When a string is divided into three segments of lengths l₁, l₂ and l₃ , the fundamental frequencies of these three segments are v₁ , v₂ and v₃ respectively. The original fundamental frequency (v) of the string is

Step-by-step solution

The fundamental frequency of string aligned v & = 1 2 l T m v₁ l₁ & =v₂ l₂=v₂ l₃=k aligned From Eq. (i) l₁= k v₁ , l₂= k v₂ , l₃= k v₃ ...(i) Original length aligned l & = k v l & =l₁+l₂+l₃ k v & = k v₁ + k v₂ + k v₃ 1 v & = 1 v₁ + 1 v₂ + 1 v₃ aligned Here, aligned & l=l₁+l₂+l₃ & k v = k v₁ + k v₂ + k v₃ & 1 v = 1 v₁ + 1 v₂ + 1 v₃ aligned