A string of length 1 m and mass 2 × 10 − 5 kg is under tension T . When the string vibrates, two successive harmonics are found to occur at frequencies 750 Hz and 1000 Hz . The value of tension T is _____ newton.

Step-by-step solution

Given: l = 1   m ,   m = 2 × 10 – 5   kg . As successive harmonics are being given, so it is the case of both ends fixed. Now, f n + 1 - f n = 1000 - 750 ⇒ n + 1 2 l T μ - n 2 l T μ = 250 ⇒ 1 2 l T μ = 250 ⇒ T 2 × 10 - 5 = 250 × 2 × 1 ⇒ T 2 × 10 - 5 = 25 × 10 4 ⇒ T = 50 × 10 - 1 ⇒ T = 5   N