absorption of the sound waves by the medium, amplitude decreases as it travels through it. Sound wavelength is the distance from one crest to the next. Sound being a compression wave has its wavelength being the distance between the maximum compressions. Sound frequency refers to the passing rate of waves at a given point. It is used interchangeably with pitch and also note for musical sounds. Wave length, frequency and velocity are related by the following expression: Velocity = wavelength frequency But for all wavelengths, sound's velocity is roughly the same. Therefore frequency comes in handy in the description of the effects of the various wavelengths. Frequency and wavelength determine the pitch of a sound wave. A high pitched sound is in corresopondence with a high frequency sound wave and vice versa for low pitched sounds. Under normal circumstances, one effect can observe the Doppler Effect any time the source's velocity moves slower than the wave's velocity. However, whenever the source's velocity is the same or faster than the wave's speed, the source becomes the leads the waves produced. When there is a time snapshot for various waves an aeroplane produces with due to moving at the same velocity as the wave, it is called a shorkwave. This also happens if the plane is swifter than the sound's speed. When a supersonic aeroplane passes an obeject, a sonic boom is heard. It happens due to a pile-up of compressional fronts on wave pattern's conical edges. This piling up interferes with one another, producing extremely high pressure zones. These zones then all reach the object at once. There follows rarefaction where the high pressure zone is immeidately followed by lower pressure one, creating loud noise. Sound speed is mainly dependent on the medium the wavesare travelling through. This is normally the material's fundamental property. Physical properties including a sound's velocity vary depending on the environmental conditions. For instance, the velocity of soundwaves in though gases is highly dependent on the temperature. The vibration of a sound source creates compression waves of sound. In order to study the effect of distance from the midpoint of a snare on the frequency emmitted, the Doppler Effect theory is employed. According to this theory, there is always a change in frequency and wavelength of sound waves and other waves in general with respect to distance. It derives its name from Christian Doppler, an Austrian physicist and mathematician. He first proposed this effect in the year 1842 in his book. Later in 1845, Buys Ballot tested this hypothesis for sound waves. He made a confirmation that the pitch of a sound is higher than the frequency of emmision for an approaching source and lower for a receding one. This same principle was again discovered by Hippolyte in the year 1848. He also discovered that same phenomenon about other waves such as electromagnetic waves. Controversy surrounds around whether frequency actually increases with an approaching object towards an observer and drop with the passing of the object. On the contrary, as an object approaches, its observed frequency is declined monotonically to an equal value at the same level and lower when as it passes. According to Brohen, sound intensity is raised as the object moves towards the observer and drops on recession from the observer. The effect is produced by a moving waves source when there is an upward frequency shift for the observer and a downward frequency shift when the source and the observer are receding. It can be heard when for instance a train sounding an alarm is approaching, passes and disappears from an observer. During approach, there is an increase in the received frequency compare to the emitted one. At the passing by instant, it is identical but decreases during recession. The Doppler effect can occur in all tpe of waves such as water waves, light waves and sound waves. For sound waves and all other waves that require a medium to be propagated, the observer's velocity and that of the source are normally related to the transmittng medium. Doppler Effect usually results from the source motion, observer motion or medium motion. On the other hand, for waves that do not require a medium to travel throgh such as gravity in special relativity or light, we consider just the relative velocity difference between the source and the observer. Since humans sense sound waves with various amplitude, sound pressure is usually measured using a decibel scale. It is defined as Lp = 10 log 10 (p2/(pref2) = 20 log10(p/pref) dB Where p represents RMS sound pressure and pref a reference pressure The most frequently used sound pressures are twenty micro Pascal through air medium and one micro Pascal through water. The Doppler Effect occurs due to the distance between the observer and the sound changing. The Doppler Effect is observed when the speed of the source moves slower than that of the waves. But if the source and the wave speed are the