Question

If $\lambda_{1}, \lambda_{2}$ and $\lambda_{3}$ are the wavelengths of the waves giving resonance with the fundamental, first and second overtones respectively of a closed organ pipe. Then, the ratio of wavelengths $\lambda_{1}: \lambda_{2}: \lambda_{3}$ is:

• A. 1 : 3 : 5
• B. 1 : 2 : 3
• C. 5 : 3 : 1
• D. $1: \frac{1}{3}: \frac{1}{5}$

Answer 1

Answer: (D)

$\ell=\frac{\lambda_{1}}{2} \Rightarrow \lambda_{1}=2 \ell$
$\ell=\frac{3 \lambda_{2}}{2} \Rightarrow \lambda_{2}=\frac{2 \ell}{3}$
$\ell=\frac{5 \lambda_{3}}{2} \Rightarrow \lambda_{3}=\frac{2 \ell}{5}$
$\therefore \lambda_{1}: \lambda_{2}: \lambda_{3}=2 \ell: \frac{2 \ell}{3}: \frac{2 \ell}{5}$
$=1: \frac{1}{3}: \frac{1}{5}$