A wire having a linear density of `0.05 gm//c` is stretched between two rigid supports with a tension supports with a tension of `4.5 xx 10^(7)` dynes. It is oberserved that the wire resonates at a frequency of `420 "cycles"//"sec"`. the next higher frequency at which the same wire resonates is `490 "cycles"//"sec"`. Find the possible mode of vibration of string initially :

Answer

6

Explanation

`V = sqrt((T)/(mu)) = sqrt((4.5 xx 10^(7))/(0.05))`
`(n)/(2l) sqrt((4.5 xx 10^(7))/(0.05)) = 420 "___"(1)`
`(n + 1)/(2l) sqrt((4..5 xx 10^(7))/(0.05)) = 490 "__"(2)`
From equation `(1)` & `(2) rArr (n)/(n + 1) = (6)/(7) rArr n = 6`
Put `n` in `(1) :. (6)/(2l) 3 xx 10^(2) = 420`
`l = (30000)/(140) , l = (1500)/(7) = 214 cm`