Saved Bookmarks
| 1. |
Explain the modes of vibration of a streched string with examples. |
|
Answer» SOLUTION :Modes of vibrations of a streched string `:` (1) In sitar of Guitar, a streched string can vibratein different frequencies and form STATIONARY waves. This mode of vibrations are known as harmonics. (2) If it vibrates in one segment,which is known as fundamental harmonic.The higher harmonics are called the overtones. (3) It vibrates in two segments then the secondharmonic is called first overtone. Similarly the pattern of vibrations are shonw figure. (4) If a stretched string vibrates with P segments ( loop ) then frequencyof vibration `v =( P)/( 2l ) sqrt((T) /(mu))`Where T = tension in the string, `mu =` LINEAR density `= ( "mass")/( "LENGTH")` (5) In first mode of vibration, P=1, then `v =(1)/( 2l) sqrt((T)/(mu))` ( `1^(st)` harmonic ( or) fundamental frequency) (6) In second mode of vibration , P =2, then `v_(1)=(2)/(2l) sqrt((T)/( mu)) =2v ` `( 2^(nd)` harmonic ( or ) `1^(st)` overtone ) (7) In thirdmode of vibration, P =3, then `v_(2) =(3)/(2l) sqrt((T)/( mu)) 3v( 3^(rd ) ` harmonic ( or) `2^(nd) ` overtone ) .The ratio of the frequency of Harmonicsare, `v: v_(1) : v_(2) =v: 2v: 3v=1: 2:3` 
|
|