In the resonance experiment, two air columns (closed at one end) of 100mathrm~cm$100\mathrm{~cm}$ and 120mathrm~cm$120\mathrm{~cm}$ long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is :

### Related Formula f_textclosed, fundamental = fracv4L_c$$f_{\text{closed, fundamental}} = \frac{v}{4L_c}$$ f_textopen, 1st overtone = frac2v2L_o$$f_{\text{open, 1st overtone}} = \frac{2v}{2L_o}$$ ### Core Logic

For a closed organ pipe, the fundamental frequency (1st harmonic) is: f_1 = fracvlambda = fracv4L_1$$f_1 = \frac{v}{\lambda} = \frac{v}{4L_1}$$ where L_1$L_1$ is the length of the closed pipe. For an open organ pipe, the first overtone (2nd harmonic) is: f_2 = frac2v2L_2 = fracvL_2$$f_2 = \frac{2v}{2L_2} = \frac{v}{L_2}$$ where L_2$L_2$ is the length of the open pipe (L_2 = 60mathrm\,cm$L_2 = 60\mathrm{\,cm}$). ### Step 2: Equating Frequencies Given f_1 = f_2$f_1 = f_2$: fracv4L_1 = fracvL_2$$\frac{v}{4L_1} = \frac{v}{L_2}$$ L_2 = 4L_1$L_2 = 4L_1$ 60 = 4 times L_1$$60 = 4 \times L_1$$ L_1 = 15mathrm\,cm$$L_1 = 15\mathrm{\,cm}$$ ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Waves