Question 471: Waves

Question

The $$4^{	ext {th }}$$ overtone of a closed organ pipe is same as that of $$3^{	ext {rd }}$$ overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is :

Accepted Answer

$$\begin{aligned}
& \mathrm{n}_{	ext {oop }}=(2 \mathrm{M}+1)^{	ext {th }} 	ext { Har. }=(2 	imes 4+1) 	imes \frac{\mathrm{V}}{4 \ell_{\mathrm{c}}}=\frac{9 \mathrm{~V}}{4 \ell_{\mathrm{c}}} \
& \mathrm{n}_{	ext {oop }}=(\mathrm{M}+1)^{	ext {th }} 	ext { Har. }=(3+1) \frac{\mathrm{V}}{2 \ell_0}=\frac{4 \mathrm{~V}}{2 \ell_0} \
& 	ext { now } \frac{9 \mathrm{~V}}{4 \ell_{\mathrm{c}}}=\frac{4 \mathrm{~V}}{2 \ell_0} \
& \frac{\ell_{\mathrm{c}}}{\ell_0}=\frac{18}{16}=\frac{9}{8}
\end{aligned}
$$

Answer

8 : 9

Answer

9 : 7

Answer

9 : 8

Answer

7 : 9

Waves

The $4^{\text {th }} overtone of a closed organ pipe is same as that of 3^{\text {rd }}$ overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is :

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