Question 256: Waves

Question

A pipe open at both ends produces a fundamental frequency $n_1$. When the pipe is kept with $\frac{3^{	ext {th }}}{4}$ of its length in water, it produces a note of fundamental frequency $\mathrm{n}_2$. The ratio of $\frac{\mathrm{n}_1}{\mathrm{n}_2}$ is

Accepted Answer

The fundamental frequency of the open pipe is,
$$ \mathrm{n}_1=\frac{\mathrm{V}}{2 \mathrm{~L}} $$
After dipping in water, the pipe behaves like a closed pipe. As the pipe is kept $\frac{3}{4}$ th of its length in water,
$$ l=\frac{25}{100} 	imes \mathrm{L}=\frac{\mathrm{L}}{4} $$
$	herefore \quad$ Fundamental frequency $\mathrm{n}_2=\frac{\mathrm{V}}{4 l}=\frac{4 \mathrm{~V}}{4 \mathrm{~L}}=\frac{\mathrm{V}}{\mathrm{L}}$
$$ 	herefore \quad \frac{\mathrm{n}_1}{\mathrm{n}_2}=\frac{\mathrm{V}}{2 \mathrm{~L}} 	imes \frac{\mathrm{L}}{\mathrm{~V}}=\frac{1}{2} $$

Answer

$\frac{4}{3}$

Answer

$\frac{3}{4}$

Answer

2

Answer

$\frac{1}{2}$

Waves

A pipe open at both ends produces a fundamental frequency n_1. When the pipe is kept with \frac{3^{\text {th }}}{4} of its length in water, it produces a note of fundamental frequency \mathrm{n}_2. The ratio of \frac{\mathrm{n}_1}{\mathrm{n}_2} is

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