14. waves and sound — Physics STD 11 Science — Question

Speed of sound, $\mathrm{v}=330 \mathrm{\,ms}^{-1}$

Length of pipe, $\mathrm{L}=30 \mathrm{\,cm}=30 \times 10^{-2} \mathrm{\,m}$

In a open pipe (open at both ends), the frequency of its $n^{\text {th }}$ harmonic is

$v_{n}=\frac{n v}{2 L}$ where $n=1,2,3........$

$\therefore \mathrm{n}=\frac{2 \mathrm{L} v_{\mathrm{n}}}{\mathrm{v}}$

Let $n^{\text {th }}$ harmonic of open pipe resonate with $1.1$ $\mathrm{\,kHz}$ source.

$\therefore \mathrm{v}_{\mathrm{n}}=1.1 \mathrm{\,kHz}=1.1 \times 10^{3} \mathrm{\,Hz}$

$\therefore \mathrm{n}=\frac{2 \times 30 \times 10^{-2} \times 1.1 \times 10^{3}}{330}=2$