Question 18: Waves

Question

The fundamental frequency of sound produced in an open pipe of length $\mathbf{L}_1$ is same as the frequency of the $3^{	ext {rd }}$ harmonic of the sound produced in the closed pipe of length $\mathbf{L}_2$ Then the ratio of $\frac{L_1}{L_2}$ is :

Accepted Answer

Let $v$ be the speed of sound.
Open pipe (both ends open), fundamental frequency:
$$f_{	ext{open}} = \frac{v}{2L_1}.$$
Closed pipe (one end closed), only odd harmonics. The 3rd harmonic is $n=3$:
$$f_{	ext{closed},3} = \frac{3\,v}{4L_2}.$$
Setting them equal,
$$\frac{v}{2L_1} \;=\;\frac{3v}{4L_2}     \quad\Longrightarrow\quad     \frac{1}{2L_1} = \frac{3}{4L_2}     \quad\Longrightarrow\quad     \frac{L_1}{L_2} = \frac{2}{3}.$$
Answer: $\displaystyle \frac{L_1}{L_2} = 	frac{2}{3}.$

Answer

$\frac{L_1}{L_2}=\frac{3}{1}$

Answer

$\frac{L_1}{L_2}=\frac{1}{3}$

Answer

$\frac{L_1}{L_2}=\frac{2}{3}$

Answer

$\frac{L_1}{L_2}=\frac{3}{2}$

Waves

The fundamental frequency of sound produced in an open pipe of length \mathbf{L}_1 is same as the frequency of the 3^{\text {rd }} harmonic of the sound produced in the closed pipe of length \mathbf{L}_2 Then the ratio of \frac{L_1}{L_2} is :

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