Question 274: Waves

Question

The length of closed and open pipe is same. The ratio of frequency of $\mathrm{n}^{	ext {th }}$ overtone for closed pipe to that of open pipe is (Neglect end correction)

Accepted Answer

For a closed pipe
The frequency of $\mathrm{n}^{	ext {th }}$ overtone is given by
$$ f=(2 n+1) f_1=(2 n+1) \frac{V}{4 L} $$
For an open pipe
The frequency of $\mathrm{n}^{	ext {th }}$ overtone is given by
$$ \begin{aligned} & f^{\prime}=(n+1) f_1=(n+1) \frac{V}{2 L} \ 	herefore & \frac{f}{f^{\prime}}=\frac{(2 n+1)}{2(n+1)} \end{aligned} $$

Answer

$\frac{(2 n+1)}{2(n+1)}$

Answer

$\frac{(\mathrm{n}+1)}{(2 \mathrm{n}+1)}$

Answer

$\quad \frac{(2 n-1)}{2(n+1)}$

Answer

$\frac{(n-1)}{2(n+1)}$

Waves

The length of closed and open pipe is same. The ratio of frequency of \mathrm{n}^{\text {th }} overtone for closed pipe to that of open pipe is (Neglect end correction)

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