Design and Construction of a Sonometer
CHAPTER ONE
AIM AND OBJECTIVE OF THE STUDY
To design and construct a sonometer which will used to verify that the frequency of vibrating (F) is inversely proportional the vibrating length for a given tension per unit mass and also to verify that the frequency of vibrating of stretched spring is directly proportional to the square root of tension for a given length (L) and mass per unit length mass.
CHAPTER TWO
LITERATURE REVIEW
MEANING OF WAVE
A wave allows energy to be transferred from one point to another, some distance away without any particles of the medium traveling between the two points. For example, if a string, energy to move the weight be obtained by repeatedly shaking the other end of string up and down through a small distance wave, which carries energy, suspends a small weight then travel along string from the top to the bottom.
Likewise, neater wave may spread along the surface from one point A, to another point B, where an object floating and the water will be disturbed by the wave. No particles of water from A actually travel to B in the process. Again sound wave carry energy from the sound to the ear by disturbance of the air.
TYPES OF WAVE
According to Nelcon and Parker, they said that waves is of three types of waves:
TRANSVERSE WAVE
A wave, which is propagated by vibration perpendicular to the direction of travel of the wave is called transverse wave. Examples of transverse wave are wave on plucked string and on water, electromagnetic wave, which includes light wave, an transverse waves, the propagation of a transverse wave.
PRODUCTION OF SOUND
Thwelis stated that sound is said to consist of a mechanical vibration of the air, or some substances at frequency within the frequency range over which the ear response. Thus, the sources of a sound must always be the movement of a body although this movement may often be so small that the eye cannot detect it. Sounds are produced by anything that will cause the air to vibrate sufficiently, such as the firing of a rusty of a gate.
There are two aspect of sound; one is the physical aspect, which involves the physics of the production, propagation, reception and detection of a sound. The other, which is the sensation of sound as perceived by the individual, depends on physiological and psychological effects. A vocabulary has been developed to describe the sensation experienced, which a musical not is heard. Such terms as the pitch of the sound, its loudness, and its ton quality or timber are used described the musical sound. The physical, in the other hand, speak of the frequency of the sound, its intensity and the number and intensified of the over tones present in a musical sound.
According to Okinola (1933), he said that sound is characterized by pitch.
The pitch of a sound is its frequency of not as judged by the listener. Pitch is mainly determined by frequency but depends to some extent upon intensity also a high frequency gives rise to a high-pitched note. Similarly, a low frequency produced a low-pitched note. If the sound observed is complex that is, comprise two or more frequencies of the pitch, depends upon the ratio of the fundamental frequencies of the sound heard and not on the differences of the sound and not on the differences between the frequencies. For example, if a person hears three sounds, one after the other, and their fundamental frequencies are 800hz, 1600hz, and 3,200hz the difference in pitch is the same in each case since the frequency ration is constant.
CHAPTER THREE
MATERIALS AND METHOD
MATERIALS
- A fairly hard and light wooden board of about 105cm x1.5cm.
- Dimension
- Two spring balance capable of reading tension between 0 and 50 Newton.
- Two short iron pegs.
- Bolts and nuts.
- Wire and a meter rule.
METHODOLOGY
A wooden board was cut to a suitable dimension as shown in the diagram, and smoothened with the carpenter’s plane and energy paper. Two flat iron bars were cut to a suitable size and several holes drilled at intervals on them to match the size of nuts and bolts they would accommodate. Similar holes were drilled near each and of the board and at corresponding intervals as those on the iron bars.
Two other shorter flat iron bars each with a drilled hole were joined by brazing to one of the former iron bars near its two ends; they are used for folding the spring balance. The iron bars were fixed with nuts and bolts to the wooden board of the position where matching holes were drilled on the flat iron bars and the wood. These rods were the points where the wires from the spring balance are tightened to vary tension. The wood board was finally polished and the two-spring balance fixed to their position.
CHAPTER FOUR
VERIFICATION OF THE LAWS OF VIBRATION IN STRETCHED STRING USING THE CONSTRUCTED SONOMETER
To verify that the frequency of vibration (F) is inversely proportional to the vibrating length for a given tension (T) and mass per unit length (M).
THEORY
Refer to the mode of vibration of stretched string (chapter two, section iii).
