On closing an open organ pipe from one end, it is noticed that the frequency of third harmonic is $50…
On closing an open organ pipe from one end, it is noticed that the frequency of third harmonic is $50 \mathrm{~Hz}$ more than the fundamental frequency of vibration in open organ
pipe. The fundamental frequency of open organ pipe is
$250 \mathrm{~Hz}$
$100 \mathrm{~Hz}$
$50 \mathrm{~Hz}$
$200 \mathrm{~Hz}$
Solution
Fundamental frequency of closed pipe $=\mathrm{n}_{1}=\frac{\mathrm{V}}{4 \ell}$
Frequency of third harmonic $n_{3}=\frac{3 \mathrm{~V}}{4 \ell}$
Fundamental frequency of open pipe $=n_{1}{ }^{\prime}=\frac{V}{2 \ell}$
$\frac{3 \mathrm{~V}}{4 \ell}-\frac{\mathrm{V}}{2 \ell}=50$
$\therefore \frac{V}{4 \ell}=50 \quad \therefore \frac{V}{2 \ell}=100 \mathrm{~Hz}$