Physics - Sound Wave Question with Solution | TestHub

Let $L$ be the length of the open pipe. The fundamental frequency of the open pipe is given by $v=\frac{v}{2L},v=$ velocity of sound in air The second overtone of the open pipe has a frequency $3v_O=\frac{3v}{2L_O}\mathrm{Hz}$ The length of the closed pipe $L_C=2\mathrm{m}$. The fundamental frequency of the closed pipe is given by $v=\frac{v}{4L}$ The first overtone of the closed pipe has a frequency $$3v_C=\frac{3v}{4L_C}=\frac{3v}{4\times 2}=\frac{3v}{8}\mathrm{Hz}$$ Now $3v_O=3v_C$ or $\frac{3v}{2L_O}=\frac{3v}{8}$ or $2L_O=8$ or $L_O=4\mathrm{m}$