Q. 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
Electromagnetic Waves
Solution:
According to the question
$l = \frac{\lambda_1}{2}$
$\Rightarrow \lambda_1 = 2 l$
$l = \frac{3 \lambda_2}{2} \Rightarrow \lambda_2 = \frac{2l}{3}$
$l = \frac{5 \lambda_3}{2} \Rightarrow \lambda_3 = \frac{2l}{5}$
$\therefore \lambda_1 : \lambda_2 : \lambda_3 = 2l : \frac{2l}{3} : \frac{2l}{5}$
$= 1 : \frac{1}{3} : \frac{1}{5}$
