Question 387: Waves

Question

The fundamental frequency of air column in pipe 'A' closed at one end is in unison with second overtone of an air column in pipe 'B' open at both ends. The ratio of length of air column in pipe '$$\mathrm{A}$$' to that of air column in pipe '$$\mathrm{B}$$' is

Accepted Answer

Fundamental frequency of a closed pipe, $$\mathrm{n}_1=\frac{\mathrm{v}}{4 \mathrm{~L}_1}$$
Frequency of the second overtone, $$n_2=\frac{3 v}{2 L_2}$$
Given $$\mathrm{n}_1=\mathrm{n}_2$$
$$\Rightarrow \frac{\mathrm{v}}{4 \mathrm{~L}_1}=\frac{3 \mathrm{v}}{2 \mathrm{~L}_2}
$$
$$	herefore \quad \frac{\mathrm{L}_1}{\mathrm{~L}_2}=\frac{1}{6}$$

Answer

$$1: 6$$

Answer

$$3: 8$$

Answer

$$2: 3$$

Answer

$$3: 4$$

Waves

The fundamental frequency of air column in pipe 'A' closed at one end is in unison with second overtone of an air column in pipe 'B' open at both ends. The ratio of length of air column in pipe '$\mathrm{A}' to that of air column in pipe '\mathrm{B}$' is

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