State and explain laws of vibrating strings.
Answers
The vibrations generated by a string is nothing but a wave. The sound produced by a string has almost same frequency. There are three laws in the case of vibrating string. First law tells that, when the tension and the linear density are constant, the frequency of the vibration is inversely proportional to the length. Second law states that, If the length and linear density are constant, the frequency is directly proportional to the square root of the tension. Third law is that, when the length and and tension are constant, the frequency is inversely proportional to the square root of linear density. The below experiment is the verification of these three laws.
The laws of vibration of strings are easily verified by means of a sonometer. It consists of a rectangular wooden box , Having holes on the sides for free vibrations of air inside. A thin wire is stretched over two movable bridges ( B1 , B2 ) by means of a weight hanging over a pulley. One end of the wire will be usually fixed and the other end carries a weight hanger. The length of the wire 'l' ( vibrating segment ) can conveniently changed by moving the bridges. The vibrations in the wire are set up by striking a tuning fork of standard frequency with a hammer and placing (l) is adjusted till resonance occurs when the frequency of the tuning fork. This can be observed by placing a light paper rider in the middle of the wire. When resonance occurs the paper rider is thrown off the wire .
The three laws of vibrating strings can be verified as given below .
Verification of First law
Keep certain minimum weight such that the wire is free from kinks . This tension is kept constant throughout the experiment . A tuning fork of known frequency is excited and placed on the wooden box . The distance between the bridges is adjusted until the paper rider falls down in resonance condition . The corresponding vibrating length 'l' is measured . The experiment is repeated for different frequencies by changing the tuning forks and corresponding lengths of same wire are measured.
It is difficult to verify the second and third laws directly . These two laws are equivalent to prove respectively that T√l and l m−−√ are constants for verifying second and third laws .
Verification of second law
In this part of the experiment for a given tuning fork and for a given wire the tension is changed in steps , the resonating lengths corresponding to the different tensions used are measured and if the ratio T√l is found to be constant , the second law is said to be verified .
Verification of third law
The same tuning fork is used for the wires made of different materials under constant tension . The resonating lengths corresponding to different wires are measured and if the product l m−−√ is found to be a constant , the third law is said to be verified .
Answer:
YOUR ANSWER IS IN THE ABOVE PIC :)
