91Ó°ÊÓ

The length of the tube is$L=121cm=1.21m$.

For the open-open tube, the two open ends exhibit antinodes of a standing wave. The possible wavelengths for this case are ${\mathrm{λ}}_m=\frac{2L}{m}$where $m=1,2,3,⋯$

The three longest wavelengths are as follows

(1)

$$\begin{gathered} {\mathrm{λ}}_1=\frac{2×1.21}{1} \\ =2.42m \end{gathered}$$

(2)

$$\begin{gathered} {\mathrm{λ}}_2=\frac{2×1.21}{2} \\ =1.21m \end{gathered}$$

(3)

$$\begin{gathered} {\mathrm{λ}}_3=\frac{2×1.21}{3} \\ =0.81m \end{gathered}$$

Therefore, the three longest wavelengths for standing sound waves in a tube open at both ends are $2.42m,1.21m,$and $0.81m$respectively.

In the case of an open-closed tube, wavelengths are

${\mathrm{λ}}_m=\frac{4L}{m}$where $m=1,2,3,…$

The three longest wavelengths are as follows

(1)

$$\begin{gathered} {\mathrm{λ}}_1=\frac{4×1.21}{1} \\ =4.84m \end{gathered}$$

(2)

$$\begin{gathered} {\mathrm{λ}}_2=\frac{4×1.21}{2} \\ =1.61m \end{gathered}$$

(3)

$$\begin{gathered} {\mathrm{λ}}_3=\frac{4×1.21}{3} \\ =0.97m \end{gathered}$$

Therefore, the three longest wavelengths for standing sound waves in a tube open at one end, closed at the other are$4.84m,1.61m,$and$0.97m$respectively.$0.97m$