A closed organ and an open organ tube filled by two different gases having the same bulk modulus but different…

Question

A closed organ and an open organ tube filled by two different gases having the same bulk modulus but different densities $\rho_1$ and $\rho_2$ , respectively. The frequency of the 9th harmonic of the closed tube is identical with the 4th harmonic of the open tube. If the length of the closed tube is $10 \, \text{cm}$ and the density ratio of the gases is $\rho_1 : \rho_2 = 1 : 16$ , then the length of the open tube is:

A
$\frac{20}{7} \, \text{cm}$
B
$\frac{15}{7} \, \text{cm}$
C
$\frac{20}{9} \, \text{cm}$
D
$\frac{15}{9} \, \text{cm}$

Accepted Answer

C. $$\frac{20}{9} \, 	ext{cm}$$

Answer

A. $$\frac{20}{7} \, 	ext{cm}$$

Answer

B. $$\frac{15}{7} \, 	ext{cm}$$

Answer

D. $$\frac{15}{9} \, 	ext{cm}$$

Answer & step-by-step solution

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