NTA Abhyas JEE Main2020PhysicsOscillationsPractice
When a string is divided into three segments of lengths l 1 , l 2 and l 3 the fundamental frequencies of these three segments are ν 1 , ν 2 and ν 3 respectively. The original fundamental frequency ν of the string is
Options
- Aν = ν 1 + ν 2 + ν 3
- Bν = ν 1 + ν 2 + ν 3
- C1 ν = 1 ν 1 + 1 ν 2 + 1 ν 3
- D1 ν = 1 ν 1 + 1 ν 2 + 1 ν 3
Correct answer
C. 1 ν = 1 ν 1 + 1 ν 2 + 1 ν 3
Step-by-step solution
Let l be the length of the string. The fundamental frequency is given by ν = 1 2 l T ⁡ μ or ν ∝ 1 l ⁡ ( ∵   T and μ are constant ) or ν ∝ k l ⁡ ( where k is a constant ) Here, l 1 = k ν 1 , l 2 = k ν 2 , l 3 = k ν 3 and l = k ν But l = l 1 + l 2 + l 3 ∴   1 ν = 1 ν 1 + 1 ν 2 + 1 ν 3