A wire of length 30 cm , stretched between rigid supports, has it's n th and n + 1 th harmonics at 400 Hz and 450 Hz , respectively. If tension in the string is 2700 N , it's linear mass density is _____ kg m - 1 .

Step-by-step solution

Frequency of n t h harmonic is n v 2 l = 400 ⇒ n v 0 . 6 = 400       . . . 1 And frequency of n + 1 t h harmonic is n + 1 v 2 l = 450 ⇒ n + 1 v 0 . 6 = 450         . . . 2 , here, v is speed of wave on string. From equation 1 , we have n = 400 × 0 . 6 v Putting in equation 2 , ⇒ 0 . 6 × 400 v + 1 v 0 . 6 = 450 ⇒ 400 + v 0 . 6 = 450 ⇒ v = 30   m   s - 1 Speed of wave on string is stated as v = T μ = 30 , here, μ is linear