A `20 cm` long string, having a mass of `1.0 g`, is fixed at both the ends. The tension in the string is `0.5 N`. The string is set into vibrations using an external vibrator of frequency `100 Hz` Find the separation (in cm) between the successive nodes on the string.
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Answer

A

Explanation

`(lambda_(1))/(2) = l rArr_(1) = 2l`
`lambda_(2) = l rArr :. (lambda_(1))/(lambda_(2)) = 2`
`(v_(1)//f)/(v_(2)//f) = 2`
`(v_(1))/(v_(2)) = 2 = sqrt((T_(1)//mu)/(T_(2)//mu)) rArr (T_(1))/(T_(2)) = 4 "__("1)`
Now moment about `P : T_(1) xx = T_(2) (l - x)`
`l - x = 4x , x = l//5` ltbr.