Q. When a string is divided into three segments of length l₁, l₂ and l₃, the fundamental frequencies of these three segments are ν₁, ν₂ and ν₃ respectively. The original fundamental frequency (ν) of the string is
A) 1/√ν = 1/√ν₁ + 1/√ν₂ + 1/√ν₃
B) √ν = √ν₁ + √ν₂ + √ν₃
C) ν = ν₁ + ν₂ + ν₃
D) 1/ν = 1/ν₁ + 1/ν₂ + 1/ν₃
Explanation
[Solution from source] For the same string (same tension and linear density) the fundamental frequency ν = v/(2l) is inversely proportional to length. Since l = l₁ + l₂ + l₃, 1/ν = 1/ν₁ + 1/ν₂ + 1/ν₃. Adding frequencies directly would wrongly treat ν as proportional to length. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.