same, or if the source moves faster than the wave, a different phenomenon is observed. The relationship between the emitted frequency 0 and the observed frequency f is normally expressed as: = (v/ (v + vs, r)) 0 where v represents the medium wave velocity. vs, r represents radial component of source velocity from the source to the observer. Observed frequency increases if the source moves towards observer. It decreases if the source moves away. For the paths of an approaching object, observed frequency first heard is usually higher than the emitted one of the object. Then there follows a decrease of the observed frequency as it nears observer. It equalizes at the same level as the observer and the decrease continues as it moves away. When the observer is near the object's path, there is a very abrupt change from high frequency to low frequency. However, when he is farther away from the object's path, there is a low transition from high frequency to low frequency. For some waves such as electromagnetic waves like light, the wave speed is greater than observer's and the source's relative speed. The relationship between the emitted frequency 0 and observed frequency f1 is then expressed as: Frequency shift, d = -( 0 vs,r ) / c = -(vs,r)/ And the observed frequency = (1- ((vs,r) / c) 0 where 0 represents the transmitted frequency vs,r represents the transmitter velocity relative to receiver c represents the speed the wave represents the wavelength of the wave The two equations can only be accurate to an approximation of the first order. They however work excellently in the case Doppler studied. That is, when there is a slow velocity between the receiver and the receiver compared to the wave velocity, and there is a large distance between the receiver and the source compared to the waves' wavelength. If we violate any of these approximations, then the formulae will not be accurate. Supposing the moving source emits sound waves through a medium of frequency 0, then a stationary observer relative detects waves of frequency f and is expressed as: = 0 (v / (v + vs) where v represents the speed of waves vs represents the source speed Analyzing a moving observer with a stationary source results in observed frequency and is given by: = 0 (v / (v + vr)) where vr becomes negative when moving away from the source and positive when approaching the source Generalizing these equations to one with both the receiver and the source moving, we have = 0 (v / (v + vs, r)) This can also be written as = 0 (1 - vs, r / (v + vs, r)) where vs, r represents the radial component of the source to receiver velocity For a moving source, vs, r is so minute compared to v and the expression changes to: = 0 (1 - (vs, r) / v) In reality though, the above-mentioned limitations are still applicable. When we derive the final equation with approximations, several interesting results are found. When sound is moved, we can hear a symphony playing backwards. The Doppler Effect generally depends on time. In some circumstances two wave signals can be received from a source. The alarm of a passing car starts out louder than its stationary pitch, and then come when it nears. It eventually goes lower than the stationary pitch again when moving farther away. Since the vehicle passes by, its radial velocity changes as a function between the siren's velocity and the angle between the line of sight. This can be expressed as: vs, r = vs . cos where vs represents the wave velocity of the source w. r. t. medium represents the angle between the object's forward velocities Light is also a wave, and therefore relative motion of the light wave source usually leads to a Doppler effect for light. Here, it is not the pitch but the color is that is changed source motion. Its wavelength shifts to larger values if the source motion is far away from the observer and to much smaller values if the motion is moving toward the observer. Astronomers first studied this effect in the visible electromagnetic spectrum. Currently, it applies to all the electromagnetic waves in all spectrum portions. Due to its inverse relationship between wavelength and frequency, this effect can be illustrated using wavelength. Radiation redshifts when the wavelength is raised and blueshifts when it goes down. Astronomers use this to precisely make calculations of how fast astronomical objects like stars move away from the earth or towards the earth. For instance, the lines hydrogen emits in far off galaxies is always redshifted. This spectral emission has a wavelength of 21 cm on Earth but can be instead be 21.1 cm. The 0.1 cm difference indicates that the gas is receding from the earth. This is usually at velocity of approximately 1,400 kilometers per second. There are two other phenomena that can shift to any electromagnetic radiation's frequency other than the relative motion. First, the gravitational redshift, which has an association with very strong gravitational fields. Second, the Cosmological redshift