Question 384: Waves

Question

The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe of length '$$L$$'. The length of the open pipe will be

Accepted Answer

The length of closed pipe is denoted using L.
Let $$l$$ be the length of open pipe and $$\mathrm{v}$$ be the velocity.
Frequency of second overtone of an open organ pipe is $$\mathrm{n}_{\mathrm{o}}=\frac{3 \mathrm{v}}{2 l}$$
Frequency of first overtone of a closed pipe is $$\mathrm{n}_{\mathrm{c}}=\frac{3 \mathrm{v}}{4 \mathrm{~L}}$$
Given: $$\mathrm{n}_0=\mathrm{n}_{\mathrm{c}}$$
$$\begin{aligned}
\frac{3 \mathrm{v}}{2 l} & =\frac{3 \mathrm{v}}{4 \mathrm{~L}} \
\mathrm{~L} & =\frac{l}{2} \
	herefore \quad l & =2 \mathrm{~L}
\end{aligned}$$

Answer

$$\frac{\mathrm{L}}{2}$$

Answer

$$\mathrm{L}$$

Answer

$$2 \mathrm{~L}$$

Answer

$$4 \mathrm{~L}$$

Waves

The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe of length '$L$'. The length of the open pipe will be

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