Design And Construction Of A Sonometer

Project and Seminar Material for Science Laboratory Technology SLT

Design And Construction Of A Sonometer


Abstract


When one thinks about various musical sound he listened to daily he would realize the very important role played by some instrument include. The guitar, piano and violin, which operate on the principles of vibration of, stretched string. CF has therefore become necessary that it study the condition under, which stringed instrument vibrates to give high quality musical notes.

This study is basically the investigation of the laws governing the vibration of a stretched string, it is carried out by the use of SONOMETER.


Table of Contents


  • Title Page
  • Certification
  • Dedication
  • Acknowledgement
  • Abstract

Chapter One

  • 1.1 Introduction
  • 1.2 Aim and Objective of the Study
  • 1.3 Hypothesis
  • 1.4 Statement of Problem of the Study
  • 1.5 Significance of the Study
  • 1.6 Limitation of the Study

Chapter Two

  • 2.1 Literature Review
  • 2.2 Meaning of Wave
  • 2.3 Types of Waves
  • 2.4 Definition
  • 2.5 Production of Sound
  • 2.6 Characteristics
  • 2.7 Loudness
  • 2.8 Mode of Vibration of Stretched String
  • 2.9 Overtone of Stretched String
  • 2.10 Force of Vibration and Resonance
  • 2.11 Calibration of the Constructed Meter Rule
  • 2.12 Mounting of the Calibrated Meter Rule

Chapter Three

  • 3.1 Materials
  • 3.2 Methodology

Chapter Four

  • 4.1 Verification of the Law
  • 4.2 Frequency of Vibration is Inversely Proportional to the Square Roof of Tension
  • 4.3 Frequency of Vibration is Inversely Proportional to the Square Roof of Mass

Chapter Five

  • 5.1 Conclusion and Recommendation
  • 5.2 Experimental Problem and Precaution
  • 5.3 Application of Stretched String Vibration
  • Reference

Chapter One


1.1 Introduction

Sonometer is an instrumental used in the verification of the law of stretched string. It can be classified into two, based on how the tension in the wire can be adjusted, hence, spring and weight types. The weight types is getting absolute and is therefore giving way for the spring type, this is because the former introduce its weight error in the system unlike the later which its tension in the wire is read directly from the spring balance.

The verification of the law became inevitable since most of the musical instrument of string. It was then standard in the 5th century B.C when Pythagoras found out that the retch of a mole united by a vibrating string depend on the length of the string, other condition removing constant. After a gap of twenty-one countries, Galileo showed that the pitch of note depend upon the frequency of the vibration causing it.

Working largely as a result of Galileoโ€™s inspiration, mersennes. In 1636, showed how the frequency of the emitted note by a stretched string depended not merely on the length, but also on the thickness tension and density of the string (1613). A British man call Nelkon M. invested on the use of sonometer.


1.2 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.


1.3 Hypothesis

The law are then started a below, that the frequency of vibration (F) of a stretched spring is inversely proportional to the vibrating length (L) for a given tension (T) and mass per unit (M).

F & 1/L————- (1)

(ii) That the frequency of vibration of stretched spring (F) is directly proportional to the square root of tension (โˆšT) for a given length (L) and mass per unit length (M).

F & โˆšT ———– (2)

(iii) That the frequency of vibration of a stretched spring (F) is inversely proportional to the square root of mass per unit length of the spring (โˆšM) for a given length and tension.

F & L/โˆšM————– (3)

An English mathematics, book Taylor (1685-1731) expressed terseness result in single equation, which in the modern form is written;

F = 1/21 โˆšT/M ———— (4)


1.4 Statement of Problem of the Study

The instrument sonometer when designed and constructed, will be affected by bad weather if exposed, past attalk where hard wood is not used and rough handling by the user. The use and accuracy of the instrument will depend on the person using it to carryout experiment. This work, is a designed and construction of a sonometer is that it will be used in the laboratory for verification of the law governing tension under stretched spring.


1.5 Significance of the Study

The significance of this project is to beef up the number of sonometer in the laboratory as the number in the laboratory are not enough for the number of student admitted.


1.6 Limitation of the Study

One does not have to limit oneself to the verification of the laws of vibration, but it is pertinent to discuss sound and characteristics of sound wave, the wave associated with vibrating spring and the properties of materials used in the construction of a sonometer.


Chapter Five


Conclusion and Recommendation

5.1 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.


5.2 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.


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