that resulted from space expansion after the Big Bang. The Doppler Effect has found its application in various fields. Among these fields are astronomy, sirens, temperature measurement, radar, medical imaging and blood flow measurement, flow measurement, velocity profile measurement and underwater acoustics and audio devices. A passing car siren starts at a higher pitch than when in stationary status. But the pitch decreases as it moves away. As the car passes, radial velocity also varies in relation to the angle between the velocity of the siren and the observer's sight line. This effect, specifically that of electromagnetic waves, is very useful in astronomy since it results in blueshifts and redshifts. This phenomenon is often used to measure the approaching and receding speeds of stars and galaxies. However, the use of this phenomenon for light in astronomy relies on the fact that star spectra are not continuous. The Doppler Effect has been found to be very useful in temperature measurement, usually in astronomy. It mainly estimates a gas temperature emitting a spectral line. Radars also make use of this effect in measuring the speed of detected objects. Radar beams are fired at moving targets receding or approaching the source. Every successive wave travels further to reach the vehicle. Doppler Effect therefore successfully determines the moving object's velocity. In medical imaging, an echocardiogram produces an assessment blood flow direction. It has one shortcoming though. The ultrasound beam must be parallel to the flow of blood. This measurement has also been found useful in medical ultrasonography. Laser Doppler velocimeter was designed to measure speeds in fluids. This flow is then calculated in relation to water velocity. The technique has an advantage of being useful even with measurements of non-intrusive type at high frequency. Hypothesis Frequency will be greater as I hit closer to the border of the snare, because when I hear it I can tell it has a higher pitch. The pitch of a sound wave is in direct proportional with the frequency of the instrument producing the sound. The Doppler Effect has been used especially in the military to read a submarine's speed. This uses the sonar system, which is usually fixed on a mobile ship, then calculating the relative velocity. The Doppler Effect has also been very applicable in the measurement of velocity profile. The Ultrasonic Doppler Velocimeter measures this profile in many fluids that contain suspended particles. Finally, the Doppler Effect has been applied in audio devices, notably the Leslie speaker that uses an electric motor that rotates it continuously. Method Get a Prologger or any other device that can record frequencies. Create an ideal situation. Create a place where the microphone is always in the same place. The snare should also not move and the strainers should have always the same tension. All external factors that can modify your results have to be controlled as much as possible to minimize the margin of error. Get a snare and label each centimetre on the snare from one border to the other, and set up a midpoint. Most snares have a whole number centimetre, so the midpoint will be a whole number too. Hit the first centimetre and record the frequency. Repeat this for all the centimetres and record the data. Data collection and processing From the experiment, I measured the distance in centimetres and read their corresponding frequencies. My distance ranged from zero to twelve centimetres. I read the frequencies from on the computer. I then recorded the data in a table form for both the receding and approaching sound source. The frequencies were recorded for specific points marked with a one centimetre distance between them. Table 1: Frequencies of an approaching source of sound waves Snare distance (in cm) Recorded frequencies (in Hertz) 12 322 11 322 10 323 9 326 8 328 7 330 6 333 5 344 4 359 3 379 2 411 1 451 0 500 Fig 1: Graph of an approaching source of sound waves Table 2: Frequencies of a receding source Snare distance (in cm) Recorded frequencies (in Hertz) 0 500 1 454 2 412 3 381 4 363 5 346 6 335 7 332 8 327 9 325 10 324 11 322 12 320 Fig 2: graph of a receding force Analysis Figure 1 is a graphical representation of the relationship between frequency and distance for an approaching source. It can be observed that there is a smooth frequency change. As the source moves toward the observer, frequency increases. The largest increase is when the source is closest to the observer. With decreasing distance towards the observer, the Doppler Effect increases in magnitude due to this increase in frequency. The frequency change also affects the pitch of the sound. High frequencies result in sound with a higher pitch and vice versa. There is an increase in pitch as the source tends towards the observer, in this case the recorder. The pitch is therefore highest as the source passes the observer. We can see from the table 1 and figure 1 that the pitch