Question

A string of length \(L\) fixed at both ends vibrates in third harmonic. The distance between consecutive nodes is}

• A. [option in figure]
• B. [option in figure]
• C. [option in figure]
• D. [option in figure]
• E. [option in figure]

Hint:

In stationary waves, distance between two consecutive nodes is always: \[ \frac{\lambda}{2} \]

Answer 1

The Correct Option is C

For a string fixed at both ends, in \(n^{\text{th}}\) harmonic: \[ L=n\frac{\lambda}{2} \] For third harmonic: \[ L=3\frac{\lambda}{2} \] So, \[ \lambda=\frac{2L}{3} \] Distance between consecutive nodes is: \[ \frac{\lambda}{2} \] Thus: \[ \frac{\lambda}{2}=\frac{1}{2}\cdot \frac{2L}{3}=\frac{L}{3} \]
Hence, the correct answer is the option corresponding to: \[ \boxed{\frac{L}{3}} \]