Question

A pipe produces notes of frequencies \[300Hz,{\text{ }}600Hz,{\text{ }}900Hz\] , the pipe is
A) Open at one end
B) Open at both the end
C) A and B
D) Kundt’s tube

Answer 1

Hint: In this question, we have to find the ratio of frequencies of the harmonics. In an open organ pipe, the frequencies of the harmonics are in the order of \[1:2:3 \ldots ..n\]

Complete step by step solution: We know that the pipe whose both ends are open is known as open organ pipe. The frequencies of harmonics in an open organ pipe are in the ratio of \[1:2:3 \ldots ..n\]for the infinite number of harmonics.
According to the question, we have three frequencies which are \[300Hz,{\text{ }}600Hz,{\text{ }}900Hz\]. These frequencies are the frequencies of harmonics. So, when we find the ratio of these three harmonic frequencies then it gives \[1:2:3\] .
So, the pipe given in the question is open at both ends.
Hence, a pipe produces notes of frequencies \[300Hz,{\text{ }}600Hz,{\text{ }}900Hz\], the pipe is open at both the ends.

Therefore, option B is correct.

Additional Information: There are two types of organ pipes. One is a closed organ pipe and the other is an open organ pipe. Closed organ pipe is closed at one end while open organ pipe does not have any closed end. In both the pipes, antinode is formed at the open end. There is a node formed at closed end. One node is always present between two antinodes.

Note: In this question, we have to remember that a closed organ pipe (which is open at one end) has an order of odd number of frequencies of the harmonics while an open organ pipe (which is open at both ends) has an order of positive integer number of frequencies.