Physics - Sound Wave Question with Solution | TestHub

Frequency of ${\mathrm{m}}^{\text{th }}$ harmonic in an open organ pipe is $f_m=\frac{mv}{2L}$ Fundamental frequency in an open organ pipe, for $m=1f_1=\frac{v}{2L}$ Frequency of nth harmonic in a closed organ pipe, $f_n^{\prime }=\frac{nv}{4L}$ Frequency of 3rd harmonic in a closed organ pipe, $f^{\prime }{}_3=\frac{3v}{4L}$ Now, $f_3^{\prime }-f_1=50$ $\frac{3v}{4L}-\frac{v}{2L}=50\Rightarrow \frac{v}{L}=200$ Thus, fundamental frequency in an open organ pipe, $f_1=\frac{v}{2L}=\frac{200}{2}\mathrm{Hz}=100\mathrm{Hz}$