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. 1:03:05
• B. 1:02:03
• C. 5:03:01
• D. 1 : $\frac{1}{3}$ : $\frac{1}{5}$

Answer 1

Answer: (D)

1 : $\frac{1}{3}$ : $\frac{1}{5}$

Answer 2

According to the question \hspace40mm l = \frac{\lambda_1}{2} \Rightarrow \hspace30mm \lambda_1 = 2 l \hspace40mm l = \frac{3 \lambda_2}{2} \Rightarrow \lambda_2 = \frac{2l}{3} \hspace40mm l = \frac{5 \lambda_3}{2} \Rightarrow \lambda_3 = \frac{2l}{5} \therefore \hspace20mm \lambda_1 : \lambda_2 : \lambda_3 = 2l : \frac{2l}{3} : \frac{2l}{5} \hspace40mm = 1 : \frac{1}{3} : \frac{1}{5}