Question

Statement-1 : An open organ pipe of certain length have the same fundamental frequency as closed organ pipe of half the length
Statement-2 : In the case of open organ pipe, at both the ends antinodes are formed, while in the closed organ pipe at one end antinode and at the other end node is formed

• A. Both the statements are true and statement-2 is the correct explanation of statement-1
• B. Both the statements are true but statement-2 is not the correct explanation of statement-1
• C. Statement-1 is true and statement-2 is false
• D. Statement-1 is false and statement-2 is true

Answer 1

The correct option is B Both the statements are true but statement-2 is not the correct explanation of statement-1

For open organ pipe, ${\lambda }_1=2L_1$

For closed organ pipe, ${\lambda }_2=4L_2$

They will be equal when:

${\lambda }_1={\lambda }_2$

$2L_1=4L_2$

Thus when $L_2=\frac{L_1}{2}$ they have same fundamental frequency.