Question 207: Waves

Question

A cylindrical tube, open at both ends, has a fundamental frequency, $$f,$$ in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now :

Accepted Answer

The fundamental frequency of open tube
$${v_0} = {v \over {2{l_0}}}\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)$$
That of closed pipe
$${v_c} = {\upsilon  \over {4{l_c}}}\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} \right)$$
According to the problem $${l_c} = {{{l_0}} \over 2}$$
Thus $${v_c} = {\upsilon  \over {{l_0}/2}} \Rightarrow {v_c}{\upsilon  \over {2l}}\,\,\,\,...\left( {iii} \right)$$
From equations $$(i)$$ and $$(iii)$$
$${v_0} = {v_c}$$
Thus, $${v_c} = f$$ $$\,\,\,\left( {\,\,} \right.$$ as $${v_0} = f$$ is given $$\left. {\,\,} \right)$$

Answer

$$f$$

Answer

$$f/2$$

Answer

$$3/4$$

Answer

$$2f$$

Waves

A cylindrical tube, open at both ends, has a fundamental frequency, $f,$ in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now :

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