PROCEDURE
The tension in the spring balances, and hence in the wire kept constant by tightening the wire at the peg D. A small piece of paper rider in the form of an inverted V was placed at middle of the wire between x, y. the length (L) of the wire between x, y, was varied by moving x until the note obtained by placing the stem of a sounding tuning fork on the sonometer board caused the piece of paper to vibrate violently.
The length (L) was then measured using a meter rule. The experiment was repeated using tuning fork of different frequencies (F) at the end. A graph was plotted with the values of against 1/E.
CHAPTER FIVE
CONCLUSION AND RECOMMENDATION
EXPERIMENTAL PROBLEMS AND PRECAUTIONS
The verification of the laws of vibration is not accompanied by some difficult problem, one of which is the detection of resonance point. One method of detecting resonance point is by plucking the string and comparing the note emitted with the note emitted by a sounding tuning fork (tension, length, or mass per unit length of string varying) until the two notes sound equal to listener, the problem hence is that a person whose ear is poorly sensitive to sound notes would not be able to detect the resonance point.
In view of this, a paper rider in the form of an inverted V is usually placed at the middle of the violently and at times is thrown of the resonating frequency, or all the three factor affecting the vibration of a stretched string the most difficult to verify, is the effect of mass per unit length on the frequency of vibration of a given tension and vibration length. The problem encountered was finding the exact value of frequency, which caused the vibrating length of resonance.
Hence, the experiment was not performed by the usually very difficult method of comparing the note emitted by a fixed length of wire, say A, with that emitted by a varying length, say B of constant tension and varying wire. Instead the vibrating length (I) and tension (T) were kept constant for a chosen wire, and a range of sounding tuning fork, which set (I) into vibration. The sounding fork, which set the paper rider to violent vibration, was taken to have caused resonance in the vibration wire. With the same value of (I) and (T) as before, the experiment was repeated with wires of different masses per unit length, a graph of resonating frequency (F) against the reciprocal of the square root of mass per unit length was observed to be a straight line graph passing through the origin.
Some important precautions were taken to ensure good experimental results. One was to ensure that the whole length of wire was in no way bent, any bending of wire could introduce non-uniformity of tension along the wire and the accurate vibrating length would not be measured if the bending occurred within the vibrating length.
Since paper rider was used to detect resonance point throughout the experiments, the experiments were not carried out under breezy environment, the breeze would likely set the paper rider agitating thereby giving false impression of resonance.
Another precaution was to ensure that the samples of wire weighed for the determination of the was per unit length were free of contamination, any contamination would make the sample weigh more then the actual weight thereby introducing error, in the mass permit length of the wires.
APPLICATION OF STRING VIBRATION
The structure and use of stringed instrument illustrate the application of many of the characteristics of string vibration. In the violin, for example, the four strings are tuned to notes, which occur at intervals of a fifth, i.e. g, d, a, e, the initial tuning being done by altering the tension, the mass per unit length is chosen to be of suitable magnitude by the manufacture, the low frequency G-string having the greatest linear density and the high-pitched E string the least. The fingering of the player achieves the required notes by altering the effective length of the string in use, the body of the instrument acts as a sounding board, transmitting the vibration to the air with greater intensity than could be effected by the bar string, and its design also effect the quality of the note.
In the piano, the not are (ready-mode) by tuning steel wire to the required notes. The long wires, the final adjustment made by the piano tuner being affected by altering tension, produce the two notes. The pressing of a key on the keyboard causes of felt covered hammer to strike the group of wires (three in the case of the high note) which sound the corresponding note, the point of impact is near one end of the wires. Thereby, reducing the intensity of some of the overtone, which might introduce discord, e.g. the 7th harmonize well with other overtones.
REFERENCE
- Nelkon .M. and Parker (1816): ADVANCED LEVEL PHYSICS, Heinemann Education Books Ltd, first Edition Pg. 580-585, P6
- Olumuyiwa .A. and Okinola .O.O (1933): COMPREHENSIVE CERTIFICATE PHYSICS, University press Plc, Second Edition, Pg. 167-169, Pg. 4-7
- Okeke P.N and Anyakoha. M.W. (1997): SENIOR SECONDARY PHYSICS, Revised Edition, Pg. 67-69, P 1
- Semart and Kate (1820): GENERAL PHYSICS, First Edition, Pg. 389, P 5
- Thwelis (1940): ENCYCLOPADEA OF PHYSICS, Pregannon press volume six, Pg. 558, P 2
- Whiteley .W.Y (1950): GENERAL PHYSICS, University tutoria Press Volume 3 Pg. 392, P3