A string in a musical instrument is 50 ~cm long and its fundamental frequency is 800 ~Hz . If a frequency of 1000 ~Hz is to be produced, then required length of string is

Step-by-step solution

Initial length of string (l₁ )=50 ~cm =0.5 ~m Initial fundamental frequency (n₁ )=800 ~Hz and final frequency (n₂ )=1000 ~Hz . Frequency of vibration of the string, n= 1 2 l T m 1 l n₁ n₂ = l₂ l₁ or l₂= n₁ l₁ n₂ = 800 50 1000 =40 ~cm . (where l₂= final length of the string).