raises smoothly as the source approaches the recorder. It is highest at the point where it is at the same level as the recorder. Figure 2 is a representation of the same relationship between the frequency and distance. However, this one is for a receding source after it passes the observer or recorder. We can see that the frequency is 500 hertz when the source and the observer are at the same spot. There is also a very fast change in frequency fast change in frequency within the first four centimeters. After that, the frequency drop becomes slower. It then settles at a steady frequency of about 320 hertz. With increasing distance away from the observer, the Doppler Effect decreases in magnitude, due to the fall in frequency, then diminishes altogether. We can safely interpret that frequency and the distance from the midpoint of the snare are inversely proportional to each other. This is because as the distance increases, the frequency falls by the same proportion. The wave velocity is a constant because it stays the same in the medium. When I tried to calculate the velocity in this experiment, I found some very little or no variation. The variation can be ignored. It is therefore a constant. Evaluation Generally the experiment ran smoothly save for a few hitches here and there. Just like most experiments several errors may have been done. These errors are of both systematic and random type. I could however consider these errors as unavoidable in this type of experiment. Random errors are most likely to have occurred during measurement of frequency using the Prologger. This could have been due to inaccurate setting. Another source of error could have been in graduating and measuring of the distances of the source frequency. The systematic errors could have occurred due to the frequency generator not operating properly. These margin of error could possibly be minimized by doing more trials to collect more sets of data and also if more accurate devices were used to determine frequency and distance. Despite all these, the experiment was carried out well, the data collected, analyzed and compiled. The graphs obtained show a close consistence with the general principles of the behaviour of frequency and pitch with relation to the distance the sound waves have to travel. In spite of all these, my results were very close to those already done earlier in the scientific community. I can therefore assert that they were fairly accurate. Conclusion In conclusion, the experiment has clearly demonstrated that frequency of a sound and the distance from the midpoint of a snare are inversely related. This can be seen from two graphs in figure 1 and 2. However, due to various sources of error, the results may not be very entirely accurate. If the universal wave equation is rearranged, we can verify that that distance and frequency are inversely proportional to each other because as the distance increases, frequency decreases almost by the same proportion. Also, as frequency changes, so does the pitch. Frequency is therefore directly proportional to the pitch. From the experiment, the pitch kept increasing as the source approached and decreased proportionally as it moved away from the recorder. In reality though, the sound frequency emitted by the source does not really change. Wavelength does. Consequently, the received frequency changes too. The wave velocity also remains constant hence only the frequency is affected. Measuring of the distance between two points was difficult and inaccurate due to the points being estimated one. I might also have made errors by measuring incorrectly by not properly lining up the ruler. It is also possible that I read the wrong measurement on the ruler. Despite the few shortcomings, the experiment added some value to the science world. It particularly achieved the following: It gives a very good idea of how to integrate the sound-light effect to achieve a system. Provides a clear visual representation of the Doppler Effect, a physical phenomenon, which is quite an effective way to inform people. Provides a successful exhibition of science and illustrates some of the good ideas and experience about the Doppler Effect. From the above, we can conclude that the experiment achieved all its objectives and proved right the hypothesis. It can therefore with no doubt be considered a great success since it demonstrated the Doppler Effect quite accurately. References Berge, C. (1979). The Doppler Effect. Small Press Distribution. Dana, J. D. and Dana, E. S. (1909). The Doopler Effect. American Journal of Science. Harvard University. Gill, T. P. (1965). The Doppler Effect-An Introduction to the Theory of the Effect. Logos Press. Lockyer, N. (1906). Nature. Macmillan Publishers Ltd. Pearce, J. M. (2008). Doppler Effect, retrieved from http://www.webphysics.davidson.edu, on October 31, 2008. Russel, D. (2008). The Doppler Effect and the Sonic Booms, retrieved from http://www.kettering.edu, on October 31, 2008. Read More